Solution Manual For Macroeconomics Ninth Edition
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Chapter 1—The Science of Macroeconomics 1
Answers to Textbook Questions and Problems
CHAPTER 1 The Science of Macroeconomics
Questions for Review
1. Microeconomics is the study of how individual firms and households make decisions, and how they
interact with one another. Microeconomic models of firms and households are based on principles of
optimization—firms and households do the best they can given the constraints they face. For example,
households choose which goods to purchase in order to maximize their utility, whereas firms decide
how much to produce in order to maximize profits. In contrast, macroeconomics is the study of the
economy as a whole; it focuses on issues such as how total output, total employment, and the overall
price level are determined. These economy-wide variables are based on the interaction of many
households and many firms; therefore, microeconomics forms the basis for macroeconomics.
2. Economists build models as a means of summarizing the relationships among economic variables.
Models are useful because they abstract from the many details in the economy and allow one to focus
on the most important economic connections.
3. A market-clearing model is one in which prices adjust to equilibrate supply and demand. Market-
clearing models are useful in situations where prices are flexible. Yet in many situations, flexible
prices may not be a realistic assumption. For example, labor contracts often set wages for up to three
years. Or, firms such as magazine publishers change their prices only every three to four years. Most
macroeconomists believe that price flexibility is a reasonable assumption for studying long-run issues.
Over the long run, prices respond to changes in demand or supply, even though in the short run they
may be slow to adjust.
Problems and Applications
1. Monetary policy in the United States and the European Union has been a big topic of conversation in
early 2015. The EU embarked upon a quantitative easing policy in March 2015 in an attempt to
stimulate growth and prevent deflation. There has been some concern that the inflation rate in Europe
will turn negative. In the United States, there is continued discussion and speculation concerning when
the Federal Reserve might choose to increase the target federal funds rate. Also in the United States,
the unemployment rate has declined to about 5.5 percent and this suggests that wages may begin to
increase. The Federal Reserve will be watching for wage and price increases as they decide when to
increase interest rates.
2. Many philosophers of science believe that the defining characteristic of a science is the use of the
scientific method of inquiry to establish stable relationships. Scientists examine data, often provided by
controlled experiments, to support or disprove a hypothesis. Economists are more limited in their use
of experiments. They cannot conduct controlled experiments on the economy; they must rely on the
natural course of developments in the economy to collect data. To the extent that economists use the
scientific method of inquiry, that is, developing hypotheses and testing them, economics has the
characteristics of a science.
3. We can use a simple variant of the supply-and-demand model for pizza to answer this question.
Assume that the quantity of ice cream demanded depends not only on the price of ice cream and
income, but also on the price of frozen yogurt:
Qd = D(PIC, PFY, Y).
We expect that demand for ice cream rises when the price of frozen yogurt rises, because ice cream
and frozen yogurt are substitutes. That is, when the price of frozen yogurt goes up, I consume less of it
and, instead, fulfill more of my frozen dessert urges through the consumption of ice cream.
Answers to Textbook Questions and Problems
CHAPTER 1 The Science of Macroeconomics
Questions for Review
1. Microeconomics is the study of how individual firms and households make decisions, and how they
interact with one another. Microeconomic models of firms and households are based on principles of
optimization—firms and households do the best they can given the constraints they face. For example,
households choose which goods to purchase in order to maximize their utility, whereas firms decide
how much to produce in order to maximize profits. In contrast, macroeconomics is the study of the
economy as a whole; it focuses on issues such as how total output, total employment, and the overall
price level are determined. These economy-wide variables are based on the interaction of many
households and many firms; therefore, microeconomics forms the basis for macroeconomics.
2. Economists build models as a means of summarizing the relationships among economic variables.
Models are useful because they abstract from the many details in the economy and allow one to focus
on the most important economic connections.
3. A market-clearing model is one in which prices adjust to equilibrate supply and demand. Market-
clearing models are useful in situations where prices are flexible. Yet in many situations, flexible
prices may not be a realistic assumption. For example, labor contracts often set wages for up to three
years. Or, firms such as magazine publishers change their prices only every three to four years. Most
macroeconomists believe that price flexibility is a reasonable assumption for studying long-run issues.
Over the long run, prices respond to changes in demand or supply, even though in the short run they
may be slow to adjust.
Problems and Applications
1. Monetary policy in the United States and the European Union has been a big topic of conversation in
early 2015. The EU embarked upon a quantitative easing policy in March 2015 in an attempt to
stimulate growth and prevent deflation. There has been some concern that the inflation rate in Europe
will turn negative. In the United States, there is continued discussion and speculation concerning when
the Federal Reserve might choose to increase the target federal funds rate. Also in the United States,
the unemployment rate has declined to about 5.5 percent and this suggests that wages may begin to
increase. The Federal Reserve will be watching for wage and price increases as they decide when to
increase interest rates.
2. Many philosophers of science believe that the defining characteristic of a science is the use of the
scientific method of inquiry to establish stable relationships. Scientists examine data, often provided by
controlled experiments, to support or disprove a hypothesis. Economists are more limited in their use
of experiments. They cannot conduct controlled experiments on the economy; they must rely on the
natural course of developments in the economy to collect data. To the extent that economists use the
scientific method of inquiry, that is, developing hypotheses and testing them, economics has the
characteristics of a science.
3. We can use a simple variant of the supply-and-demand model for pizza to answer this question.
Assume that the quantity of ice cream demanded depends not only on the price of ice cream and
income, but also on the price of frozen yogurt:
Qd = D(PIC, PFY, Y).
We expect that demand for ice cream rises when the price of frozen yogurt rises, because ice cream
and frozen yogurt are substitutes. That is, when the price of frozen yogurt goes up, I consume less of it
and, instead, fulfill more of my frozen dessert urges through the consumption of ice cream.
Chapter 1—The Science of Macroeconomics 1
Answers to Textbook Questions and Problems
CHAPTER 1 The Science of Macroeconomics
Questions for Review
1. Microeconomics is the study of how individual firms and households make decisions, and how they
interact with one another. Microeconomic models of firms and households are based on principles of
optimization—firms and households do the best they can given the constraints they face. For example,
households choose which goods to purchase in order to maximize their utility, whereas firms decide
how much to produce in order to maximize profits. In contrast, macroeconomics is the study of the
economy as a whole; it focuses on issues such as how total output, total employment, and the overall
price level are determined. These economy-wide variables are based on the interaction of many
households and many firms; therefore, microeconomics forms the basis for macroeconomics.
2. Economists build models as a means of summarizing the relationships among economic variables.
Models are useful because they abstract from the many details in the economy and allow one to focus
on the most important economic connections.
3. A market-clearing model is one in which prices adjust to equilibrate supply and demand. Market-
clearing models are useful in situations where prices are flexible. Yet in many situations, flexible
prices may not be a realistic assumption. For example, labor contracts often set wages for up to three
years. Or, firms such as magazine publishers change their prices only every three to four years. Most
macroeconomists believe that price flexibility is a reasonable assumption for studying long-run issues.
Over the long run, prices respond to changes in demand or supply, even though in the short run they
may be slow to adjust.
Problems and Applications
1. Monetary policy in the United States and the European Union has been a big topic of conversation in
early 2015. The EU embarked upon a quantitative easing policy in March 2015 in an attempt to
stimulate growth and prevent deflation. There has been some concern that the inflation rate in Europe
will turn negative. In the United States, there is continued discussion and speculation concerning when
the Federal Reserve might choose to increase the target federal funds rate. Also in the United States,
the unemployment rate has declined to about 5.5 percent and this suggests that wages may begin to
increase. The Federal Reserve will be watching for wage and price increases as they decide when to
increase interest rates.
2. Many philosophers of science believe that the defining characteristic of a science is the use of the
scientific method of inquiry to establish stable relationships. Scientists examine data, often provided by
controlled experiments, to support or disprove a hypothesis. Economists are more limited in their use
of experiments. They cannot conduct controlled experiments on the economy; they must rely on the
natural course of developments in the economy to collect data. To the extent that economists use the
scientific method of inquiry, that is, developing hypotheses and testing them, economics has the
characteristics of a science.
3. We can use a simple variant of the supply-and-demand model for pizza to answer this question.
Assume that the quantity of ice cream demanded depends not only on the price of ice cream and
income, but also on the price of frozen yogurt:
Qd = D(PIC, PFY, Y).
We expect that demand for ice cream rises when the price of frozen yogurt rises, because ice cream
and frozen yogurt are substitutes. That is, when the price of frozen yogurt goes up, I consume less of it
and, instead, fulfill more of my frozen dessert urges through the consumption of ice cream.
Answers to Textbook Questions and Problems
CHAPTER 1 The Science of Macroeconomics
Questions for Review
1. Microeconomics is the study of how individual firms and households make decisions, and how they
interact with one another. Microeconomic models of firms and households are based on principles of
optimization—firms and households do the best they can given the constraints they face. For example,
households choose which goods to purchase in order to maximize their utility, whereas firms decide
how much to produce in order to maximize profits. In contrast, macroeconomics is the study of the
economy as a whole; it focuses on issues such as how total output, total employment, and the overall
price level are determined. These economy-wide variables are based on the interaction of many
households and many firms; therefore, microeconomics forms the basis for macroeconomics.
2. Economists build models as a means of summarizing the relationships among economic variables.
Models are useful because they abstract from the many details in the economy and allow one to focus
on the most important economic connections.
3. A market-clearing model is one in which prices adjust to equilibrate supply and demand. Market-
clearing models are useful in situations where prices are flexible. Yet in many situations, flexible
prices may not be a realistic assumption. For example, labor contracts often set wages for up to three
years. Or, firms such as magazine publishers change their prices only every three to four years. Most
macroeconomists believe that price flexibility is a reasonable assumption for studying long-run issues.
Over the long run, prices respond to changes in demand or supply, even though in the short run they
may be slow to adjust.
Problems and Applications
1. Monetary policy in the United States and the European Union has been a big topic of conversation in
early 2015. The EU embarked upon a quantitative easing policy in March 2015 in an attempt to
stimulate growth and prevent deflation. There has been some concern that the inflation rate in Europe
will turn negative. In the United States, there is continued discussion and speculation concerning when
the Federal Reserve might choose to increase the target federal funds rate. Also in the United States,
the unemployment rate has declined to about 5.5 percent and this suggests that wages may begin to
increase. The Federal Reserve will be watching for wage and price increases as they decide when to
increase interest rates.
2. Many philosophers of science believe that the defining characteristic of a science is the use of the
scientific method of inquiry to establish stable relationships. Scientists examine data, often provided by
controlled experiments, to support or disprove a hypothesis. Economists are more limited in their use
of experiments. They cannot conduct controlled experiments on the economy; they must rely on the
natural course of developments in the economy to collect data. To the extent that economists use the
scientific method of inquiry, that is, developing hypotheses and testing them, economics has the
characteristics of a science.
3. We can use a simple variant of the supply-and-demand model for pizza to answer this question.
Assume that the quantity of ice cream demanded depends not only on the price of ice cream and
income, but also on the price of frozen yogurt:
Qd = D(PIC, PFY, Y).
We expect that demand for ice cream rises when the price of frozen yogurt rises, because ice cream
and frozen yogurt are substitutes. That is, when the price of frozen yogurt goes up, I consume less of it
and, instead, fulfill more of my frozen dessert urges through the consumption of ice cream.
Chapter 1—The Science of Macroeconomics 2
The next part of the model is the supply function for ice cream, Qs = S(PIC). Finally, in equilibrium,
supply must equal demand, so that Qs = Qd. Y and PFY are the exogenous variables, and Q and PIC are
the endogenous variables. Figure 1-1 uses this model to show that a fall in the price of frozen yogurt
results in an inward shift of the demand curve for ice cream. The new equilibrium has a lower price
and quantity of ice cream.
4. The price of haircuts changes rather infrequently. From casual observation, hairstylists tend to charge
the same price over a one- or two-year period irrespective of the demand for haircuts or the supply of
cutters. A market-clearing model for analyzing the market for haircuts has the unrealistic assumption
of flexible prices. Such an assumption is unrealistic in the short run when we observe that prices are
inflexible. Over the long run, however, the price of haircuts does tend to adjust; a market-clearing
model is therefore appropriate.
The next part of the model is the supply function for ice cream, Qs = S(PIC). Finally, in equilibrium,
supply must equal demand, so that Qs = Qd. Y and PFY are the exogenous variables, and Q and PIC are
the endogenous variables. Figure 1-1 uses this model to show that a fall in the price of frozen yogurt
results in an inward shift of the demand curve for ice cream. The new equilibrium has a lower price
and quantity of ice cream.
4. The price of haircuts changes rather infrequently. From casual observation, hairstylists tend to charge
the same price over a one- or two-year period irrespective of the demand for haircuts or the supply of
cutters. A market-clearing model for analyzing the market for haircuts has the unrealistic assumption
of flexible prices. Such an assumption is unrealistic in the short run when we observe that prices are
inflexible. Over the long run, however, the price of haircuts does tend to adjust; a market-clearing
model is therefore appropriate.
Chapter 1—The Science of Macroeconomics 2
The next part of the model is the supply function for ice cream, Qs = S(PIC). Finally, in equilibrium,
supply must equal demand, so that Qs = Qd. Y and PFY are the exogenous variables, and Q and PIC are
the endogenous variables. Figure 1-1 uses this model to show that a fall in the price of frozen yogurt
results in an inward shift of the demand curve for ice cream. The new equilibrium has a lower price
and quantity of ice cream.
4. The price of haircuts changes rather infrequently. From casual observation, hairstylists tend to charge
the same price over a one- or two-year period irrespective of the demand for haircuts or the supply of
cutters. A market-clearing model for analyzing the market for haircuts has the unrealistic assumption
of flexible prices. Such an assumption is unrealistic in the short run when we observe that prices are
inflexible. Over the long run, however, the price of haircuts does tend to adjust; a market-clearing
model is therefore appropriate.
The next part of the model is the supply function for ice cream, Qs = S(PIC). Finally, in equilibrium,
supply must equal demand, so that Qs = Qd. Y and PFY are the exogenous variables, and Q and PIC are
the endogenous variables. Figure 1-1 uses this model to show that a fall in the price of frozen yogurt
results in an inward shift of the demand curve for ice cream. The new equilibrium has a lower price
and quantity of ice cream.
4. The price of haircuts changes rather infrequently. From casual observation, hairstylists tend to charge
the same price over a one- or two-year period irrespective of the demand for haircuts or the supply of
cutters. A market-clearing model for analyzing the market for haircuts has the unrealistic assumption
of flexible prices. Such an assumption is unrealistic in the short run when we observe that prices are
inflexible. Over the long run, however, the price of haircuts does tend to adjust; a market-clearing
model is therefore appropriate.
Chapter 2—The Data of Macroeconomics 3
Answers to Textbook Questions and Problems
CHAPTER 2 The Data of Macroeconomics
Questions for Review
1. GDP measures the total income earned from the production of the new final goods and services in the
economy, and it measures the total expenditures on the new final goods and services produced in the
economy. GDP can measure two things at once because the total expenditures on the new final goods
and services by the buyers must be equal to the income earned by the sellers of the new final goods and
services. As the circular flow diagram in the text illustrates, these are alternative, equivalent ways of
measuring the flow of dollars in the economy.
2. The four components of GDP are consumption, investment, government purchases, and net exports.
The consumption category of GDP consists of household expenditures on new final goods and services,
such as the purchase of a new television. The investment category of GDP consists of business fixed
investment, residential fixed investment, and inventory investment. When a business buys new
equipment this counts as investment. Government purchases consists of purchases of new final goods
and services by federal, state, and local governments, such as payments for new military equipment.
Net exports measures the value of goods and services sold to other countries minus the value of goods
and services foreigners sell us. When the U.S. sells corn to foreign countries, it counts in the net export
category of GDP.
3. The consumer price index (CPI) measures the overall level of prices in the economy. It tells us the
price of a fixed basket of goods relative to the price of the same basket in the base year. The GDP
deflator is the ratio of nominal GDP to real GDP in a given year. The GDP deflator measures the prices
of all goods and services produced, whereas the CPI only measures prices of goods and services
bought by consumers. The GDP deflator includes only domestically produced goods, whereas the CPI
includes domestic and foreign goods bought by consumers. Finally, the CPI is a Laspeyres index that
assigns fixed weights to the prices of different goods, whereas the GDP deflator is a Paasche index that
assigns changing weights to the prices of different goods. In practice, the two price indices tend to
move together and do not often diverge.
4. The CPI measures the price of a fixed basket of goods relative to the price of the same basket in the
base year. The PCE deflator is the ratio of nominal consumer spending to real consumer spending. The
CPI and the PCE deflator are similar in that they both only include the prices of goods purchased by
consumers, and they both include the price of imported goods as well as domestically produced goods.
The two measures differ because the CPI measures the change in the price of a fixed basket whereas
the goods measured by the PCE deflator change from year to year depending on what consumers are
purchasing in that particular year.
5. The Bureau of Labor Statistics (BLS) classifies each person into one of the following three categories:
employed, unemployed, or not in the labor force. The unemployment rate, which is the percentage of
the labor force that is unemployed, is computed as follows:
Unemployment Rate =Number of Unemployed
Labor Force ´100 .
Note that the labor force is the number of people employed plus the number of people unemployed.
6. Every month, the Bureau of Labor Statistics undertakes two surveys to measure employment. First, the
BLS surveys about 60,000 households and thereby obtains an estimate of the share of people who say
they are working. The BLS multiplies this share by an estimate of the population to estimate the
number of people working. Second, the BLS surveys about 160,000 business establishments and asks
how many people they employ. Each survey is imperfect; so the two measures of employment are not
identical.
Answers to Textbook Questions and Problems
CHAPTER 2 The Data of Macroeconomics
Questions for Review
1. GDP measures the total income earned from the production of the new final goods and services in the
economy, and it measures the total expenditures on the new final goods and services produced in the
economy. GDP can measure two things at once because the total expenditures on the new final goods
and services by the buyers must be equal to the income earned by the sellers of the new final goods and
services. As the circular flow diagram in the text illustrates, these are alternative, equivalent ways of
measuring the flow of dollars in the economy.
2. The four components of GDP are consumption, investment, government purchases, and net exports.
The consumption category of GDP consists of household expenditures on new final goods and services,
such as the purchase of a new television. The investment category of GDP consists of business fixed
investment, residential fixed investment, and inventory investment. When a business buys new
equipment this counts as investment. Government purchases consists of purchases of new final goods
and services by federal, state, and local governments, such as payments for new military equipment.
Net exports measures the value of goods and services sold to other countries minus the value of goods
and services foreigners sell us. When the U.S. sells corn to foreign countries, it counts in the net export
category of GDP.
3. The consumer price index (CPI) measures the overall level of prices in the economy. It tells us the
price of a fixed basket of goods relative to the price of the same basket in the base year. The GDP
deflator is the ratio of nominal GDP to real GDP in a given year. The GDP deflator measures the prices
of all goods and services produced, whereas the CPI only measures prices of goods and services
bought by consumers. The GDP deflator includes only domestically produced goods, whereas the CPI
includes domestic and foreign goods bought by consumers. Finally, the CPI is a Laspeyres index that
assigns fixed weights to the prices of different goods, whereas the GDP deflator is a Paasche index that
assigns changing weights to the prices of different goods. In practice, the two price indices tend to
move together and do not often diverge.
4. The CPI measures the price of a fixed basket of goods relative to the price of the same basket in the
base year. The PCE deflator is the ratio of nominal consumer spending to real consumer spending. The
CPI and the PCE deflator are similar in that they both only include the prices of goods purchased by
consumers, and they both include the price of imported goods as well as domestically produced goods.
The two measures differ because the CPI measures the change in the price of a fixed basket whereas
the goods measured by the PCE deflator change from year to year depending on what consumers are
purchasing in that particular year.
5. The Bureau of Labor Statistics (BLS) classifies each person into one of the following three categories:
employed, unemployed, or not in the labor force. The unemployment rate, which is the percentage of
the labor force that is unemployed, is computed as follows:
Unemployment Rate =Number of Unemployed
Labor Force ´100 .
Note that the labor force is the number of people employed plus the number of people unemployed.
6. Every month, the Bureau of Labor Statistics undertakes two surveys to measure employment. First, the
BLS surveys about 60,000 households and thereby obtains an estimate of the share of people who say
they are working. The BLS multiplies this share by an estimate of the population to estimate the
number of people working. Second, the BLS surveys about 160,000 business establishments and asks
how many people they employ. Each survey is imperfect; so the two measures of employment are not
identical.
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Chapter 2—The Data of Macroeconomics 4
Problems and Applications
1. From the main bea.gov Web page click on the interactive data tab at the top, select GDP, begin using
the data, section 1, and then table 1.1.1. Real GDP grew at a rate of 2.2 percent in quarter 4 of 2014.
When compared to growth rates of −2.1 percent, 4.6 percent, and 5 percent for the first three quarters
of 2014, the rate of 2.2 percent was slightly below average. From the main bls.gov Web page select the
data tools tab, then top picks. Check the box for the unemployment rate and retrieve the data. The
unemployment rate in March 2015 was 5.5 percent, which was about equal to the natural rate of
unemployment, or the long run average rate. From the main bls.gov page, select the economic releases
tab, then inflation and prices. Access the report for the CPI. In February 2015, the inflation rate for all
items was 0 percent, and if food and energy were excluded the rate was 1.7 percent. The inflation rate
was below average and below the Federal Reserve’s target of 2 percent.
2. Value added by each person is equal to the value of the good produced minus the amount the person
paid for the materials needed to make the good. Therefore, the value added by the farmer is $1.00 ($1 –
0 = $1). The value added by the miller is $2: she sells the flour to the baker for $3 but paid $1 for the
flour. The value added by the baker is $3: she sells the bread to the engineer for $6 but paid the miller
$3 for the flour. GDP is the total value added, or $1 + $2 + $3 = $6. Note that GDP equals the value of
the final good (the bread).
3. When a woman marries her butler, GDP falls by the amount of the butler’s salary. This happens
because GDP measures total income, and therefore GDP, falls by the amount of the butler’s loss in
salary. If GDP truly measures the value of all goods and services, then the marriage would not affect
GDP since the total amount of economic activity is unchanged. Actual GDP, however, is an imperfect
measure of economic activity because the value of some goods and services is left out. Once the
butler’s work becomes part of his household chores, his services are no longer counted in GDP. As this
example illustrates, GDP does not include the value of any output produced in the home.
4. a. The airplane sold to the U.S. Air Force counts as government purchases because the Air Force is
part of the government.
b. The airplane sold to American Airlines counts as investment because it is a capital good sold to a
private firm.
c. The airplane sold to Air France counts as an export because it is sold to a foreigner.
d. The airplane sold to Amelia Earhart counts as consumption because it is sold to a private
individual.
e. The airplane built to be sold next year counts as investment. In particular, the airplane is counted
as inventory investment, which is where goods that are produced in one year and sold in another
year are counted.
5. Data on parts (a) to (f) can be downloaded from the Bureau of Economic Analysis. Go to the bea.gov
Website, click on the interactive data tab at the top, select GDP, begin using the data, section 1, and
then table 1.1.5. Choose the “modify the data” option to select the years you in which you are
interested. By dividing each component (a) to (f) by nominal GDP and multiplying by 100, we obtain
the following percentages:
1950 1980 2014
a. Personal consumption expenditures 64.0% 61.3% 68.5%
b. Gross private domestic investment 18.8% 18.5% 16.4%
c. Government consumption purchases 16.9% 20.6% 18.2%
d. Net exports 0.2% –0.5% 3.1%
e. National defense purchases 7.6% 6.3% 4.4%
f. Imports 3.9% 10.3% 16.5%
(Note: The above data was downloaded April 3, 2015, from the BEA Web site.)
Among other things, we observe the following trends in the economy over the period 1950–2015:
a. Personal consumption expenditures have been around two-thirds of GDP between 1980 and 2015.
b. The share of GDP going to gross private domestic investment remained fairly steady.
Problems and Applications
1. From the main bea.gov Web page click on the interactive data tab at the top, select GDP, begin using
the data, section 1, and then table 1.1.1. Real GDP grew at a rate of 2.2 percent in quarter 4 of 2014.
When compared to growth rates of −2.1 percent, 4.6 percent, and 5 percent for the first three quarters
of 2014, the rate of 2.2 percent was slightly below average. From the main bls.gov Web page select the
data tools tab, then top picks. Check the box for the unemployment rate and retrieve the data. The
unemployment rate in March 2015 was 5.5 percent, which was about equal to the natural rate of
unemployment, or the long run average rate. From the main bls.gov page, select the economic releases
tab, then inflation and prices. Access the report for the CPI. In February 2015, the inflation rate for all
items was 0 percent, and if food and energy were excluded the rate was 1.7 percent. The inflation rate
was below average and below the Federal Reserve’s target of 2 percent.
2. Value added by each person is equal to the value of the good produced minus the amount the person
paid for the materials needed to make the good. Therefore, the value added by the farmer is $1.00 ($1 –
0 = $1). The value added by the miller is $2: she sells the flour to the baker for $3 but paid $1 for the
flour. The value added by the baker is $3: she sells the bread to the engineer for $6 but paid the miller
$3 for the flour. GDP is the total value added, or $1 + $2 + $3 = $6. Note that GDP equals the value of
the final good (the bread).
3. When a woman marries her butler, GDP falls by the amount of the butler’s salary. This happens
because GDP measures total income, and therefore GDP, falls by the amount of the butler’s loss in
salary. If GDP truly measures the value of all goods and services, then the marriage would not affect
GDP since the total amount of economic activity is unchanged. Actual GDP, however, is an imperfect
measure of economic activity because the value of some goods and services is left out. Once the
butler’s work becomes part of his household chores, his services are no longer counted in GDP. As this
example illustrates, GDP does not include the value of any output produced in the home.
4. a. The airplane sold to the U.S. Air Force counts as government purchases because the Air Force is
part of the government.
b. The airplane sold to American Airlines counts as investment because it is a capital good sold to a
private firm.
c. The airplane sold to Air France counts as an export because it is sold to a foreigner.
d. The airplane sold to Amelia Earhart counts as consumption because it is sold to a private
individual.
e. The airplane built to be sold next year counts as investment. In particular, the airplane is counted
as inventory investment, which is where goods that are produced in one year and sold in another
year are counted.
5. Data on parts (a) to (f) can be downloaded from the Bureau of Economic Analysis. Go to the bea.gov
Website, click on the interactive data tab at the top, select GDP, begin using the data, section 1, and
then table 1.1.5. Choose the “modify the data” option to select the years you in which you are
interested. By dividing each component (a) to (f) by nominal GDP and multiplying by 100, we obtain
the following percentages:
1950 1980 2014
a. Personal consumption expenditures 64.0% 61.3% 68.5%
b. Gross private domestic investment 18.8% 18.5% 16.4%
c. Government consumption purchases 16.9% 20.6% 18.2%
d. Net exports 0.2% –0.5% 3.1%
e. National defense purchases 7.6% 6.3% 4.4%
f. Imports 3.9% 10.3% 16.5%
(Note: The above data was downloaded April 3, 2015, from the BEA Web site.)
Among other things, we observe the following trends in the economy over the period 1950–2015:
a. Personal consumption expenditures have been around two-thirds of GDP between 1980 and 2015.
b. The share of GDP going to gross private domestic investment remained fairly steady.
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Chapter 2—The Data of Macroeconomics 5
c. The share going to government consumption purchases rose sharply from 1950 to 1980.
d. Net exports, which were positive in 1950, have been negative since that time.
e. The share going to national defense purchases has fallen.
f. Imports have grown rapidly relative to GDP.
6. a. GDP measures the value of the final goods and services produced, or $1,000,000.
b. NNP is equal to GNP minus depreciation. In this example, GDP is equal to GNP because there are
no foreign transactions. Therefore, NNP is equal to $875,000.
c. National income is equal to NNP, or $875,000.
d. Employee compensation is equal to $600,000.
e. Proprietors’ income measures the income of the owner, and is equal to 150,000.
f. Corporate profit is equal to corporate taxes plus dividends plus retained earnings, or $275,000.
Retained earnings is calculated as sales minus wages minus dividends minus depreciation minus
corporate tax, or $75,000.
g. Personal income is equal to employee compensation plus dividends, or $750,000.
h. Disposable personal income is personal income minus taxes, or $550,000.
7. a. i. Nominal GDP is the total value of goods and services measured at current prices. Therefore,
Nominal GDP2010 =Photdogs
2010 ´ Qhotdogs
2010
( )
+ Pburgers
2010 ´Qburgers
2010
( )
= ($2 200) + ($3 200)
= $400 + $600
= $1,000.
Nominal GDP2015 =Photdogs
2015 ´ Qhotdogs
2015
( )
+ Pburgers
2015 ´Qburgers
2015
( )
= ($4 250) + ($4 500)
= $1,000 + $2,000
= $3,000.
ii. Real GDP is the total value of goods and services measured at constant prices. Therefore, to
calculate real GDP in 2015 (with base year 2010), multiply the quantities purchased in the
year 2015 by the 2010 prices:
Real GDP2015 =P2010
hotdogs ´ Q2015
hotdogs
( )
+ P2010
burgers ´ Q2015
burgers
( )
= ($2 250) + ($3 500)
= $500 + $1,500
= $2,000.
Real GDP for 2010 is calculated by multiplying the quantities in 2010 by the prices in 2010.
Since the base year is 2010, real GDP2010 equals nominal GDP2010, which is $10,00. Hence,
real GDP increased between 2010 and 2015.
iii. The implicit price deflator for GDP compares the current prices of all goods and services
produced to the prices of the same goods and services in a base year. It is calculated as
follows:
Implicit Price Deflator2015 =Nominal GDP2010
Real GDP2010 = 1
Using the values for Nominal GDP2015 and real GDP2015 calculated above:
Implicit Price Deflator2015 = $3,000
$2,000
c. The share going to government consumption purchases rose sharply from 1950 to 1980.
d. Net exports, which were positive in 1950, have been negative since that time.
e. The share going to national defense purchases has fallen.
f. Imports have grown rapidly relative to GDP.
6. a. GDP measures the value of the final goods and services produced, or $1,000,000.
b. NNP is equal to GNP minus depreciation. In this example, GDP is equal to GNP because there are
no foreign transactions. Therefore, NNP is equal to $875,000.
c. National income is equal to NNP, or $875,000.
d. Employee compensation is equal to $600,000.
e. Proprietors’ income measures the income of the owner, and is equal to 150,000.
f. Corporate profit is equal to corporate taxes plus dividends plus retained earnings, or $275,000.
Retained earnings is calculated as sales minus wages minus dividends minus depreciation minus
corporate tax, or $75,000.
g. Personal income is equal to employee compensation plus dividends, or $750,000.
h. Disposable personal income is personal income minus taxes, or $550,000.
7. a. i. Nominal GDP is the total value of goods and services measured at current prices. Therefore,
Nominal GDP2010 =Photdogs
2010 ´ Qhotdogs
2010
( )
+ Pburgers
2010 ´Qburgers
2010
( )
= ($2 200) + ($3 200)
= $400 + $600
= $1,000.
Nominal GDP2015 =Photdogs
2015 ´ Qhotdogs
2015
( )
+ Pburgers
2015 ´Qburgers
2015
( )
= ($4 250) + ($4 500)
= $1,000 + $2,000
= $3,000.
ii. Real GDP is the total value of goods and services measured at constant prices. Therefore, to
calculate real GDP in 2015 (with base year 2010), multiply the quantities purchased in the
year 2015 by the 2010 prices:
Real GDP2015 =P2010
hotdogs ´ Q2015
hotdogs
( )
+ P2010
burgers ´ Q2015
burgers
( )
= ($2 250) + ($3 500)
= $500 + $1,500
= $2,000.
Real GDP for 2010 is calculated by multiplying the quantities in 2010 by the prices in 2010.
Since the base year is 2010, real GDP2010 equals nominal GDP2010, which is $10,00. Hence,
real GDP increased between 2010 and 2015.
iii. The implicit price deflator for GDP compares the current prices of all goods and services
produced to the prices of the same goods and services in a base year. It is calculated as
follows:
Implicit Price Deflator2015 =Nominal GDP2010
Real GDP2010 = 1
Using the values for Nominal GDP2015 and real GDP2015 calculated above:
Implicit Price Deflator2015 = $3,000
$2,000
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Chapter 2—The Data of Macroeconomics 6
= 1.50.
This calculation reveals that prices of the goods produced in the year 2015 increased by 50
percent compared to the prices that the goods in the economy sold for in 2010. (Because 2010
is the base year, the value for the implicit price deflator for the year 2010 is 1.0 because
nominal and real GDP are the same for the base year.)
iv. The consumer price index (CPI) measures the level of prices in the economy. The CPI is
called a fixed-weight index because it uses a fixed basket of goods over time to weight prices.
If the base year is 2010, the CPI in 2015 is measuring the cost of the basket in 2015 relative to
the cost in 2010. The CPI2015 is calculated as follows:
CPI 2015 =(P2015
hotdogs ´ Q2010
hotdogs ) + (P2015
burgers ´ Q2010
burgers )
(P2010
hotdogs ´ Q2010
hotdogs ) + (P2010
burgers ´ Q2010
burgers )
=$16,000,000
$10,000,000
= 1.6.
This calculation shows that the price of goods purchased in 2015 increased by 60 percent
compared to the prices these goods would have sold for in 2010. The CPI for 2010, the base
year, equals 1.0.
b. The implicit price deflator is a Paasche index because it is computed with a changing basket of
goods; the CPI is a Laspeyres index because it is computed with a fixed basket of goods. From
(7.a.iii), the implicit price deflator for the year 2015 is 1.50, which indicates that prices rose by 50
percent from what they were in the year 2010. From (7.a.iv.), the CPI for the year 2015 is 1.6,
which indicates that prices rose by 60 percent from what they were in the year 2010.
If prices of all goods rose by, for example, 50 percent, then one could say unambiguously that
the price level rose by 50 percent. Yet, in our example, relative prices have changed. The price of
hot dogs rose by 1020 percent; the price of hamburgers rose by 33.33 percent, making hamburgers
relatively less expensive.
As the discrepancy between the CPI and the implicit price deflator illustrates, the change in
the price level depends on how the goods’ prices are weighted. The CPI weights the price of goods
by the quantities purchased in the year 2010. The implicit price deflator weights the price of goods
by the quantities purchased in the year 2015. Since the quantity of the two goods was the same in
2010, the CPI is placing equal weight on the two price changes. In 2015, the quantity of
hamburgers was twice as large as hot dogs, so there is twice as much weight placed on the
hamburger price relative to the hot dog price. For this reason, the CPI shows a larger inflation rate
– more weight is placed on the good with the larger price increase.
8. a. The consumer price index uses the consumption bundle in year 1 to figure out how much weight
to put on the price of a given good:
CPI2 =$2 ´10
( )
+ $1´ 0
( )
$1´10
( )
+ $2 ´ 0
( )
=P2
red ´ Q1
red
( )
+ P2
green ´ Q1
green
( )
P1
red ´ Q1
red
( )
+ P1
green ´ Q1
green
( )
= 2.
According to the CPI, prices have doubled.
= 1.50.
This calculation reveals that prices of the goods produced in the year 2015 increased by 50
percent compared to the prices that the goods in the economy sold for in 2010. (Because 2010
is the base year, the value for the implicit price deflator for the year 2010 is 1.0 because
nominal and real GDP are the same for the base year.)
iv. The consumer price index (CPI) measures the level of prices in the economy. The CPI is
called a fixed-weight index because it uses a fixed basket of goods over time to weight prices.
If the base year is 2010, the CPI in 2015 is measuring the cost of the basket in 2015 relative to
the cost in 2010. The CPI2015 is calculated as follows:
CPI 2015 =(P2015
hotdogs ´ Q2010
hotdogs ) + (P2015
burgers ´ Q2010
burgers )
(P2010
hotdogs ´ Q2010
hotdogs ) + (P2010
burgers ´ Q2010
burgers )
=$16,000,000
$10,000,000
= 1.6.
This calculation shows that the price of goods purchased in 2015 increased by 60 percent
compared to the prices these goods would have sold for in 2010. The CPI for 2010, the base
year, equals 1.0.
b. The implicit price deflator is a Paasche index because it is computed with a changing basket of
goods; the CPI is a Laspeyres index because it is computed with a fixed basket of goods. From
(7.a.iii), the implicit price deflator for the year 2015 is 1.50, which indicates that prices rose by 50
percent from what they were in the year 2010. From (7.a.iv.), the CPI for the year 2015 is 1.6,
which indicates that prices rose by 60 percent from what they were in the year 2010.
If prices of all goods rose by, for example, 50 percent, then one could say unambiguously that
the price level rose by 50 percent. Yet, in our example, relative prices have changed. The price of
hot dogs rose by 1020 percent; the price of hamburgers rose by 33.33 percent, making hamburgers
relatively less expensive.
As the discrepancy between the CPI and the implicit price deflator illustrates, the change in
the price level depends on how the goods’ prices are weighted. The CPI weights the price of goods
by the quantities purchased in the year 2010. The implicit price deflator weights the price of goods
by the quantities purchased in the year 2015. Since the quantity of the two goods was the same in
2010, the CPI is placing equal weight on the two price changes. In 2015, the quantity of
hamburgers was twice as large as hot dogs, so there is twice as much weight placed on the
hamburger price relative to the hot dog price. For this reason, the CPI shows a larger inflation rate
– more weight is placed on the good with the larger price increase.
8. a. The consumer price index uses the consumption bundle in year 1 to figure out how much weight
to put on the price of a given good:
CPI2 =$2 ´10
( )
+ $1´ 0
( )
$1´10
( )
+ $2 ´ 0
( )
=P2
red ´ Q1
red
( )
+ P2
green ´ Q1
green
( )
P1
red ´ Q1
red
( )
+ P1
green ´ Q1
green
( )
= 2.
According to the CPI, prices have doubled.
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Chapter 2—The Data of Macroeconomics 7
b. Nominal spending is the total value of output produced in each year. In year 1 and year 2, Abby
buys 10 apples for $1 each, so her nominal spending remains constant at $10. For example,
Nominal Spending2 =P2
red ´ Q2
red
( )
+ P2
green ´ Q2
green
( )
= ($2 0) + ($1 10)
= $10.
c. Real spending is the total value of output produced in each year valued at the prices prevailing in
year 1. In year 1, the base year, her real spending equals her nominal spending of $10. In year 2,
she consumes 10 green apples that are each valued at their year 1 price of $2, so her real spending
is $20. That is,
Real Spending2 =P1
red ´ Q2
red
( )
+ P1
green ´ Q2
green
( )
= ($1 0) + ($2 10)
= $20.
Hence, Abby’s real spending rises from $10 to $20.
d. The implicit price deflator is calculated by dividing Abby’s nominal spending in year 2 by her real
spending that year:
Implicit Price Deflator2 =Nominal Spending2
Real Spending2
=$10
$20
= 0.5.
Thus, the implicit price deflator suggests that prices have fallen by half. The reason for this is that
the deflator estimates how much Abby values her apples using prices prevailing in year 1. From
this perspective green apples appear very valuable. In year 2, when Abby consumes 10 green
apples, it appears that her consumption has increased because the deflator values green apples
more highly than red apples. The only way she could still be spending $10 on a higher
consumption bundle is if the price of the good she was consuming fell.
e. If Abby thinks of red apples and green apples as perfect substitutes, then the cost of living in this
economy has not changed—in either year it costs $10 to consume 10 apples. According to the CPI,
however, the cost of living has doubled. This is because the CPI only takes into account the fact
that the red apple price has doubled; the CPI ignores the fall in the price of green apples because
they were not in the consumption bundle in year 1. In contrast to the CPI, the implicit price
deflator estimates the cost of living has been cut in half. Thus, the CPI, a Laspeyres index,
overstates the increase in the cost of living and the deflator, a Paasche index, understates it.
9. a. The labor force includes full time workers, part time workers, those who run their own business,
and those who do not have a job but are looking for a job. The labor force consists of 70 people.
The working age population consists of the labor force plus those not in the labor force. The 10
discouraged workers and the 10 retired people are not in the labor force, but assuming they are
capable of working, they are part of the adult population. The adult population consists of 90
people, so the labor force participation rate is equal to 70/90 or 77.8 percent.
b. The number of unemployed workers is equal to 10, so the unemployment rate is 10/70 or 14.3
percent.
b. Nominal spending is the total value of output produced in each year. In year 1 and year 2, Abby
buys 10 apples for $1 each, so her nominal spending remains constant at $10. For example,
Nominal Spending2 =P2
red ´ Q2
red
( )
+ P2
green ´ Q2
green
( )
= ($2 0) + ($1 10)
= $10.
c. Real spending is the total value of output produced in each year valued at the prices prevailing in
year 1. In year 1, the base year, her real spending equals her nominal spending of $10. In year 2,
she consumes 10 green apples that are each valued at their year 1 price of $2, so her real spending
is $20. That is,
Real Spending2 =P1
red ´ Q2
red
( )
+ P1
green ´ Q2
green
( )
= ($1 0) + ($2 10)
= $20.
Hence, Abby’s real spending rises from $10 to $20.
d. The implicit price deflator is calculated by dividing Abby’s nominal spending in year 2 by her real
spending that year:
Implicit Price Deflator2 =Nominal Spending2
Real Spending2
=$10
$20
= 0.5.
Thus, the implicit price deflator suggests that prices have fallen by half. The reason for this is that
the deflator estimates how much Abby values her apples using prices prevailing in year 1. From
this perspective green apples appear very valuable. In year 2, when Abby consumes 10 green
apples, it appears that her consumption has increased because the deflator values green apples
more highly than red apples. The only way she could still be spending $10 on a higher
consumption bundle is if the price of the good she was consuming fell.
e. If Abby thinks of red apples and green apples as perfect substitutes, then the cost of living in this
economy has not changed—in either year it costs $10 to consume 10 apples. According to the CPI,
however, the cost of living has doubled. This is because the CPI only takes into account the fact
that the red apple price has doubled; the CPI ignores the fall in the price of green apples because
they were not in the consumption bundle in year 1. In contrast to the CPI, the implicit price
deflator estimates the cost of living has been cut in half. Thus, the CPI, a Laspeyres index,
overstates the increase in the cost of living and the deflator, a Paasche index, understates it.
9. a. The labor force includes full time workers, part time workers, those who run their own business,
and those who do not have a job but are looking for a job. The labor force consists of 70 people.
The working age population consists of the labor force plus those not in the labor force. The 10
discouraged workers and the 10 retired people are not in the labor force, but assuming they are
capable of working, they are part of the adult population. The adult population consists of 90
people, so the labor force participation rate is equal to 70/90 or 77.8 percent.
b. The number of unemployed workers is equal to 10, so the unemployment rate is 10/70 or 14.3
percent.
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Chapter 2—The Data of Macroeconomics 8
c. The household survey estimates total employment by asking a sample of households about their
employment status. The household survey would report 60 people employed. The establishment
survey estimates total employment by asking a sample of businesses to report how many workers
they are employing. In this case the establishment survey would report 55 people employed. The 5
people with 2 jobs would be counted twice, and the 10 people who run their own business would
not be counted.
10. As Senator Robert Kennedy pointed out, GDP is an imperfect measure of economic performance or
well-being. In addition to the left-out items that Kennedy cited, GDP also ignores the imputed rent on
durable goods such as cars, refrigerators, and lawnmowers; many services and products produced as
part of household activity, such as cooking and cleaning; and the value of goods produced and sold in
illegal activities, such as the drug trade. These imperfections in the measurement of GDP do not
necessarily reduce its usefulness. As long as these measurement problems stay constant over time, then
GDP is useful in comparing economic activity from year to year. Moreover, a large GDP allows us to
afford better medical care for our children, newer books for their education, and more toys for their
play. Finally, countries with higher levels of GDP tend to have higher levels of life expectancy, better
access to clean water and sanitation, and higher levels of education. GDP is therefore a useful measure
for comparing the level of growth and development across countries.
11. a. Real GDP falls because Disney World does not produce any services while it is closed. This
corresponds to a decrease in economic well-being because the income of workers and shareholders
of Disney World falls (the income side of the national accounts), and people’s consumption of
Disney World falls (the expenditure side of the national accounts).
b. Real GDP rises because the original capital and labor in farm production now produce more wheat.
This corresponds to an increase in the economic well-being of society, since people can now
consume more wheat. (If people do not want to consume more wheat, then farmers and farmland
can be shifted to producing other goods that society values.)
c. Real GDP falls because with fewer workers on the job, firms produce less. This accurately reflects
a fall in economic well-being.
d. Real GDP falls because the firms that lay off workers produce less. This decreases economic well-
being because workers’ incomes fall (the income side), and there are fewer goods for people to
buy (the expenditure side).
e. Real GDP is likely to fall, as firms shift toward production methods that produce fewer goods but
emit less pollution. Economic well-being, however, may rise. The economy now produces less
measured output but more clean air. Clean air is not traded in markets and, thus, does not show up
in measured GDP, but is nevertheless a good that people value.
f. Real GDP rises because the high school students go from an activity in which they are not
producing market goods and services to one in which they are. Economic well-being, however,
may decrease. In ideal national accounts, attending school would show up as investment because it
presumably increases the future productivity of the worker. Actual national accounts do not
measure this type of investment. Note also that future GDP may be lower than it would be if the
students stayed in school, since the future work force will be less educated.
g. Measured real GDP falls because fathers spend less time producing market goods and services.
The actual production of goods and services need not have fallen because but unmeasured
production of child-rearing services rises. The well-being of the average person may very well rise
if we assume the fathers and the children enjoy the extra time they are spending together.
c. The household survey estimates total employment by asking a sample of households about their
employment status. The household survey would report 60 people employed. The establishment
survey estimates total employment by asking a sample of businesses to report how many workers
they are employing. In this case the establishment survey would report 55 people employed. The 5
people with 2 jobs would be counted twice, and the 10 people who run their own business would
not be counted.
10. As Senator Robert Kennedy pointed out, GDP is an imperfect measure of economic performance or
well-being. In addition to the left-out items that Kennedy cited, GDP also ignores the imputed rent on
durable goods such as cars, refrigerators, and lawnmowers; many services and products produced as
part of household activity, such as cooking and cleaning; and the value of goods produced and sold in
illegal activities, such as the drug trade. These imperfections in the measurement of GDP do not
necessarily reduce its usefulness. As long as these measurement problems stay constant over time, then
GDP is useful in comparing economic activity from year to year. Moreover, a large GDP allows us to
afford better medical care for our children, newer books for their education, and more toys for their
play. Finally, countries with higher levels of GDP tend to have higher levels of life expectancy, better
access to clean water and sanitation, and higher levels of education. GDP is therefore a useful measure
for comparing the level of growth and development across countries.
11. a. Real GDP falls because Disney World does not produce any services while it is closed. This
corresponds to a decrease in economic well-being because the income of workers and shareholders
of Disney World falls (the income side of the national accounts), and people’s consumption of
Disney World falls (the expenditure side of the national accounts).
b. Real GDP rises because the original capital and labor in farm production now produce more wheat.
This corresponds to an increase in the economic well-being of society, since people can now
consume more wheat. (If people do not want to consume more wheat, then farmers and farmland
can be shifted to producing other goods that society values.)
c. Real GDP falls because with fewer workers on the job, firms produce less. This accurately reflects
a fall in economic well-being.
d. Real GDP falls because the firms that lay off workers produce less. This decreases economic well-
being because workers’ incomes fall (the income side), and there are fewer goods for people to
buy (the expenditure side).
e. Real GDP is likely to fall, as firms shift toward production methods that produce fewer goods but
emit less pollution. Economic well-being, however, may rise. The economy now produces less
measured output but more clean air. Clean air is not traded in markets and, thus, does not show up
in measured GDP, but is nevertheless a good that people value.
f. Real GDP rises because the high school students go from an activity in which they are not
producing market goods and services to one in which they are. Economic well-being, however,
may decrease. In ideal national accounts, attending school would show up as investment because it
presumably increases the future productivity of the worker. Actual national accounts do not
measure this type of investment. Note also that future GDP may be lower than it would be if the
students stayed in school, since the future work force will be less educated.
g. Measured real GDP falls because fathers spend less time producing market goods and services.
The actual production of goods and services need not have fallen because but unmeasured
production of child-rearing services rises. The well-being of the average person may very well rise
if we assume the fathers and the children enjoy the extra time they are spending together.
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Chapter 3—National Income: Where It Comes From and Where It Goes 9
Answers to Textbook Questions and Problems
CHAPTER 3 National Income: Where It Comes From and Where It Goes
Questions for Review
1. The factors of production and the production technology determine the amount of output an economy
can produce. The factors of production are the inputs used to produce goods and services: the most
important factors are capital and labor. The production technology determines how much output can be
produced from any given amounts of these inputs. An increase in one of the factors of production or an
improvement in technology leads to an increase in the economy’s output.
2. When a firm decides how much of a factor of production to hire or demand, it considers how this
decision affects profits. For example, hiring an extra unit of labor increases output and therefore
increases revenue; the firm compares this additional revenue to the additional cost from the higher
wage bill. The additional revenue the firm receives depends on the marginal product of labor (MPL)
and the price of the good produced (P). An additional unit of labor produces MPL units of additional
output, which sells for P dollars per unit. Therefore, the additional revenue to the firm is P MPL. The
cost of hiring the additional unit of labor is the wage W. Thus, this hiring decision has the following
effect on profits:
ΔProfit = ΔRevenue – ΔCost
= (P MPL) – W.
If the additional revenue, P MPL, exceeds the cost (W) of hiring the additional unit of labor, then
profit increases. The firm will hire labor until it is no longer profitable to do so—that is, until the MPL
falls to the point where the change in profit is zero. In the equation above, the firm hires labor until
ΔProfit = 0, which is when (P MPL) = W.
This condition can be rewritten as:
MPL = W/P.
Therefore, a competitive profit-maximizing firm hires labor until the marginal product of labor equals
the real wage. The same logic applies to the firm’s decision regarding how much capital to hire: the
firm will hire capital until the marginal product of capital equals the real rental price.
3. A production function has constant returns to scale if an equal percentage increase in all factors of
production causes an increase in output of the same percentage. For example, if a firm increases its use
of capital and labor by 50 percent, and output increases by 50 percent, then the production function has
constant returns to scale.
If the production function has constant returns to scale, then total income (or equivalently, total
output) in an economy of competitive profit-maximizing firms is divided between the return to labor,
MPL L, and the return to capital, MPK K. That is, under constant returns to scale, economic profit
is zero.
4. A Cobb–Douglas production function has the form F(K,L) = AKαL1–α. The text showed that the
parameter α gives capital’s share of income. So if capital earns one-fourth of total income, then
=
0.25. Hence, F(K,L) = AK0.25L0.75.
5. Consumption depends positively on disposable income—i.e. the amount of income after all taxes have
been paid. Higher disposable income means higher consumption.
The quantity of investment goods demanded depends negatively on the real interest rate. For an
investment to be profitable, its return must be greater than its cost. Because the real interest rate
measures the cost of funds, a higher real interest rate makes it more costly to invest, so the demand for
investment goods falls.
Answers to Textbook Questions and Problems
CHAPTER 3 National Income: Where It Comes From and Where It Goes
Questions for Review
1. The factors of production and the production technology determine the amount of output an economy
can produce. The factors of production are the inputs used to produce goods and services: the most
important factors are capital and labor. The production technology determines how much output can be
produced from any given amounts of these inputs. An increase in one of the factors of production or an
improvement in technology leads to an increase in the economy’s output.
2. When a firm decides how much of a factor of production to hire or demand, it considers how this
decision affects profits. For example, hiring an extra unit of labor increases output and therefore
increases revenue; the firm compares this additional revenue to the additional cost from the higher
wage bill. The additional revenue the firm receives depends on the marginal product of labor (MPL)
and the price of the good produced (P). An additional unit of labor produces MPL units of additional
output, which sells for P dollars per unit. Therefore, the additional revenue to the firm is P MPL. The
cost of hiring the additional unit of labor is the wage W. Thus, this hiring decision has the following
effect on profits:
ΔProfit = ΔRevenue – ΔCost
= (P MPL) – W.
If the additional revenue, P MPL, exceeds the cost (W) of hiring the additional unit of labor, then
profit increases. The firm will hire labor until it is no longer profitable to do so—that is, until the MPL
falls to the point where the change in profit is zero. In the equation above, the firm hires labor until
ΔProfit = 0, which is when (P MPL) = W.
This condition can be rewritten as:
MPL = W/P.
Therefore, a competitive profit-maximizing firm hires labor until the marginal product of labor equals
the real wage. The same logic applies to the firm’s decision regarding how much capital to hire: the
firm will hire capital until the marginal product of capital equals the real rental price.
3. A production function has constant returns to scale if an equal percentage increase in all factors of
production causes an increase in output of the same percentage. For example, if a firm increases its use
of capital and labor by 50 percent, and output increases by 50 percent, then the production function has
constant returns to scale.
If the production function has constant returns to scale, then total income (or equivalently, total
output) in an economy of competitive profit-maximizing firms is divided between the return to labor,
MPL L, and the return to capital, MPK K. That is, under constant returns to scale, economic profit
is zero.
4. A Cobb–Douglas production function has the form F(K,L) = AKαL1–α. The text showed that the
parameter α gives capital’s share of income. So if capital earns one-fourth of total income, then
=
0.25. Hence, F(K,L) = AK0.25L0.75.
5. Consumption depends positively on disposable income—i.e. the amount of income after all taxes have
been paid. Higher disposable income means higher consumption.
The quantity of investment goods demanded depends negatively on the real interest rate. For an
investment to be profitable, its return must be greater than its cost. Because the real interest rate
measures the cost of funds, a higher real interest rate makes it more costly to invest, so the demand for
investment goods falls.
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Chapter 3—National Income: Where It Comes From and Where It Goes 10
6. Government purchases are a measure of the value of goods and services purchased directly by the
government. For example, the government buys missiles and tanks, builds roads, and provides services
such as air traffic control. All of these activities are part of GDP. Transfer payments are government
payments to individuals that are not in exchange for goods or services. They are the opposite of taxes:
taxes reduce household disposable income, whereas transfer payments increase it. Examples of transfer
payments include Social Security payments to the elderly, unemployment insurance, and veterans’
benefits.
7. Consumption, investment, and government purchases determine demand for the economy’s output,
whereas the factors of production and the production function determine the supply of output. The real
interest rate adjusts to ensure that the demand for the economy’s goods equals the supply. At the
equilibrium interest rate, the demand for goods and services equals the supply.
8. When the government increases taxes, disposable income falls, and therefore consumption falls as well.
The decrease in consumption equals the amount that taxes increase multiplied by the marginal
propensity to consume (MPC). The higher the MPC is, the greater is the negative effect of the tax
increase on consumption. Because output is fixed by the factors of production and the production
technology, and government purchases have not changed, the decrease in consumption must be offset
by an increase in investment. For investment to rise, the real interest rate must fall. Therefore, a tax
increase leads to a decrease in consumption, an increase in investment, and a fall in the real interest
rate.
Problems and Applications
1. a. According to the neoclassical theory of distribution, the real wage equals the marginal product of
labor. Because of diminishing returns to labor, an increase in the labor force causes the marginal
product of labor to fall. Hence, the real wage falls.
Given a Cobb–Douglas production function, the increase in the labor force will increase the
marginal product of capital and will increase the real rental price of capital. With more workers,
the capital will be used more intensively and will be more productive.
b. The real rental price equals the marginal product of capital. If an earthquake destroys some of the
capital stock (yet miraculously does not kill anyone and lower the labor force), the marginal
product of capital rises and, hence, the real rental price rises.
Given a Cobb–Douglas production function, the decrease in the capital stock will decrease the
marginal product of labor and will decrease the real wage. With less capital, each worker becomes
less productive.
c. If a technological advance improves the production function, this is likely to increase the marginal
products of both capital and labor. Hence, the real wage and the real rental price both increase.
d. High inflation that doubles the nominal wage and the price level will have no impact on the real
wage. Similarly, high inflation that doubles the nominal rental price of capital and the price level
will have no impact on the real rental price of capital.
2. a. To find the amount of output produced, substitute the given values for labor and land into the
production function:
Y = 1000.51000.5 = 100.
b. According to the text, the formulas for the marginal product of labor and the marginal product of
capital (land) are:
MPL = (1 – α)AKαL–α.
MPK = αAKα–1L1–α.
6. Government purchases are a measure of the value of goods and services purchased directly by the
government. For example, the government buys missiles and tanks, builds roads, and provides services
such as air traffic control. All of these activities are part of GDP. Transfer payments are government
payments to individuals that are not in exchange for goods or services. They are the opposite of taxes:
taxes reduce household disposable income, whereas transfer payments increase it. Examples of transfer
payments include Social Security payments to the elderly, unemployment insurance, and veterans’
benefits.
7. Consumption, investment, and government purchases determine demand for the economy’s output,
whereas the factors of production and the production function determine the supply of output. The real
interest rate adjusts to ensure that the demand for the economy’s goods equals the supply. At the
equilibrium interest rate, the demand for goods and services equals the supply.
8. When the government increases taxes, disposable income falls, and therefore consumption falls as well.
The decrease in consumption equals the amount that taxes increase multiplied by the marginal
propensity to consume (MPC). The higher the MPC is, the greater is the negative effect of the tax
increase on consumption. Because output is fixed by the factors of production and the production
technology, and government purchases have not changed, the decrease in consumption must be offset
by an increase in investment. For investment to rise, the real interest rate must fall. Therefore, a tax
increase leads to a decrease in consumption, an increase in investment, and a fall in the real interest
rate.
Problems and Applications
1. a. According to the neoclassical theory of distribution, the real wage equals the marginal product of
labor. Because of diminishing returns to labor, an increase in the labor force causes the marginal
product of labor to fall. Hence, the real wage falls.
Given a Cobb–Douglas production function, the increase in the labor force will increase the
marginal product of capital and will increase the real rental price of capital. With more workers,
the capital will be used more intensively and will be more productive.
b. The real rental price equals the marginal product of capital. If an earthquake destroys some of the
capital stock (yet miraculously does not kill anyone and lower the labor force), the marginal
product of capital rises and, hence, the real rental price rises.
Given a Cobb–Douglas production function, the decrease in the capital stock will decrease the
marginal product of labor and will decrease the real wage. With less capital, each worker becomes
less productive.
c. If a technological advance improves the production function, this is likely to increase the marginal
products of both capital and labor. Hence, the real wage and the real rental price both increase.
d. High inflation that doubles the nominal wage and the price level will have no impact on the real
wage. Similarly, high inflation that doubles the nominal rental price of capital and the price level
will have no impact on the real rental price of capital.
2. a. To find the amount of output produced, substitute the given values for labor and land into the
production function:
Y = 1000.51000.5 = 100.
b. According to the text, the formulas for the marginal product of labor and the marginal product of
capital (land) are:
MPL = (1 – α)AKαL–α.
MPK = αAKα–1L1–α.
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Chapter 3—National Income: Where It Comes From and Where It Goes 11
In this problem, α is 0.5 and A is 1. Substitute in the given values for labor and land to find the
marginal product of labor is 0.5 and marginal product of capital (land) is 0.5. We know that the
real wage equals the marginal product of labor and the real rental price of land equals the marginal
product of capital (land).
c. Labor’s share of the output is given by the marginal product of labor times the quantity of labor, or
50.
d. The new level of output is 70.71.
e. The new wage is 0.71. The new rental price of land is 0.35.
f. Labor now receives 35.36.
3. A production function has decreasing returns to scale if an equal percentage increase in all factors of
production leads to a smaller percentage increase in output. For example, if we double the amounts of
capital and labor output increases by less than double, then the production function has decreasing
returns to scale. This may happen if there is a fixed factor such as land in the production function, and
this fixed factor becomes scarce as the economy grows larger.
A production function has increasing returns to scale if an equal percentage increase in all factors
of production leads to a larger percentage increase in output. For example, if doubling the amount of
capital and labor increases the output by more than double, then the production function has increasing
returns to scale. This may happen if specialization of labor becomes greater as the population grows.
For example, if only one worker builds a car, then it takes him a long time because he has to learn
many different skills, and he must constantly change tasks and tools. But if many workers build a car,
then each one can specialize in a particular task and become more productive.
4. a. A Cobb–Douglas production function has the form Y = AKαL1–α. The text showed that the marginal
products for the Cobb–Douglas production function are:
MPL = (1 – α)Y/L.
MPK = αY/K.
Competitive profit-maximizing firms hire labor until its marginal product equals the real wage,
and hire capital until its marginal product equals the real rental rate. Using these facts and the
above marginal products for the Cobb–Douglas production function, we find:
W/P = MPL = (1 – α)Y/L.
R/P = MPK = αY/K.
Rewriting this:
(W/P)L = MPL L = (1 – α)Y.
(R/P)K = MPK K = αY.
Note that the terms (W/P)L and (R/P)K are the wage bill and total return to capital, respectively.
Given that the value of α = 0.3, then the above formulas indicate that labor receives 70 percent of
total output (or income) and capital receives 30 percent of total output (or income).
b. To determine what happens to total output when the labor force increases by 10 percent, consider
the formula for the Cobb–Douglas production function:
Y = AKαL1–α.
In this problem, α is 0.5 and A is 1. Substitute in the given values for labor and land to find the
marginal product of labor is 0.5 and marginal product of capital (land) is 0.5. We know that the
real wage equals the marginal product of labor and the real rental price of land equals the marginal
product of capital (land).
c. Labor’s share of the output is given by the marginal product of labor times the quantity of labor, or
50.
d. The new level of output is 70.71.
e. The new wage is 0.71. The new rental price of land is 0.35.
f. Labor now receives 35.36.
3. A production function has decreasing returns to scale if an equal percentage increase in all factors of
production leads to a smaller percentage increase in output. For example, if we double the amounts of
capital and labor output increases by less than double, then the production function has decreasing
returns to scale. This may happen if there is a fixed factor such as land in the production function, and
this fixed factor becomes scarce as the economy grows larger.
A production function has increasing returns to scale if an equal percentage increase in all factors
of production leads to a larger percentage increase in output. For example, if doubling the amount of
capital and labor increases the output by more than double, then the production function has increasing
returns to scale. This may happen if specialization of labor becomes greater as the population grows.
For example, if only one worker builds a car, then it takes him a long time because he has to learn
many different skills, and he must constantly change tasks and tools. But if many workers build a car,
then each one can specialize in a particular task and become more productive.
4. a. A Cobb–Douglas production function has the form Y = AKαL1–α. The text showed that the marginal
products for the Cobb–Douglas production function are:
MPL = (1 – α)Y/L.
MPK = αY/K.
Competitive profit-maximizing firms hire labor until its marginal product equals the real wage,
and hire capital until its marginal product equals the real rental rate. Using these facts and the
above marginal products for the Cobb–Douglas production function, we find:
W/P = MPL = (1 – α)Y/L.
R/P = MPK = αY/K.
Rewriting this:
(W/P)L = MPL L = (1 – α)Y.
(R/P)K = MPK K = αY.
Note that the terms (W/P)L and (R/P)K are the wage bill and total return to capital, respectively.
Given that the value of α = 0.3, then the above formulas indicate that labor receives 70 percent of
total output (or income) and capital receives 30 percent of total output (or income).
b. To determine what happens to total output when the labor force increases by 10 percent, consider
the formula for the Cobb–Douglas production function:
Y = AKαL1–α.
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Chapter 3—National Income: Where It Comes From and Where It Goes 12
Let Y1 equal the initial value of output and Y2 equal final output. We know that α = 0.3. We also
know that labor L increases by 10 percent:
Y1 = AK0.3L0.7.
Y2 = AK0.3(1.1L)0.7.
Note that we multiplied L by 1.1 to reflect the 10-percent increase in the labor force.
To calculate the percentage change in output, divide Y2 by Y1:Y2
Y1
= AK 0.3 1.1L
( )
0.7
AK 0.3L0.7
= 1.1
( )
0.7
= 1.069.
That is, output increases by 6.9 percent.
To determine how the increase in the labor force affects the rental price of capital, consider
the formula for the real rental price of capital R/P:
R/P = MPK = αAKα–1L1–α.
We know that α = 0.3. We also know that labor (L) increases by 10 percent. Let (R/P)1 equal the
initial value of the rental price of capital, and let (R/P)2 equal the final rental price of capital after
the labor force increases by 10 percent. To find (R/P)2, multiply L by 1.1 to reflect the 10-percent
increase in the labor force:
(R/P)1 = 0.3AK–0.7L0.7.
(R/P)2 = 0.3AK–0.7(1.1L)0.7.
The rental price increases by the ratioR / P
( )
2
R / P
( )
1
= 0.3AK -0.7 1.1L
( )
0.7
0.3AK -0.7 L0.7
= 1.1
( )
0.7
= 1.069
So the rental price increases by 6.9 percent. To determine how the increase in the labor force
affects the real wage, consider the formula for the real wage W/P:
W/P = MPL = (1 – α)AKαL–α.
We know that α = 0.3. We also know that labor (L) increases by 10 percent. Let (W/P)1 equal the
initial value of the real wage, and let (W/P)2 equal the final value of the real wage. To find (W/P)2,
multiply L by 1.1 to reflect the 10-percent increase in the labor force:
(W/P)1 = (1 – 0.3)AK0.3L–0.3.
(W/P)2 = (1 – 0.3)AK0.3(1.1L)–0.3.
To calculate the percentage change in the real wage, divide (W/P)2 by (W/P)1:
Let Y1 equal the initial value of output and Y2 equal final output. We know that α = 0.3. We also
know that labor L increases by 10 percent:
Y1 = AK0.3L0.7.
Y2 = AK0.3(1.1L)0.7.
Note that we multiplied L by 1.1 to reflect the 10-percent increase in the labor force.
To calculate the percentage change in output, divide Y2 by Y1:Y2
Y1
= AK 0.3 1.1L
( )
0.7
AK 0.3L0.7
= 1.1
( )
0.7
= 1.069.
That is, output increases by 6.9 percent.
To determine how the increase in the labor force affects the rental price of capital, consider
the formula for the real rental price of capital R/P:
R/P = MPK = αAKα–1L1–α.
We know that α = 0.3. We also know that labor (L) increases by 10 percent. Let (R/P)1 equal the
initial value of the rental price of capital, and let (R/P)2 equal the final rental price of capital after
the labor force increases by 10 percent. To find (R/P)2, multiply L by 1.1 to reflect the 10-percent
increase in the labor force:
(R/P)1 = 0.3AK–0.7L0.7.
(R/P)2 = 0.3AK–0.7(1.1L)0.7.
The rental price increases by the ratioR / P
( )
2
R / P
( )
1
= 0.3AK -0.7 1.1L
( )
0.7
0.3AK -0.7 L0.7
= 1.1
( )
0.7
= 1.069
So the rental price increases by 6.9 percent. To determine how the increase in the labor force
affects the real wage, consider the formula for the real wage W/P:
W/P = MPL = (1 – α)AKαL–α.
We know that α = 0.3. We also know that labor (L) increases by 10 percent. Let (W/P)1 equal the
initial value of the real wage, and let (W/P)2 equal the final value of the real wage. To find (W/P)2,
multiply L by 1.1 to reflect the 10-percent increase in the labor force:
(W/P)1 = (1 – 0.3)AK0.3L–0.3.
(W/P)2 = (1 – 0.3)AK0.3(1.1L)–0.3.
To calculate the percentage change in the real wage, divide (W/P)2 by (W/P)1:
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Chapter 3—National Income: Where It Comes From and Where It Goes 13W / P
( )
2
W / P
( )
1
= 1- 0.3
( )
AK 0.3 1.1L
( )
-0.3
1- 0.3
( )
AK 0.3L-0.3
= 1.1
( )
-0.3
= 0.972
That is, the real wage falls by 2.8 percent.
c. We can use the same logic as in part (b) to set
Y1 = AK0.3L0.7.
Y2 = A(1.1K)0.3L0.7.
Therefore, we have:Y2
Y1
= A 1.1K
( )
0.3
L0.7
AK 0.3L0.7
= 1.1
( )
0.3
= 1.029
This equation shows that output increases by about 3 percent. Notice that α < 0.5 means that
proportional increases to capital will increase output by less than the same proportional increase to
labor.
Again using the same logic as in part (b) for the change in the real rental price of capital:R / P
( )
2
R / P
( )
1
= 0.3A 1.1K
( )
-0.7
L0.7
0.3AK -0.7 L0.7
= 1.1
( )
-0.7
= 0.935
The real rental price of capital falls by 6.5 percent because there are diminishing returns to capital;
that is, when capital increases, its marginal product falls.
Finally, the change in the real wage is:W / P
( )
2
W / P
( )
1
= 0.7 A 1.1K
( )
0.3
L-0.3
0.7 AK 0.3 L-0.3
= 1.1
( )
0.3
= 1.029
Hence, real wages increase by 2.9 percent because the added capital increases the marginal
productivity of the existing workers. (Notice that the wage and output have both increased by the
same amount, leaving the labor share unchanged—a feature of Cobb–Douglas technologies.)
d. Using the same formula, we find that the change in output is:Y2
Y1
= 1.1A
( )
K 0.3 L0.7
AK 0.3 L0.7
= 1.1
( )
2
W / P
( )
1
= 1- 0.3
( )
AK 0.3 1.1L
( )
-0.3
1- 0.3
( )
AK 0.3L-0.3
= 1.1
( )
-0.3
= 0.972
That is, the real wage falls by 2.8 percent.
c. We can use the same logic as in part (b) to set
Y1 = AK0.3L0.7.
Y2 = A(1.1K)0.3L0.7.
Therefore, we have:Y2
Y1
= A 1.1K
( )
0.3
L0.7
AK 0.3L0.7
= 1.1
( )
0.3
= 1.029
This equation shows that output increases by about 3 percent. Notice that α < 0.5 means that
proportional increases to capital will increase output by less than the same proportional increase to
labor.
Again using the same logic as in part (b) for the change in the real rental price of capital:R / P
( )
2
R / P
( )
1
= 0.3A 1.1K
( )
-0.7
L0.7
0.3AK -0.7 L0.7
= 1.1
( )
-0.7
= 0.935
The real rental price of capital falls by 6.5 percent because there are diminishing returns to capital;
that is, when capital increases, its marginal product falls.
Finally, the change in the real wage is:W / P
( )
2
W / P
( )
1
= 0.7 A 1.1K
( )
0.3
L-0.3
0.7 AK 0.3 L-0.3
= 1.1
( )
0.3
= 1.029
Hence, real wages increase by 2.9 percent because the added capital increases the marginal
productivity of the existing workers. (Notice that the wage and output have both increased by the
same amount, leaving the labor share unchanged—a feature of Cobb–Douglas technologies.)
d. Using the same formula, we find that the change in output is:Y2
Y1
= 1.1A
( )
K 0.3 L0.7
AK 0.3 L0.7
= 1.1
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Chapter 3—National Income: Where It Comes From and Where It Goes 14
This equation shows that output increases by 10 percent. Similarly, the rental price of capital and
the real wage also increase by 10 percent:R / P
( )
2
R / P
( )
1
= 0.3 1.1A
( )
K -0.7 L0.7
0.3AK -0.7 L0.7
= 1.1W / P
( )
2
W / P
( )
1
= 0.7 1.1A
( )
K 0.3L-0.3
0.7 AK 0.3 L-0.3
= 1.1
5. Labor income is defined asW
P ´ L = WL
P
Labor’s share of income is defined asWL
P
æ
è
çç
ö
ø
÷÷ / Y = WL
PY
For example, if this ratio is about constant at a value of 0.7, then the value of W/P = 0.7*Y/L. This
means that the real wage is roughly proportional to labor productivity. Hence, any trend in labor
productivity must be matched by an equal trend in real wages. Otherwise, labor’s share would deviate
from 0.7. Thus, the first fact (a constant labor share) implies the second fact (the trend in real wages
closely tracks the trend in labor productivity).
6. a. Nominal wages are measured as dollars per hour worked. Prices are measured as dollars per unit
produced (either a haircut or a unit of farm output). Marginal productivity is measured as units of
output produced per hour worked.
b. According to the neoclassical theory, technical progress that increases the marginal product of
farmers causes their real wage to rise. The real wage for farmers is measured as units of farm
output per hour worked. The real wage is W/PF, and this is equal to ($/hour worked)/($/unit of
farm output).
c. If the marginal productivity of barbers is unchanged, then their real wage is unchanged. The real
wage for barbers is measured as haircuts per hour worked. The real wage is W/PB, and this is equal
to ($/hour worked)/($/haircut).
d. If workers can move freely between being farmers and being barbers, then they must be paid the
same wage W in each sector.
e. If the nominal wage W is the same in both sectors, but the real wage in terms of farm goods is
greater than the real wage in terms of haircuts, then the price of haircuts must have risen relative to
the price of farm goods. We know that W/P = MPL so that W = P MPL. This means that
PFMPLF = PHMPLB, given that the nominal wages are the same. Since the marginal product of
labor for barbers has not changed and the marginal product of labor for farmers has risen, the price
of a haircut must have risen relative to the price of the farm output. If we express this in growth
rate terms, then the growth of the farm price + the growth of the marginal product of the farm
labor = the growth of the haircut price.
f. The farmers and the barbers are equally well off after the technological progress in farming, given
This equation shows that output increases by 10 percent. Similarly, the rental price of capital and
the real wage also increase by 10 percent:R / P
( )
2
R / P
( )
1
= 0.3 1.1A
( )
K -0.7 L0.7
0.3AK -0.7 L0.7
= 1.1W / P
( )
2
W / P
( )
1
= 0.7 1.1A
( )
K 0.3L-0.3
0.7 AK 0.3 L-0.3
= 1.1
5. Labor income is defined asW
P ´ L = WL
P
Labor’s share of income is defined asWL
P
æ
è
çç
ö
ø
÷÷ / Y = WL
PY
For example, if this ratio is about constant at a value of 0.7, then the value of W/P = 0.7*Y/L. This
means that the real wage is roughly proportional to labor productivity. Hence, any trend in labor
productivity must be matched by an equal trend in real wages. Otherwise, labor’s share would deviate
from 0.7. Thus, the first fact (a constant labor share) implies the second fact (the trend in real wages
closely tracks the trend in labor productivity).
6. a. Nominal wages are measured as dollars per hour worked. Prices are measured as dollars per unit
produced (either a haircut or a unit of farm output). Marginal productivity is measured as units of
output produced per hour worked.
b. According to the neoclassical theory, technical progress that increases the marginal product of
farmers causes their real wage to rise. The real wage for farmers is measured as units of farm
output per hour worked. The real wage is W/PF, and this is equal to ($/hour worked)/($/unit of
farm output).
c. If the marginal productivity of barbers is unchanged, then their real wage is unchanged. The real
wage for barbers is measured as haircuts per hour worked. The real wage is W/PB, and this is equal
to ($/hour worked)/($/haircut).
d. If workers can move freely between being farmers and being barbers, then they must be paid the
same wage W in each sector.
e. If the nominal wage W is the same in both sectors, but the real wage in terms of farm goods is
greater than the real wage in terms of haircuts, then the price of haircuts must have risen relative to
the price of farm goods. We know that W/P = MPL so that W = P MPL. This means that
PFMPLF = PHMPLB, given that the nominal wages are the same. Since the marginal product of
labor for barbers has not changed and the marginal product of labor for farmers has risen, the price
of a haircut must have risen relative to the price of the farm output. If we express this in growth
rate terms, then the growth of the farm price + the growth of the marginal product of the farm
labor = the growth of the haircut price.
f. The farmers and the barbers are equally well off after the technological progress in farming, given
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Chapter 3—National Income: Where It Comes From and Where It Goes 15
the assumption that labor is freely mobile between the two sectors and both types of people
consume the same basket of goods. Given that the nominal wage ends up equal for each type of
worker and that they pay the same prices for final goods, they are equally well off in terms of what
they can buy with their nominal income. The real wage is a measure of how many units of output
are produced per worker. Technological progress in farming increased the units of farm output
produced per hour worked. Movement of labor between sectors then equalized the nominal wage.
7. a. The marginal product of labor (MPL) is found by differentiating the production function with
respect to labor:MPL = dY
dL
= 1
3 K1/3H1/3L-2/3
An increase in human capital will increase the marginal product of labor because more human
capital makes all the existing labor more productive.
b. The marginal product of human capital (MPH)is found by differentiating the production function
with respect to human capital:MPH = dY
dH
= 1
3 K1/3 L1/3H -2/3
An increase in human capital will decrease the marginal product of human capital because there
are diminishing returns.
c. The labor share of output is the proportion of output that goes to labor. The total amount of output
that goes to labor is the real wage (which, under perfect competition, equals the marginal product
of labor) times the quantity of labor. This quantity is divided by the total amount of output to
compute the labor share:Labor Share = (1
3 K1/3H1/3L-2/3 )L
K1/3H1/3L1/3
= 1
3
We can use the same logic to find the human capital share:Human Capital Share = (1
3 K1/3L1/3 H -2/3 )H
K1/3H1/3 L1/3
= 1
3
so labor gets one-third of the output, and human capital gets one-third of the output. Since workers
own their human capital (we hope!), it will appear that labor gets two-thirds of output.
d. The ratio of the skilled wage to the unskilled wage is:
the assumption that labor is freely mobile between the two sectors and both types of people
consume the same basket of goods. Given that the nominal wage ends up equal for each type of
worker and that they pay the same prices for final goods, they are equally well off in terms of what
they can buy with their nominal income. The real wage is a measure of how many units of output
are produced per worker. Technological progress in farming increased the units of farm output
produced per hour worked. Movement of labor between sectors then equalized the nominal wage.
7. a. The marginal product of labor (MPL) is found by differentiating the production function with
respect to labor:MPL = dY
dL
= 1
3 K1/3H1/3L-2/3
An increase in human capital will increase the marginal product of labor because more human
capital makes all the existing labor more productive.
b. The marginal product of human capital (MPH)is found by differentiating the production function
with respect to human capital:MPH = dY
dH
= 1
3 K1/3 L1/3H -2/3
An increase in human capital will decrease the marginal product of human capital because there
are diminishing returns.
c. The labor share of output is the proportion of output that goes to labor. The total amount of output
that goes to labor is the real wage (which, under perfect competition, equals the marginal product
of labor) times the quantity of labor. This quantity is divided by the total amount of output to
compute the labor share:Labor Share = (1
3 K1/3H1/3L-2/3 )L
K1/3H1/3L1/3
= 1
3
We can use the same logic to find the human capital share:Human Capital Share = (1
3 K1/3L1/3 H -2/3 )H
K1/3H1/3 L1/3
= 1
3
so labor gets one-third of the output, and human capital gets one-third of the output. Since workers
own their human capital (we hope!), it will appear that labor gets two-thirds of output.
d. The ratio of the skilled wage to the unskilled wage is:
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Chapter 3—National Income: Where It Comes From and Where It Goes 16Wskilled
Wunskilled
= MPL + MPH
MPL
= 1
3 K1/3L-2/3H1/3 + 1
3 K1/3 L1/3H -2/3
1
3 K1/3L-2/3H1/3
= 1+ L
H
Notice that the ratio is always greater than 1 because skilled workers get paid more than unskilled
workers. Also, when H increases this ratio falls because the diminishing returns to human capital
lower its return, while at the same time increasing the marginal product of unskilled workers.
e. If more colleges provide scholarships, it will increase H, and it does lead to a more egalitarian
society. The policy lowers the returns to education, decreasing the gap between the wages of more
and less educated workers. More importantly, the policy even raises the absolute wage of unskilled
workers because their marginal product rises when the number of skilled workers rises.
8. The effect of a government tax increase of $100 billion on (a) public saving, (b) private saving, and (c)
national saving can be analyzed by using the following relationships:
National Saving = [Private Saving] + [Public Saving]
= [Y – T – C(Y – T)] + [T – G]
= Y – C(Y – T) – G.
a. Public Saving—The tax increase causes a 1-for-1 increase in public saving. T increases by $100
billion and, therefore, public saving increases by $100 billion.
b. Private Saving—The increase in taxes decreases disposable income, Y – T, by $100 billion. Since
the marginal propensity to consume (MPC) is 0.6, consumption falls by 0.6 $100 billion, or $60
billion. Hence,
ΔPrivate Saving = –$100b – 0.6 (–$100b) = –$40b.
Private saving falls $40 billion.
c. National Saving—Because national saving is the sum of private and public saving, we can
conclude that the $100 billion tax increase leads to a $60 billion increase in national saving.
Another way to see this is by using the third equation for national saving expressed above,
that national saving equals Y – C(Y – T) – G. The $100 billion tax increase reduces disposable
income and causes consumption to fall by $60 billion. Since neither G nor Y changes, national
saving thus rises by $60 billion.
d. Investment—To determine the effect of the tax increase on investment, recall the national
accounts identity:
Y = C(Y – T) + I(r) + G.
Rearranging, we find
Y – C(Y – T) – G = I(r).
The left side of this equation is national saving, so the equation just says that national saving
equals investment. Since national saving increases by $60 billion, investment must also increase
by $60 billion.
How does this increase in investment take place? We know that investment depends on the
Wunskilled
= MPL + MPH
MPL
= 1
3 K1/3L-2/3H1/3 + 1
3 K1/3 L1/3H -2/3
1
3 K1/3L-2/3H1/3
= 1+ L
H
Notice that the ratio is always greater than 1 because skilled workers get paid more than unskilled
workers. Also, when H increases this ratio falls because the diminishing returns to human capital
lower its return, while at the same time increasing the marginal product of unskilled workers.
e. If more colleges provide scholarships, it will increase H, and it does lead to a more egalitarian
society. The policy lowers the returns to education, decreasing the gap between the wages of more
and less educated workers. More importantly, the policy even raises the absolute wage of unskilled
workers because their marginal product rises when the number of skilled workers rises.
8. The effect of a government tax increase of $100 billion on (a) public saving, (b) private saving, and (c)
national saving can be analyzed by using the following relationships:
National Saving = [Private Saving] + [Public Saving]
= [Y – T – C(Y – T)] + [T – G]
= Y – C(Y – T) – G.
a. Public Saving—The tax increase causes a 1-for-1 increase in public saving. T increases by $100
billion and, therefore, public saving increases by $100 billion.
b. Private Saving—The increase in taxes decreases disposable income, Y – T, by $100 billion. Since
the marginal propensity to consume (MPC) is 0.6, consumption falls by 0.6 $100 billion, or $60
billion. Hence,
ΔPrivate Saving = –$100b – 0.6 (–$100b) = –$40b.
Private saving falls $40 billion.
c. National Saving—Because national saving is the sum of private and public saving, we can
conclude that the $100 billion tax increase leads to a $60 billion increase in national saving.
Another way to see this is by using the third equation for national saving expressed above,
that national saving equals Y – C(Y – T) – G. The $100 billion tax increase reduces disposable
income and causes consumption to fall by $60 billion. Since neither G nor Y changes, national
saving thus rises by $60 billion.
d. Investment—To determine the effect of the tax increase on investment, recall the national
accounts identity:
Y = C(Y – T) + I(r) + G.
Rearranging, we find
Y – C(Y – T) – G = I(r).
The left side of this equation is national saving, so the equation just says that national saving
equals investment. Since national saving increases by $60 billion, investment must also increase
by $60 billion.
How does this increase in investment take place? We know that investment depends on the
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Chapter 3—National Income: Where It Comes From and Where It Goes 17
real interest rate. For investment to rise, the real interest rate must fall. Figure 3-1 illustrates saving
and investment as a function of the real interest rate.
The tax increase causes national saving to rise, so the supply curve for loanable funds shifts to
the right. The equilibrium real interest rate falls, and investment rises.
9. If consumers increase the amount that they consume today, then private saving and, therefore, national
saving will fall. We know this from the definition of national saving:
National Saving = [Private Saving] + [Public Saving]
= [Y – T – C(Y – T)] + [T – G].
An increase in consumption decreases private saving, so national saving falls.
Figure 3-2 illustrates saving and investment as a function of the real interest rate. If national
saving decreases, the supply curve for loanable funds shifts to the left, thereby raising the real interest
rate and reducing investment.
10. a. Private saving is the amount of disposable income, Y – T, that is not consumed:
Sprivate = Y – T – C
= 8,000 – 2,000 – [1,000 + (2/3)(8,000 – 2,000)]
= 1,000.
Public saving is the amount of taxes the government has left over after it makes its purchases:
real interest rate. For investment to rise, the real interest rate must fall. Figure 3-1 illustrates saving
and investment as a function of the real interest rate.
The tax increase causes national saving to rise, so the supply curve for loanable funds shifts to
the right. The equilibrium real interest rate falls, and investment rises.
9. If consumers increase the amount that they consume today, then private saving and, therefore, national
saving will fall. We know this from the definition of national saving:
National Saving = [Private Saving] + [Public Saving]
= [Y – T – C(Y – T)] + [T – G].
An increase in consumption decreases private saving, so national saving falls.
Figure 3-2 illustrates saving and investment as a function of the real interest rate. If national
saving decreases, the supply curve for loanable funds shifts to the left, thereby raising the real interest
rate and reducing investment.
10. a. Private saving is the amount of disposable income, Y – T, that is not consumed:
Sprivate = Y – T – C
= 8,000 – 2,000 – [1,000 + (2/3)(8,000 – 2,000)]
= 1,000.
Public saving is the amount of taxes the government has left over after it makes its purchases:
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Chapter 3—National Income: Where It Comes From and Where It Goes 18
Spublic = T – G
= 2,000 – 2,500
= –500.
National saving is the sum of private saving and public saving:
Snational = Sprivate + Spublic
= 1,000 + (500)
= 500.
b. The equilibrium interest rate is the value of r that clears the market for loanable funds. We already
know that national saving is 500, so we just need to set it equal to investment:
Snational = I
500 = 1,200 – 100r
Solving this equation for r, we find:
r = 0.07 or 7%.
c. When the government increases its spending, private saving remains the same as before (notice
that G does not appear in the Sprivate equation above) while government saving decreases. Putting
the new G into the equations above:
Sprivate = 1,000
Spublic = T – G
= 2,000 – 2,000
= 0.
Thus,
Snational = Sprivate + Spublic
= 1,000 + (0)
= 1,000.
d. Once again the equilibrium interest rate clears the market for loanable funds:
Snational = I
1,000 = 1,200 – 100r
Solving this equation for r, we find:
r = 0.02 or 2%.
11. To determine the effect on investment of an equal increase in both taxes and government spending,
consider the national income accounts identity for national saving:
National Saving = [Private Saving] + [Public Saving]
= [Y – T – C(Y – T)] + [T – G].
We know that Y is fixed by the factors of production. We also know that the change in consumption
equals the marginal propensity to consume (MPC) times the change in disposable income. This tells us
that
ΔNational Saving = {–ΔT – [MPC (– ΔT)]} + [ΔT – ΔG]
= [– ΔT + (MPC ΔT)] + 0
Spublic = T – G
= 2,000 – 2,500
= –500.
National saving is the sum of private saving and public saving:
Snational = Sprivate + Spublic
= 1,000 + (500)
= 500.
b. The equilibrium interest rate is the value of r that clears the market for loanable funds. We already
know that national saving is 500, so we just need to set it equal to investment:
Snational = I
500 = 1,200 – 100r
Solving this equation for r, we find:
r = 0.07 or 7%.
c. When the government increases its spending, private saving remains the same as before (notice
that G does not appear in the Sprivate equation above) while government saving decreases. Putting
the new G into the equations above:
Sprivate = 1,000
Spublic = T – G
= 2,000 – 2,000
= 0.
Thus,
Snational = Sprivate + Spublic
= 1,000 + (0)
= 1,000.
d. Once again the equilibrium interest rate clears the market for loanable funds:
Snational = I
1,000 = 1,200 – 100r
Solving this equation for r, we find:
r = 0.02 or 2%.
11. To determine the effect on investment of an equal increase in both taxes and government spending,
consider the national income accounts identity for national saving:
National Saving = [Private Saving] + [Public Saving]
= [Y – T – C(Y – T)] + [T – G].
We know that Y is fixed by the factors of production. We also know that the change in consumption
equals the marginal propensity to consume (MPC) times the change in disposable income. This tells us
that
ΔNational Saving = {–ΔT – [MPC (– ΔT)]} + [ΔT – ΔG]
= [– ΔT + (MPC ΔT)] + 0
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Chapter 3—National Income: Where It Comes From and Where It Goes 19
= (MPC – 1) ΔT.
The above expression tells us that the impact on national saving of an equal increase in T and G
depends on the size of the marginal propensity to consume. The closer the MPC is to 1, the smaller is
the fall in saving. For example, if the MPC equals 1, then the fall in consumption equals the rise in
government purchases, so national saving [Y – C(Y – T) – G] is unchanged. The closer the MPC is to 0
(and therefore the larger is the amount saved rather than spent for a one-dollar change in disposable
income), the greater is the impact on saving. Because we assume that the MPC is less than 1, we
expect that national saving falls in response to an equal increase in taxes and government spending.
The reduction in saving means that the supply of loanable funds curve will shift to the left in
Figure 3-3. The real interest rate rises, and investment falls.
12. a. The demand curve for business investment shifts out to the right because the subsidy increases the
number of profitable investment opportunities for any given interest rate. The demand curve for
residential investment remains unchanged.
b. The total demand curve for investment in the economy shifts out to the right since it represents the
sum of business investment, which shifts out to the right, and residential investment, which is
unchanged. As a result the real interest rate rises as in Figure 3-4.
c. The total quantity of investment does not change because it is constrained by the inelastic supply
of savings. The investment tax credit leads to a rise in business investment, but an offsetting fall in
residential investment. That is, the higher interest rate means that residential investment falls (a
movement along the curve), whereas the rightward shift of the business investment curve leads
business investment to rise by an equal amount. Figure 3-5 shows this change. Note thatI1
B + I1
R + I2
B + I2
R = S
.
= (MPC – 1) ΔT.
The above expression tells us that the impact on national saving of an equal increase in T and G
depends on the size of the marginal propensity to consume. The closer the MPC is to 1, the smaller is
the fall in saving. For example, if the MPC equals 1, then the fall in consumption equals the rise in
government purchases, so national saving [Y – C(Y – T) – G] is unchanged. The closer the MPC is to 0
(and therefore the larger is the amount saved rather than spent for a one-dollar change in disposable
income), the greater is the impact on saving. Because we assume that the MPC is less than 1, we
expect that national saving falls in response to an equal increase in taxes and government spending.
The reduction in saving means that the supply of loanable funds curve will shift to the left in
Figure 3-3. The real interest rate rises, and investment falls.
12. a. The demand curve for business investment shifts out to the right because the subsidy increases the
number of profitable investment opportunities for any given interest rate. The demand curve for
residential investment remains unchanged.
b. The total demand curve for investment in the economy shifts out to the right since it represents the
sum of business investment, which shifts out to the right, and residential investment, which is
unchanged. As a result the real interest rate rises as in Figure 3-4.
c. The total quantity of investment does not change because it is constrained by the inelastic supply
of savings. The investment tax credit leads to a rise in business investment, but an offsetting fall in
residential investment. That is, the higher interest rate means that residential investment falls (a
movement along the curve), whereas the rightward shift of the business investment curve leads
business investment to rise by an equal amount. Figure 3-5 shows this change. Note thatI1
B + I1
R + I2
B + I2
R = S
.
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Chapter 3—National Income: Where It Comes From and Where It Goes 20
13. In this chapter, we concluded that an increase in government expenditures reduces national saving and
raises the interest rate. The increase in government expenditure therefore crowds out investment by the
full amount of the increase. Similarly, a tax cut increases disposable income and hence consumption.
This increase in consumption translates into a fall in national saving, and the increase in consumption
crowds out investment by the full amount of the increase.
If consumption depends on the interest rate, then saving will also depend on it. The higher the
interest rate, the greater the return to saving. Hence, it seems reasonable to think that an increase in the
interest rate might increase saving and reduce consumption. Figure 3-6 shows saving as an increasing
function of the interest rate.
Consider what happens when government purchases increase. At any given level of the interest
rate, national saving falls by the change in government purchases, as shown in Figure 3-7. The figure
shows that if the saving function slopes upward, investment falls by less than the amount that
government purchases rises by. This happens because consumption falls and saving increases in
response to the higher interest rate. Hence, the more responsive consumption is to the interest rate, the
less investment is crowded out by government purchases.
13. In this chapter, we concluded that an increase in government expenditures reduces national saving and
raises the interest rate. The increase in government expenditure therefore crowds out investment by the
full amount of the increase. Similarly, a tax cut increases disposable income and hence consumption.
This increase in consumption translates into a fall in national saving, and the increase in consumption
crowds out investment by the full amount of the increase.
If consumption depends on the interest rate, then saving will also depend on it. The higher the
interest rate, the greater the return to saving. Hence, it seems reasonable to think that an increase in the
interest rate might increase saving and reduce consumption. Figure 3-6 shows saving as an increasing
function of the interest rate.
Consider what happens when government purchases increase. At any given level of the interest
rate, national saving falls by the change in government purchases, as shown in Figure 3-7. The figure
shows that if the saving function slopes upward, investment falls by less than the amount that
government purchases rises by. This happens because consumption falls and saving increases in
response to the higher interest rate. Hence, the more responsive consumption is to the interest rate, the
less investment is crowded out by government purchases.
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Chapter 3—National Income: Where It Comes From and Where It Goes 21
14. a. Figure 3-8 shows the case where the demand for loanable funds is stable but the supply of funds
(the saving schedule) fluctuates perhaps reflecting temporary shocks to income, changes in
government spending, or changes in consumer confidence. In this case, when interest rates fall,
investment rises; when interest rates rise, investment falls. We would expect a negative correlation
between investment and interest rates.
b. Figure 3-9 shows the case where the supply of loanable funds (saving) is stable, whereas the
demand for loanable funds fluctuates, perhaps reflecting changes in firms’ expectations about the
marginal product of capital. We would now find a positive correlation between investment and the
interest rate—when demand for funds rises, it pushes up the interest rate, so we observe that
investment and the real interest rate increase at the same time.
c. If both curves shift, we might generate a scatter plot as in Figure 3-10, where the economy
fluctuates among points A, B, C, and D. Depending on how often the economy is at each of these
points, we might find little clear relationship between investment and interest rates.
d. Situation (c) seems fairly reasonable—as both the supply of and demand for loanable funds
fluctuate over time in response to changes in the economy.
14. a. Figure 3-8 shows the case where the demand for loanable funds is stable but the supply of funds
(the saving schedule) fluctuates perhaps reflecting temporary shocks to income, changes in
government spending, or changes in consumer confidence. In this case, when interest rates fall,
investment rises; when interest rates rise, investment falls. We would expect a negative correlation
between investment and interest rates.
b. Figure 3-9 shows the case where the supply of loanable funds (saving) is stable, whereas the
demand for loanable funds fluctuates, perhaps reflecting changes in firms’ expectations about the
marginal product of capital. We would now find a positive correlation between investment and the
interest rate—when demand for funds rises, it pushes up the interest rate, so we observe that
investment and the real interest rate increase at the same time.
c. If both curves shift, we might generate a scatter plot as in Figure 3-10, where the economy
fluctuates among points A, B, C, and D. Depending on how often the economy is at each of these
points, we might find little clear relationship between investment and interest rates.
d. Situation (c) seems fairly reasonable—as both the supply of and demand for loanable funds
fluctuate over time in response to changes in the economy.
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Chapter 4—The Monetary System: What It Is and How It Works 22
Answers to Textbook Questions and Problems
CHAPTER 4 The Monetary System: What It Is and How It Works
Questions for Review
1. Money has three functions: it is a store of value, a unit of account, and a medium of exchange. As a
store of value, money provides a way to transfer purchasing power from the present to the future. As a
unit of account, money provides the terms in which prices are quoted and debts are recorded. As a
medium of exchange, money is what we use to buy goods and services.
2. Fiat money is established as money by the government but has no intrinsic value. For example, a U.S.
dollar bill is fiat money. Commodity money is money that is based on a commodity with some intrinsic
value. Gold, when used as money, is an example of commodity money.
3. Open market operations are the purchase and sale of government bonds by the Federal Reserve. If the
Fed buys government bonds from the public, then the dollars it pays for the bonds increase the
monetary base and thus the money supply. If the Fed sells government bonds to the public, then the
dollars paid to the Fed for the bonds decrease the monetary base and thus the money supply.
4. In a system of fractional-reserve banking, banks create money because they ordinarily keep only a
fraction of their deposits in reserve. They use the rest of their deposits to make loans. The easiest way
to see how this creates money is to consider the bank balance sheets shown in Figure 4-1.
A. Balance Sheet – Firstbank Money Supply = $1,000
Assets Liabilities_______
Reserves $1,000 Deposits $1,000
B. Balance Sheet – Firstbank Money Supply = $1,800
Assets Liabilities_______
Reserves $200 Deposits $1,000
Loans $800
C. Balance Sheet – Secondbank Money Supply = $2,400
Assets Liabilities_______
Reserves $160 Deposits $800
Loans $640
Suppose that people deposit $1,000 into Firstbank, as in Figure 4-1(A). Although the money
supply is still $1,000, it is now in the form of demand deposits rather than currency. If the bank holds
100 percent of these deposits in reserve, then the bank has no influence on the money supply. Yet
under a system of fractional-reserve banking, the bank need not keep all of its deposits in reserve; it
must have enough reserves on hand so that reserves are available whenever depositors want to make
withdrawals, but it makes loans with the rest of its deposits. If Firstbank has a reserve–deposit ratio of
20 percent, then it keeps $200 of the $1,000 in reserve and lends out the remaining $800. Figure 4-1(B)
shows the balance sheet of Firstbank after $800 in loans have been made. By making these loans,
Firstbank increases the money supply by $800. There are still $1,000 in demand deposits, but now
borrowers also hold an additional $800 in currency. The total money supply equals $1,800.
Money creation does not stop with Firstbank. If the borrowers deposit their $800 of currency in
Secondbank, then Secondbank can use these deposits to make loans. If Secondbank also has a reserve–
deposit ratio of 20 percent, then it keeps $160 of the $800 in reserves and lends out the remaining $640.
By lending out this money, Secondbank increases the money supply by $640, as in Figure 4-1(C). The
total money supply is now $2,440.
Answers to Textbook Questions and Problems
CHAPTER 4 The Monetary System: What It Is and How It Works
Questions for Review
1. Money has three functions: it is a store of value, a unit of account, and a medium of exchange. As a
store of value, money provides a way to transfer purchasing power from the present to the future. As a
unit of account, money provides the terms in which prices are quoted and debts are recorded. As a
medium of exchange, money is what we use to buy goods and services.
2. Fiat money is established as money by the government but has no intrinsic value. For example, a U.S.
dollar bill is fiat money. Commodity money is money that is based on a commodity with some intrinsic
value. Gold, when used as money, is an example of commodity money.
3. Open market operations are the purchase and sale of government bonds by the Federal Reserve. If the
Fed buys government bonds from the public, then the dollars it pays for the bonds increase the
monetary base and thus the money supply. If the Fed sells government bonds to the public, then the
dollars paid to the Fed for the bonds decrease the monetary base and thus the money supply.
4. In a system of fractional-reserve banking, banks create money because they ordinarily keep only a
fraction of their deposits in reserve. They use the rest of their deposits to make loans. The easiest way
to see how this creates money is to consider the bank balance sheets shown in Figure 4-1.
A. Balance Sheet – Firstbank Money Supply = $1,000
Assets Liabilities_______
Reserves $1,000 Deposits $1,000
B. Balance Sheet – Firstbank Money Supply = $1,800
Assets Liabilities_______
Reserves $200 Deposits $1,000
Loans $800
C. Balance Sheet – Secondbank Money Supply = $2,400
Assets Liabilities_______
Reserves $160 Deposits $800
Loans $640
Suppose that people deposit $1,000 into Firstbank, as in Figure 4-1(A). Although the money
supply is still $1,000, it is now in the form of demand deposits rather than currency. If the bank holds
100 percent of these deposits in reserve, then the bank has no influence on the money supply. Yet
under a system of fractional-reserve banking, the bank need not keep all of its deposits in reserve; it
must have enough reserves on hand so that reserves are available whenever depositors want to make
withdrawals, but it makes loans with the rest of its deposits. If Firstbank has a reserve–deposit ratio of
20 percent, then it keeps $200 of the $1,000 in reserve and lends out the remaining $800. Figure 4-1(B)
shows the balance sheet of Firstbank after $800 in loans have been made. By making these loans,
Firstbank increases the money supply by $800. There are still $1,000 in demand deposits, but now
borrowers also hold an additional $800 in currency. The total money supply equals $1,800.
Money creation does not stop with Firstbank. If the borrowers deposit their $800 of currency in
Secondbank, then Secondbank can use these deposits to make loans. If Secondbank also has a reserve–
deposit ratio of 20 percent, then it keeps $160 of the $800 in reserves and lends out the remaining $640.
By lending out this money, Secondbank increases the money supply by $640, as in Figure 4-1(C). The
total money supply is now $2,440.
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Chapter 4—The Monetary System: What It Is and How It Works 23
This process of money creation continues with each deposit and subsequent loans made. The text
demonstrated that each dollar of reserves generates ($1/rr) of money, where rr is the reserve–deposit
ratio. In this example, rr = 0.20, so the $1,000 originally deposited in Firstbank generates $5,000 of
money.
5. The Fed influences the money supply through open-market operations, reserve requirements, and the
discount rate. Open-market operations are the purchases and sales of government bonds by the Fed. If
the Fed buys government bonds, the dollars it pays for the bonds increase the monetary base and,
therefore, the money supply. If the Fed sells government bonds, the dollars it receives for the bonds
reduce the monetary base and therefore the money supply. Reserve requirements are regulations
imposed by the Fed that require banks to maintain a minimum reserve–deposit ratio. A decrease in the
reserve requirements lowers the reserve–deposit ratio, which allows banks to make more loans on a
given amount of deposits and, therefore, increases the money multiplier and the money supply. The
discount rate is the interest rate that the Fed charges banks to borrow money. Banks borrow from the
Fed if their reserves fall below the reserve requirements. A decrease in the discount rate makes it less
expensive for banks to borrow reserves. Therefore, banks will be likely to borrow more from the Fed;
this increases the monetary base and therefore the money supply.
6. To understand why a banking crisis might lead to a decrease in the money supply, first consider what
determines the money supply. The model of the money supply we developed shows that
M = m B.
The money supply M depends on the money multiplier m and the monetary base B. The money
multiplier can also be expressed in terms of the reserve–deposit ratio rr and the currency–deposit ratio
cr. This expression becomes
M = B.
This equation shows that the money supply depends on the currency–deposit ratio, the reserve–deposit
ratio, and the monetary base.
A banking crisis that involved a considerable number of bank failures might change the behavior
of depositors and bankers and alter the currency–deposit ratio and the reserve–deposit ratio. Suppose
that the number of bank failures reduced public confidence in the banking system. People would then
prefer to hold their money in currency (and perhaps stuff it in their mattresses) rather than deposit it in
banks. This change in the behavior of depositors would cause massive withdrawals of deposits and,
therefore, increase the currency–deposit ratio. In addition, the banking crisis would change the
behavior of banks. Fearing massive withdrawals of deposits, banks would become more cautious and
increase the amount of money they held in reserves, thereby increasing the reserve–deposit ratio. As
the preceding formula for the money multiplier indicates, increases in both the currency–deposit ratio
and the reserve–deposit ratio result in a decrease in the money multiplier and, therefore, a fall in the
money supply.
Problems and Applications
1. Money functions as a store of value, a medium of exchange, and a unit of account.
a. A credit card can serve as a medium of exchange because it is accepted in exchange for goods and
services. A credit card is, arguably, a (negative) store of value because you can accumulate debt
with it. A credit card is not a unit of account because, for example, a car does not cost 5 VISA
cards.
b. A Rembrandt painting is a store of value only.M = cr +1
( )
cr + rr
( )
é
ë
ê
ê
ù
û
ú
ú B
This process of money creation continues with each deposit and subsequent loans made. The text
demonstrated that each dollar of reserves generates ($1/rr) of money, where rr is the reserve–deposit
ratio. In this example, rr = 0.20, so the $1,000 originally deposited in Firstbank generates $5,000 of
money.
5. The Fed influences the money supply through open-market operations, reserve requirements, and the
discount rate. Open-market operations are the purchases and sales of government bonds by the Fed. If
the Fed buys government bonds, the dollars it pays for the bonds increase the monetary base and,
therefore, the money supply. If the Fed sells government bonds, the dollars it receives for the bonds
reduce the monetary base and therefore the money supply. Reserve requirements are regulations
imposed by the Fed that require banks to maintain a minimum reserve–deposit ratio. A decrease in the
reserve requirements lowers the reserve–deposit ratio, which allows banks to make more loans on a
given amount of deposits and, therefore, increases the money multiplier and the money supply. The
discount rate is the interest rate that the Fed charges banks to borrow money. Banks borrow from the
Fed if their reserves fall below the reserve requirements. A decrease in the discount rate makes it less
expensive for banks to borrow reserves. Therefore, banks will be likely to borrow more from the Fed;
this increases the monetary base and therefore the money supply.
6. To understand why a banking crisis might lead to a decrease in the money supply, first consider what
determines the money supply. The model of the money supply we developed shows that
M = m B.
The money supply M depends on the money multiplier m and the monetary base B. The money
multiplier can also be expressed in terms of the reserve–deposit ratio rr and the currency–deposit ratio
cr. This expression becomes
M = B.
This equation shows that the money supply depends on the currency–deposit ratio, the reserve–deposit
ratio, and the monetary base.
A banking crisis that involved a considerable number of bank failures might change the behavior
of depositors and bankers and alter the currency–deposit ratio and the reserve–deposit ratio. Suppose
that the number of bank failures reduced public confidence in the banking system. People would then
prefer to hold their money in currency (and perhaps stuff it in their mattresses) rather than deposit it in
banks. This change in the behavior of depositors would cause massive withdrawals of deposits and,
therefore, increase the currency–deposit ratio. In addition, the banking crisis would change the
behavior of banks. Fearing massive withdrawals of deposits, banks would become more cautious and
increase the amount of money they held in reserves, thereby increasing the reserve–deposit ratio. As
the preceding formula for the money multiplier indicates, increases in both the currency–deposit ratio
and the reserve–deposit ratio result in a decrease in the money multiplier and, therefore, a fall in the
money supply.
Problems and Applications
1. Money functions as a store of value, a medium of exchange, and a unit of account.
a. A credit card can serve as a medium of exchange because it is accepted in exchange for goods and
services. A credit card is, arguably, a (negative) store of value because you can accumulate debt
with it. A credit card is not a unit of account because, for example, a car does not cost 5 VISA
cards.
b. A Rembrandt painting is a store of value only.M = cr +1
( )
cr + rr
( )
é
ë
ê
ê
ù
û
ú
ú B
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Chapter 4—The Monetary System: What It Is and How It Works 24
c. A subway token, within the subway system, satisfies all three functions of money. Yet outside the
subway system, it is not widely used as a unit of account or a medium of exchange, so it is not a
form of money.
2. a. When the Fed buys bonds, the dollars that it pays to the public for the bonds increase the monetary
base, and this in turn increases the money supply. The money multiplier is not affected, assuming
no change in the reserve–deposit ratio or the currency–deposit ratio.
b. When the Fed increases the interest rate, it pays banks to hold reserves. This gives banks an
incentive to hold more reserves relative to deposits. The increase in the reserve deposit ratio will
decrease the money multiplier. The decline in the money multiplier will lead to a decrease in the
money supply. Since banks are holding more reserves (because they are making fewer loans), the
monetary base will increase.
c. If the Fed reduces its lending to banks through the Term Auction Facility, then the monetary base
will decrease, and this in turn will decrease the money supply. The money multiplier is not
affected, assuming no change in the reserve–deposit ratio or the currency–deposit ratio.
d. If consumers lose confidence in ATMs and prefer to hold more cash, then the currency–deposit
ratio will increase, and this will reduce the money multiplier. The money supply will fall because
banks have fewer reserves to lend. The monetary base will increase because people are holding
more currency, but will decrease because banks are holding fewer reserves. The net effect on the
monetary base is zero.
e. If the Fed drops newly minted $100 bills from a helicopter, then this will increase the monetary
base and the money supply. If any of the currency ends up in the bank, then there will be a further
increase in the money supply. If people end up holding more currency relative to deposits, then the
money multiplier would fall.
3. a. If all money is held as currency, then the money supply is equal to the monetary base. The money
supply will be $1,000.
b. If all money is held as deposits, but banks hold 100 percent of deposits on reserve, then there are
no loans. The money supply will be $1,000.
c. If all money is held as deposits and banks hold 20 percent of deposits on reserve, then the reserve–
deposit ratio is 0.20. The currency–deposit ratio is 0, and the money multiplier will be 1/0.2, or 5.
The money supply will be $5,000.
d. If people hold an equal amount of currency and deposits, then the currency–deposit ratio is 1. The
reserve–deposit ratio is 0.2 and the money multiplier is (1 + 1)/(1 + 0.2) = 1.67. The money supply
will be $1,666.67.
e. The money supply is proportional to the monetary base and is given by M = m B, where M is the
money supply, m is the money multiplier, and B is the monetary base. Since m is a constant
number defined by the currency–deposit ratio and the reserve–deposit ratio, a 10-percent increase
in the monetary base B will lead to a 10-percent increase in the money supply M.
4. a. The money supply is equal to currency plus demand deposits or $5,000. The monetary base is
equal to currency plus reserves. If we assume banks are not holding any excess reserves, then
reserves must be 25percent of deposits, or $1,000. In this case the monetary base is equal to
$2,000. The money multiplier is equal to the money supply divided by the monetary base, or 2.5.
Alternatively, the money multiplier can be calculated using the formula m = (cr+1)/(cr+rr), where
cr is the currency deposit ratio (0.25) and rr is the reserve deposit ratio (0.25).
c. A subway token, within the subway system, satisfies all three functions of money. Yet outside the
subway system, it is not widely used as a unit of account or a medium of exchange, so it is not a
form of money.
2. a. When the Fed buys bonds, the dollars that it pays to the public for the bonds increase the monetary
base, and this in turn increases the money supply. The money multiplier is not affected, assuming
no change in the reserve–deposit ratio or the currency–deposit ratio.
b. When the Fed increases the interest rate, it pays banks to hold reserves. This gives banks an
incentive to hold more reserves relative to deposits. The increase in the reserve deposit ratio will
decrease the money multiplier. The decline in the money multiplier will lead to a decrease in the
money supply. Since banks are holding more reserves (because they are making fewer loans), the
monetary base will increase.
c. If the Fed reduces its lending to banks through the Term Auction Facility, then the monetary base
will decrease, and this in turn will decrease the money supply. The money multiplier is not
affected, assuming no change in the reserve–deposit ratio or the currency–deposit ratio.
d. If consumers lose confidence in ATMs and prefer to hold more cash, then the currency–deposit
ratio will increase, and this will reduce the money multiplier. The money supply will fall because
banks have fewer reserves to lend. The monetary base will increase because people are holding
more currency, but will decrease because banks are holding fewer reserves. The net effect on the
monetary base is zero.
e. If the Fed drops newly minted $100 bills from a helicopter, then this will increase the monetary
base and the money supply. If any of the currency ends up in the bank, then there will be a further
increase in the money supply. If people end up holding more currency relative to deposits, then the
money multiplier would fall.
3. a. If all money is held as currency, then the money supply is equal to the monetary base. The money
supply will be $1,000.
b. If all money is held as deposits, but banks hold 100 percent of deposits on reserve, then there are
no loans. The money supply will be $1,000.
c. If all money is held as deposits and banks hold 20 percent of deposits on reserve, then the reserve–
deposit ratio is 0.20. The currency–deposit ratio is 0, and the money multiplier will be 1/0.2, or 5.
The money supply will be $5,000.
d. If people hold an equal amount of currency and deposits, then the currency–deposit ratio is 1. The
reserve–deposit ratio is 0.2 and the money multiplier is (1 + 1)/(1 + 0.2) = 1.67. The money supply
will be $1,666.67.
e. The money supply is proportional to the monetary base and is given by M = m B, where M is the
money supply, m is the money multiplier, and B is the monetary base. Since m is a constant
number defined by the currency–deposit ratio and the reserve–deposit ratio, a 10-percent increase
in the monetary base B will lead to a 10-percent increase in the money supply M.
4. a. The money supply is equal to currency plus demand deposits or $5,000. The monetary base is
equal to currency plus reserves. If we assume banks are not holding any excess reserves, then
reserves must be 25percent of deposits, or $1,000. In this case the monetary base is equal to
$2,000. The money multiplier is equal to the money supply divided by the monetary base, or 2.5.
Alternatively, the money multiplier can be calculated using the formula m = (cr+1)/(cr+rr), where
cr is the currency deposit ratio (0.25) and rr is the reserve deposit ratio (0.25).
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Chapter 4—The Monetary System: What It Is and How It Works 25
b. The bank balance sheet is illustrated below. If we assume the bank is not holding any excess
reserves then reserves in the bank are 25 percent of deposits, or $1,000. This means outstanding
loans must be $3,000.
Table 4-1
Assets Liabilities ______
Reserves $1,000 Deposits $4,000
Loans $3,000
c. To increase the money supply the central bank should buy government bonds because this will
increase reserves in the banking system, allowing loans, deposits, and the money supply to
increase. We know that M=mB, so
M = m
B. If the central bank wants the money supply to
increase by 10 percent then they want the change in the money supply to equal $400. We know the
money multiplier is 2.5 so therefore the monetary base must increase by $160, meaning the central
bank must buy $160 of government bonds.
5. a. Given that banks hold one third of their deposits on reserve, the reserve deposit ratio (rr) is 1/3.
Given that people hold one third of their money in currency and two thirds in deposits, we can
express the currency deposit ratio as
𝑐𝑟 = 𝐶𝑢
𝐷 =
1
3 𝑀
2
3 𝑀
= 1
2.
Therefore, the money multiplier is equal to
𝑚 = 𝑐𝑟 + 1
𝑐𝑟 + 𝑟𝑟 =
1
2 + 1
1
2 + 1
3
= 1.8.
The money supply is equal to the monetary base times the money multiplier, or $1,800.
b. If people hold half of their money in currency, then currency holdings are equal to deposits, and
the currency deposit ratio is equal to 1. Therefore, the money multiplier is equal to 1.5, and the
money supply is equal to $1,500.
c. The central bank wants to increase the money supply by $300 so they will need to buy government
bonds. We know
M = m
B, so therefore $300 = 1.5
B, and the central bank will want to
buy $200 of government bonds.
6. The model of the money supply developed in Chapter 4 shows that
M = mB.
The money supply M depends on the money multiplier m and the monetary base B. The money
multiplier can also be expressed in terms of the reserve–deposit ratio rr and the currency–deposit ratio
cr. Rewriting the money supply equation:
.
This equation shows that the money supply depends on the currency–deposit ratio, the reserve–deposit
ratio, and the monetary base.
To answer parts (a) through (c), we use the values for the money supply, the monetary base, the
money multiplier, the reserve–deposit ratio, and the currency–deposit ratio from Table 4-2:M = cr +1
( )
cr + rr
( )
é
ë
ê
ê
ù
û
ú
ú B
b. The bank balance sheet is illustrated below. If we assume the bank is not holding any excess
reserves then reserves in the bank are 25 percent of deposits, or $1,000. This means outstanding
loans must be $3,000.
Table 4-1
Assets Liabilities ______
Reserves $1,000 Deposits $4,000
Loans $3,000
c. To increase the money supply the central bank should buy government bonds because this will
increase reserves in the banking system, allowing loans, deposits, and the money supply to
increase. We know that M=mB, so
M = m
B. If the central bank wants the money supply to
increase by 10 percent then they want the change in the money supply to equal $400. We know the
money multiplier is 2.5 so therefore the monetary base must increase by $160, meaning the central
bank must buy $160 of government bonds.
5. a. Given that banks hold one third of their deposits on reserve, the reserve deposit ratio (rr) is 1/3.
Given that people hold one third of their money in currency and two thirds in deposits, we can
express the currency deposit ratio as
𝑐𝑟 = 𝐶𝑢
𝐷 =
1
3 𝑀
2
3 𝑀
= 1
2.
Therefore, the money multiplier is equal to
𝑚 = 𝑐𝑟 + 1
𝑐𝑟 + 𝑟𝑟 =
1
2 + 1
1
2 + 1
3
= 1.8.
The money supply is equal to the monetary base times the money multiplier, or $1,800.
b. If people hold half of their money in currency, then currency holdings are equal to deposits, and
the currency deposit ratio is equal to 1. Therefore, the money multiplier is equal to 1.5, and the
money supply is equal to $1,500.
c. The central bank wants to increase the money supply by $300 so they will need to buy government
bonds. We know
M = m
B, so therefore $300 = 1.5
B, and the central bank will want to
buy $200 of government bonds.
6. The model of the money supply developed in Chapter 4 shows that
M = mB.
The money supply M depends on the money multiplier m and the monetary base B. The money
multiplier can also be expressed in terms of the reserve–deposit ratio rr and the currency–deposit ratio
cr. Rewriting the money supply equation:
.
This equation shows that the money supply depends on the currency–deposit ratio, the reserve–deposit
ratio, and the monetary base.
To answer parts (a) through (c), we use the values for the money supply, the monetary base, the
money multiplier, the reserve–deposit ratio, and the currency–deposit ratio from Table 4-2:M = cr +1
( )
cr + rr
( )
é
ë
ê
ê
ù
û
ú
ú B
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Chapter 4—The Monetary System: What It Is and How It Works 26
Table 4-2
August 1929 March 1933
Money supply 26.50 19.00
Monetary base 7.10 8.40
Money multiplier 3.70 2.30
Reserve–deposit ratio 0.14 0.21
Currency–deposit ratio 0.17 0.41
a. To determine what would happen to the money supply if the currency–deposit ratio had risen but
the reserve–deposit ratio had remained the same, we need to recalculate the money multiplier and
then plug this value into the money supply equation M = mB. To recalculate the money multiplier,
use the 1933 value of the currency–deposit ratio and the 1929 value of the reserve–deposit ratio:
m = (cr1933 + 1)/(cr1933 + rr1929)
m = (0.41 + 1)/(0.41 + 0.14)
m = 2.56.
To determine the money supply under these conditions in 1933:
M1933 = mB1933.
Plugging in the value for m just calculated and the 1933 value for B:
M1933 = 2.56 8.4
M1933 = 21.504.
Therefore, under these circumstances, the money supply would have fallen from its 1929 level of
26.5 to 21.504 in 1933.
b. To determine what would have happened to the money supply if the reserve–deposit ratio had
risen but the currency–deposit ratio had remained the same, we need to recalculate the money
multiplier and then plug this value into the money supply equation M = mB. To recalculate the
money multiplier, use the 1933 value of the reserve–deposit ratio and the 1929 value of the
currency–deposit ratio:
m = (cr1929 + 1)/(cr1929 + rr1933)
m = (0.17 + 1)/(0.17 + 0.21)
m = 3.09.
To determine the money supply under these conditions in 1933:
M1933 = mB1933.
Plugging in the value for m just calculated and the 1933 value for B:
M1933 = 3.09 8.4
M1933 = 25.96.
Therefore, under these circumstances, the money supply would have fallen from its 1929 level of
26.5 to 25.96 in 1933.
c. From the calculations in parts (a) and (b), it is clear that the decline in the currency– deposit ratio
was most responsible for the drop in the money multiplier and, therefore, the money supply.
Table 4-2
August 1929 March 1933
Money supply 26.50 19.00
Monetary base 7.10 8.40
Money multiplier 3.70 2.30
Reserve–deposit ratio 0.14 0.21
Currency–deposit ratio 0.17 0.41
a. To determine what would happen to the money supply if the currency–deposit ratio had risen but
the reserve–deposit ratio had remained the same, we need to recalculate the money multiplier and
then plug this value into the money supply equation M = mB. To recalculate the money multiplier,
use the 1933 value of the currency–deposit ratio and the 1929 value of the reserve–deposit ratio:
m = (cr1933 + 1)/(cr1933 + rr1929)
m = (0.41 + 1)/(0.41 + 0.14)
m = 2.56.
To determine the money supply under these conditions in 1933:
M1933 = mB1933.
Plugging in the value for m just calculated and the 1933 value for B:
M1933 = 2.56 8.4
M1933 = 21.504.
Therefore, under these circumstances, the money supply would have fallen from its 1929 level of
26.5 to 21.504 in 1933.
b. To determine what would have happened to the money supply if the reserve–deposit ratio had
risen but the currency–deposit ratio had remained the same, we need to recalculate the money
multiplier and then plug this value into the money supply equation M = mB. To recalculate the
money multiplier, use the 1933 value of the reserve–deposit ratio and the 1929 value of the
currency–deposit ratio:
m = (cr1929 + 1)/(cr1929 + rr1933)
m = (0.17 + 1)/(0.17 + 0.21)
m = 3.09.
To determine the money supply under these conditions in 1933:
M1933 = mB1933.
Plugging in the value for m just calculated and the 1933 value for B:
M1933 = 3.09 8.4
M1933 = 25.96.
Therefore, under these circumstances, the money supply would have fallen from its 1929 level of
26.5 to 25.96 in 1933.
c. From the calculations in parts (a) and (b), it is clear that the decline in the currency– deposit ratio
was most responsible for the drop in the money multiplier and, therefore, the money supply.
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Chapter 4—The Monetary System: What It Is and How It Works 27
7. a. The introduction of a tax on checks makes people more reluctant to use checking accounts as a
means of exchange. Therefore, they hold more cash for transactions purposes, raising the
currency–deposit ratio cr.
b. The money supply falls because the money multiplier,cr +1
cr + rr , is decreasing in cr. Intuitively, the
higher the currency–deposit ratio, the lower the proportion of the monetary base that is held by
banks in the form of reserves and, hence, the less money banks can create.
c. The check tax was not a good policy to implement in the middle of the Great Depression because
it resulted in a decrease in the money supply as people preferred to pay in currency rather than
write a check. Banks had fewer reserves and were able to make fewer loans.
8. The leverage ratio is the ratio of a bank’s total assets to its bank capital. If the leverage ratio is 20, this
means that for each dollar of capital contributed by the bank owners, the bank has $20 of assets, and
therefore $19 of deposits and debts. The balance sheet below has a leverage ratio of 20: total assets are
$1,200 and capital is $60.
Assets Liabilities and Owners’ Equity__
Reserves $200 Deposits $800
Loans $600 Debt $340
Securities $400 Capital (owners’ equity) $ 60
If the value of the bank’s assets rises by 2 percent and deposits and debt do not change, then owner’s
equity will rise by 2 percent of the asset value. Since the sum of the entries on each side of the balance
sheet must be the same, a 2 percent rise in the asset value must be balanced by a 2 percent rise in the
right-hand-side value. To reduce the bank’s capital to zero, assets must decline in value by $60, which
is 5 percent of the current asset value.
9. a. JPM’s balance sheet is illustrated below. We know reserves are equal to $3,000 because total
assets must equal total liabilities.
Assets Liabilities and Owners’ Equity_____
Reserves $ 3,000 Deposits $14,000
Loans $10,000 Debt $ 4,000
Securities $ 7,000 Capital (owners’ equity) $ 2,000
The leverage ratio is the ratio of a bank’s total assets to its bank capital, or 10.
b. If the value of the bank’s assets fall by 5 percent due to loan default, and deposits and debt do not
change, then the value of owners’ equity will fall by 5 percent of the asset value. Loans and
owner’s equity both fall by $500. Owners’ equity (JPM’s capital) fell by 25 percent.
Assets Liabilities and Owners’ Equity_____
Reserves $3,000 Deposits $14,000
Loans $9,500 Debt $ 4,000
Securities $7,000 Capital (owners’ equity) $ 1,500
7. a. The introduction of a tax on checks makes people more reluctant to use checking accounts as a
means of exchange. Therefore, they hold more cash for transactions purposes, raising the
currency–deposit ratio cr.
b. The money supply falls because the money multiplier,cr +1
cr + rr , is decreasing in cr. Intuitively, the
higher the currency–deposit ratio, the lower the proportion of the monetary base that is held by
banks in the form of reserves and, hence, the less money banks can create.
c. The check tax was not a good policy to implement in the middle of the Great Depression because
it resulted in a decrease in the money supply as people preferred to pay in currency rather than
write a check. Banks had fewer reserves and were able to make fewer loans.
8. The leverage ratio is the ratio of a bank’s total assets to its bank capital. If the leverage ratio is 20, this
means that for each dollar of capital contributed by the bank owners, the bank has $20 of assets, and
therefore $19 of deposits and debts. The balance sheet below has a leverage ratio of 20: total assets are
$1,200 and capital is $60.
Assets Liabilities and Owners’ Equity__
Reserves $200 Deposits $800
Loans $600 Debt $340
Securities $400 Capital (owners’ equity) $ 60
If the value of the bank’s assets rises by 2 percent and deposits and debt do not change, then owner’s
equity will rise by 2 percent of the asset value. Since the sum of the entries on each side of the balance
sheet must be the same, a 2 percent rise in the asset value must be balanced by a 2 percent rise in the
right-hand-side value. To reduce the bank’s capital to zero, assets must decline in value by $60, which
is 5 percent of the current asset value.
9. a. JPM’s balance sheet is illustrated below. We know reserves are equal to $3,000 because total
assets must equal total liabilities.
Assets Liabilities and Owners’ Equity_____
Reserves $ 3,000 Deposits $14,000
Loans $10,000 Debt $ 4,000
Securities $ 7,000 Capital (owners’ equity) $ 2,000
The leverage ratio is the ratio of a bank’s total assets to its bank capital, or 10.
b. If the value of the bank’s assets fall by 5 percent due to loan default, and deposits and debt do not
change, then the value of owners’ equity will fall by 5 percent of the asset value. Loans and
owner’s equity both fall by $500. Owners’ equity (JPM’s capital) fell by 25 percent.
Assets Liabilities and Owners’ Equity_____
Reserves $3,000 Deposits $14,000
Loans $9,500 Debt $ 4,000
Securities $7,000 Capital (owners’ equity) $ 1,500
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Chapter 5—Inflation: Its Causes, Effects, and Social Costs 28
Answers to Textbook Questions and Problems
CHAPTER 5 Inflation: Its Causes, Effects, and Social Costs
Questions for Review
1. The quantity equation is an identity that expresses the link between the number of transactions that
people make and how much money they hold. We write it as
Money Velocity = Price Transactions
M V = P T.
The right side of the quantity equation tells us about the value of transactions in monetary terms that
occur during a given period of time, for example, a year. T represents the total number of transactions.
P represents the price of a typical transaction. Hence, the product P T represents the amount of
dollars exchanged in a year.
The left side of the quantity equation tells us about the money used to make these transactions. M
represents the quantity of money in the economy. V represents the transactions velocity of money—the
rate at which money circulates in the economy.
Because the number of transactions is difficult to measure, economists usually use a slightly
different version of the quantity equation, in which the total output of the economy Y replaces the
number of transactions T:
Money Velocity = Price Output
M V = P Y.
P now represents the price of one unit of output, so that P Y is the dollar value of output—nominal
GDP. V represents the income velocity of money—the number of times a dollar bill becomes a part of
someone’s income.
2. If we assume that velocity in the quantity equation is constant, then we can view the quantity equation
as a theory to study the effect of changes in the money supple (M). The quantity equation with fixed
velocity states that:
MV = PY.
If velocity V is constant, then a change in the quantity of money (M) causes a proportionate change in
nominal GDP (PY). If we assume further that output is fixed by the factors of production and the
production technology such that Y is constant in the equation, then we can conclude that the quantity of
money determines the price level. This is called the quantity theory of money.
3. The holders of money pay the inflation tax. As prices rise, the real value of the money that people hold
falls—that is, a given amount of money buys fewer goods and services since prices are higher. This
loss of real purchasing power is akin to a ‘tax’ on the money held.
4. The Fisher equation expresses the relationship between nominal and real interest rates. It says that the
nominal interest rate i equals the real interest rate r plus the inflation rate π:
i = r + π.
This tells us that the nominal interest rate can change either because the real interest rate changes or the
inflation rate changes. The real interest rate is assumed to be unaffected by inflation; as discussed in
Chapter 3, it adjusts to equilibrate saving and investment. There is thus a one-to-one relationship
between the inflation rate and the nominal interest rate: if inflation increases by 1 percent, then the
Answers to Textbook Questions and Problems
CHAPTER 5 Inflation: Its Causes, Effects, and Social Costs
Questions for Review
1. The quantity equation is an identity that expresses the link between the number of transactions that
people make and how much money they hold. We write it as
Money Velocity = Price Transactions
M V = P T.
The right side of the quantity equation tells us about the value of transactions in monetary terms that
occur during a given period of time, for example, a year. T represents the total number of transactions.
P represents the price of a typical transaction. Hence, the product P T represents the amount of
dollars exchanged in a year.
The left side of the quantity equation tells us about the money used to make these transactions. M
represents the quantity of money in the economy. V represents the transactions velocity of money—the
rate at which money circulates in the economy.
Because the number of transactions is difficult to measure, economists usually use a slightly
different version of the quantity equation, in which the total output of the economy Y replaces the
number of transactions T:
Money Velocity = Price Output
M V = P Y.
P now represents the price of one unit of output, so that P Y is the dollar value of output—nominal
GDP. V represents the income velocity of money—the number of times a dollar bill becomes a part of
someone’s income.
2. If we assume that velocity in the quantity equation is constant, then we can view the quantity equation
as a theory to study the effect of changes in the money supple (M). The quantity equation with fixed
velocity states that:
MV = PY.
If velocity V is constant, then a change in the quantity of money (M) causes a proportionate change in
nominal GDP (PY). If we assume further that output is fixed by the factors of production and the
production technology such that Y is constant in the equation, then we can conclude that the quantity of
money determines the price level. This is called the quantity theory of money.
3. The holders of money pay the inflation tax. As prices rise, the real value of the money that people hold
falls—that is, a given amount of money buys fewer goods and services since prices are higher. This
loss of real purchasing power is akin to a ‘tax’ on the money held.
4. The Fisher equation expresses the relationship between nominal and real interest rates. It says that the
nominal interest rate i equals the real interest rate r plus the inflation rate π:
i = r + π.
This tells us that the nominal interest rate can change either because the real interest rate changes or the
inflation rate changes. The real interest rate is assumed to be unaffected by inflation; as discussed in
Chapter 3, it adjusts to equilibrate saving and investment. There is thus a one-to-one relationship
between the inflation rate and the nominal interest rate: if inflation increases by 1 percent, then the
Loading page 29...
Chapter 5—Inflation: Its Causes, Effects, and Social Costs 29
nominal interest rate also increases by 1 percent. This one-to-one relationship is called the Fisher
effect.
If inflation increases from 6 to 8 percent, then the Fisher effect implies that the nominal interest
rate increases by 2 percentage points, while the real interest rate remains constant.
5. The costs of expected inflation include the following:
a. Shoeleather costs. Higher inflation means higher nominal interest rates, which means that people
want to hold lower real money balances. If people hold lower money balances, they must make
more frequent trips to the bank to withdraw money. There is an element of inconvenience involved,
which is referred to as the ‘shoeleather tax’ because colloquially, more trips to the bank to
withdraw money results in the wearing out of the shoes.
b. Menu costs. Higher inflation induces firms to change their posted prices more often. This may be
costly if they must reprint their menus and catalogs.
c. Greater variability in relative prices. If firms change their prices infrequently, then inflation
causes greater variability in relative prices. Since free-market economies rely on relative prices to
allocate resources efficiently, inflation leads to microeconomic inefficiencies.
d. Altered tax liabilities. Many provisions of the tax code do not take into account the effect of
inflation. Hence, inflation can alter individuals’ and firms’ tax liabilities, often in ways that
lawmakers did not intend.
e. The inconvenience of a changing price level. It is inconvenient to live in a world with a
changing price level. Money is the yardstick with which we measure economic transactions.
Money is a less useful measure when its value is always changing.
There is an additional cost to unexpected inflation:
f. Arbitrary redistributions of wealth. Unexpected inflation arbitrarily redistributes wealth among
individuals. For example, if inflation is higher than expected, debtors gain and creditors lose. Also,
people with fixed pensions are hurt because their dollars buy fewer goods.
6. Hyperinflation is always a reflection of monetary policy. That is, the price level cannot grow rapidly
unless the supply of money also grows rapidly, and hyperinflations do not end unless the government
drastically reduces money growth. This explanation, however, begs a central question: why does the
government start and then stop printing large quantities of lots of money? The answer almost always
lies in fiscal policy: when the government has a large budget deficit (for example due to a recent war
or some other major event) that it cannot fund by borrowing, it resorts to printing money to pay its bills.
Only when the fiscal problem is alleviated,—by reducing government spending and / or collecting
more taxes,—can the government hope to slow its rate of money growth.
7. Real variables are measured in physical units, and nominal variables are measured in terms of money.
Real variables have been adjusted for inflation and are often measured in terms of constant dollars,
while nominal variables are measured in terms of current dollars. For example, real GDP is measured
in terms of constant base-year dollars, while nominal GDP is measured in current dollars. An increase
in real GDP means we have produced a larger total quantity of goods and services, valued in base-year
dollars. As another example, the real interest rate measures the increase in your purchasing power, the
quantity of goods and services you can buy with your dollars, while the nominal interest rate measures
the increase in the amount of current dollars you possess. The interest rate you are quoted by your bank,
for example 8 percent, is a nominal rate. If the inflation rate is 3 percent, then the real interest rate is 5
percent, meaning your purchasing power has only increased by 5 percent and not 8 percent. The
quantity of dollars you possess has increased by 8 percent but you can only afford to buy 5 percent
more goods and services with these dollars.
nominal interest rate also increases by 1 percent. This one-to-one relationship is called the Fisher
effect.
If inflation increases from 6 to 8 percent, then the Fisher effect implies that the nominal interest
rate increases by 2 percentage points, while the real interest rate remains constant.
5. The costs of expected inflation include the following:
a. Shoeleather costs. Higher inflation means higher nominal interest rates, which means that people
want to hold lower real money balances. If people hold lower money balances, they must make
more frequent trips to the bank to withdraw money. There is an element of inconvenience involved,
which is referred to as the ‘shoeleather tax’ because colloquially, more trips to the bank to
withdraw money results in the wearing out of the shoes.
b. Menu costs. Higher inflation induces firms to change their posted prices more often. This may be
costly if they must reprint their menus and catalogs.
c. Greater variability in relative prices. If firms change their prices infrequently, then inflation
causes greater variability in relative prices. Since free-market economies rely on relative prices to
allocate resources efficiently, inflation leads to microeconomic inefficiencies.
d. Altered tax liabilities. Many provisions of the tax code do not take into account the effect of
inflation. Hence, inflation can alter individuals’ and firms’ tax liabilities, often in ways that
lawmakers did not intend.
e. The inconvenience of a changing price level. It is inconvenient to live in a world with a
changing price level. Money is the yardstick with which we measure economic transactions.
Money is a less useful measure when its value is always changing.
There is an additional cost to unexpected inflation:
f. Arbitrary redistributions of wealth. Unexpected inflation arbitrarily redistributes wealth among
individuals. For example, if inflation is higher than expected, debtors gain and creditors lose. Also,
people with fixed pensions are hurt because their dollars buy fewer goods.
6. Hyperinflation is always a reflection of monetary policy. That is, the price level cannot grow rapidly
unless the supply of money also grows rapidly, and hyperinflations do not end unless the government
drastically reduces money growth. This explanation, however, begs a central question: why does the
government start and then stop printing large quantities of lots of money? The answer almost always
lies in fiscal policy: when the government has a large budget deficit (for example due to a recent war
or some other major event) that it cannot fund by borrowing, it resorts to printing money to pay its bills.
Only when the fiscal problem is alleviated,—by reducing government spending and / or collecting
more taxes,—can the government hope to slow its rate of money growth.
7. Real variables are measured in physical units, and nominal variables are measured in terms of money.
Real variables have been adjusted for inflation and are often measured in terms of constant dollars,
while nominal variables are measured in terms of current dollars. For example, real GDP is measured
in terms of constant base-year dollars, while nominal GDP is measured in current dollars. An increase
in real GDP means we have produced a larger total quantity of goods and services, valued in base-year
dollars. As another example, the real interest rate measures the increase in your purchasing power, the
quantity of goods and services you can buy with your dollars, while the nominal interest rate measures
the increase in the amount of current dollars you possess. The interest rate you are quoted by your bank,
for example 8 percent, is a nominal rate. If the inflation rate is 3 percent, then the real interest rate is 5
percent, meaning your purchasing power has only increased by 5 percent and not 8 percent. The
quantity of dollars you possess has increased by 8 percent but you can only afford to buy 5 percent
more goods and services with these dollars.
Loading page 30...
Chapter 5—Inflation: Its Causes, Effects, and Social Costs 30
Problems and Applications
1. a. To find the growth rate of nominal GDP, we start with the quantity equation MV = PY, and
note that PY is equal to nominal GDP, or the value of the goods and services produced
measured in current dollars. If we express this formula in percentage change form we have:
% Change in M + % Change in V = % Change in PY.
If we assume the percentage change in velocity is zero, then the percentage change in nominal
GDP is equal to the percentage change in the money supply, or 8 percent.
b. To find the inflation rate, express the quantity equation in percentage change form:
b. To find the inflation rate, express the quantity equation in percentage change form:
% Change in M + % Change in V = % Change in P + % Change in Y.
Rearranging this equation tells us that the inflation rate is given by:
% Change in P = % Change in M + % Change in V – % Change in Y.
Substituting the information given in the problem, we thus find:
% Change in P = 8% + 0% – 3%
= 5%.
c. The real interest rate is 4 percent: the nominal interest rate of 9 percent minus the inflation rate of
5 percent.
2. The money demand function is given asM
P
æ
è
çç
ö
ø
÷÷
d
= kY
.
a. To find the average inflation rate the money demand function can be expressed in terms of growth
rates:
% Growth Md – % Growth P = % Growth Y.
The parameter k is a constant, so it can be ignored. The percentage change in nominal money
demand Md is the same as the growth in the money supply because nominal money demand has to
equal nominal money supply. If nominal money demand grows 12 percent and real income (Y)
grows 4 percent then the growth of the price level or the inflation rate is 8 percent.
b. From the answer to part (a), it follows that an increase in real income growth will result in a lower
average inflation rate. For example, if real income grows at 6 percent and money supply growth
remains at 12 percent, then inflation falls to 6 percent. In this case, a larger money supply is
required to support a higher level of GDP, resulting in lower inflation.
c. The parameter k defines how much money people want to hold for every dollar of income. The
parameter k is inversely related to the velocity of money. All else remaining the same, if people
are holding fewer dollars, then each dollar must be used more times to purchase the same quantity
of goods and services.
d. If velocity growth is positive, then all remaining else the same inflation will be higher. From the
quantity equation we know that:
Problems and Applications
1. a. To find the growth rate of nominal GDP, we start with the quantity equation MV = PY, and
note that PY is equal to nominal GDP, or the value of the goods and services produced
measured in current dollars. If we express this formula in percentage change form we have:
% Change in M + % Change in V = % Change in PY.
If we assume the percentage change in velocity is zero, then the percentage change in nominal
GDP is equal to the percentage change in the money supply, or 8 percent.
b. To find the inflation rate, express the quantity equation in percentage change form:
b. To find the inflation rate, express the quantity equation in percentage change form:
% Change in M + % Change in V = % Change in P + % Change in Y.
Rearranging this equation tells us that the inflation rate is given by:
% Change in P = % Change in M + % Change in V – % Change in Y.
Substituting the information given in the problem, we thus find:
% Change in P = 8% + 0% – 3%
= 5%.
c. The real interest rate is 4 percent: the nominal interest rate of 9 percent minus the inflation rate of
5 percent.
2. The money demand function is given asM
P
æ
è
çç
ö
ø
÷÷
d
= kY
.
a. To find the average inflation rate the money demand function can be expressed in terms of growth
rates:
% Growth Md – % Growth P = % Growth Y.
The parameter k is a constant, so it can be ignored. The percentage change in nominal money
demand Md is the same as the growth in the money supply because nominal money demand has to
equal nominal money supply. If nominal money demand grows 12 percent and real income (Y)
grows 4 percent then the growth of the price level or the inflation rate is 8 percent.
b. From the answer to part (a), it follows that an increase in real income growth will result in a lower
average inflation rate. For example, if real income grows at 6 percent and money supply growth
remains at 12 percent, then inflation falls to 6 percent. In this case, a larger money supply is
required to support a higher level of GDP, resulting in lower inflation.
c. The parameter k defines how much money people want to hold for every dollar of income. The
parameter k is inversely related to the velocity of money. All else remaining the same, if people
are holding fewer dollars, then each dollar must be used more times to purchase the same quantity
of goods and services.
d. If velocity growth is positive, then all remaining else the same inflation will be higher. From the
quantity equation we know that:
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Economics