Solution Manual for Microeconomics, 9th Edition
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Instructor’s Manual
By
Duncan M. Holthausen
North Carolina State University
For
Microeconomics
Ninth Edition
Robert S. Pindyck
Massachusetts Institute of Technology
Daniel L. Rubinfeld
University of California, Berkeley
By
Duncan M. Holthausen
North Carolina State University
For
Microeconomics
Ninth Edition
Robert S. Pindyck
Massachusetts Institute of Technology
Daniel L. Rubinfeld
University of California, Berkeley
ISBN-13: 978-0-13-418486-9
ISBN-10: 0-13-418486-6
Contents
PART 1: Introduction: Markets and Prices ................................................................................ 1
Chapter 1 Preliminaries................................................................................................................... 2
Chapter 2 The Basics of Supply and Demand .................................................................................. 8
PART 2: Producers, Consumers, and Competitive Markets ...................................................... 28
Chapter 3 Consumer Behavior......................................................................................................... 29
Chapter 4 Individual and Market Demand ....................................................................................... 50
Appendix Demand Theory—A Mathematical Treatment ................................................................. 72
Chapter 5 Uncertainty and Consumer Behavior ............................................................................... 78
Chapter 6 Production ...................................................................................................................... 90
Chapter 7 The Cost of Production ................................................................................................... 102
Appendix Production and Cost Theory—A Mathematical Treatment............................................... 118
Chapter 8 Profit Maximization and Competitive Supply .................................................................. 123
Chapter 9 The Analysis of Competitive Markets.............................................................................. 141
PART 3: Market Structure and Competitive Strategy................................................................ 163
Chapter 10 Market Power: Monopoly and Monopsony...................................................................... 164
Chapter 11 Pricing with Market Power.............................................................................................. 190
Appendix The Vertically Integrated Firm ........................................................................................ 215
Chapter 12 Monopolistic Competition and Oligopoly........................................................................ 222
Chapter 13 Game Theory and Competitive Strategy .......................................................................... 251
Chapter 14 Markets for Factor Inputs ................................................................................................ 268
Chapter 15 Investment, Time, and Capital Markets ........................................................................... 280
PART 4: Information, Market Failure, and the Role of Government ........................................ 294
Chapter 16 General Equilibrium and Economic Efficiency................................................................ 295
Chapter 17 Markets with Asymmetric Information............................................................................ 310
Chapter 18 Externalities and Public Goods........................................................................................ 323
Chapter 19 Behavioral Economics……………………………………………………………………... 342
ISBN-10: 0-13-418486-6
Contents
PART 1: Introduction: Markets and Prices ................................................................................ 1
Chapter 1 Preliminaries................................................................................................................... 2
Chapter 2 The Basics of Supply and Demand .................................................................................. 8
PART 2: Producers, Consumers, and Competitive Markets ...................................................... 28
Chapter 3 Consumer Behavior......................................................................................................... 29
Chapter 4 Individual and Market Demand ....................................................................................... 50
Appendix Demand Theory—A Mathematical Treatment ................................................................. 72
Chapter 5 Uncertainty and Consumer Behavior ............................................................................... 78
Chapter 6 Production ...................................................................................................................... 90
Chapter 7 The Cost of Production ................................................................................................... 102
Appendix Production and Cost Theory—A Mathematical Treatment............................................... 118
Chapter 8 Profit Maximization and Competitive Supply .................................................................. 123
Chapter 9 The Analysis of Competitive Markets.............................................................................. 141
PART 3: Market Structure and Competitive Strategy................................................................ 163
Chapter 10 Market Power: Monopoly and Monopsony...................................................................... 164
Chapter 11 Pricing with Market Power.............................................................................................. 190
Appendix The Vertically Integrated Firm ........................................................................................ 215
Chapter 12 Monopolistic Competition and Oligopoly........................................................................ 222
Chapter 13 Game Theory and Competitive Strategy .......................................................................... 251
Chapter 14 Markets for Factor Inputs ................................................................................................ 268
Chapter 15 Investment, Time, and Capital Markets ........................................................................... 280
PART 4: Information, Market Failure, and the Role of Government ........................................ 294
Chapter 16 General Equilibrium and Economic Efficiency................................................................ 295
Chapter 17 Markets with Asymmetric Information............................................................................ 310
Chapter 18 Externalities and Public Goods........................................................................................ 323
Chapter 19 Behavioral Economics……………………………………………………………………... 342
PART ONE
Introduction:
Markets and Prices
Introduction:
Markets and Prices
Loading page 4...
Chapter 1
Preliminaries
Teaching Notes
Chapter 1 covers basic concepts students first saw in their introductory course but could bear some
repeating. Since most students will not have read this chapter before the first class, it is a good time to get
them talking about some of the concepts presented. You might start by asking for a definition of economics.
Make sure to emphasize scarcity and trade-offs. Remind students that the objective of economics is to
explain observed phenomena and predict behavior of consumers and firms as economic conditions change.
Ask about the differences (and similarities) between microeconomics and macroeconomics and the
difference between positive and normative analysis. Review the concept of a market and the role prices
play in allocating resources. Discussions of economic theories and models may be a bit abstract at this
point in the course, but you can lay the groundwork for a deeper discussion that might take place when
you cover consumer behavior in Chapter 3.
Section 1.3 considers real and nominal prices. Given the reliance on dollar prices in the economy, students
must understand the difference between real and nominal prices and how to compute real prices. Most
students know about the Consumer Price Index, so you might also mention other price indexes such as the
Producer Price Index and the Personal Consumption Expenditures (PCE) Price Index, which is the Fed’s
preferred inflation measure.1 It is very useful to go over some numerical examples using goods that are in
the news and/or that students often purchase such as cell phones, food, textbooks, and a college education.
In general, the first class is a good time to pique student interest in the course. It is also a good time to tell
students that they need to work hard to learn how to do economic analysis, and that memorization alone
will not get them through the course. Students must learn to think like economists, so encourage them to
work lots of problems. Also encourage them to draw graphs neatly and large enough to make them easy to
interpret. It always amazes me to see the tiny, poorly drawn graphs some students produce. It is no wonder
their answers are often incorrect. You might even suggest they bring a small ruler and colored pencils to
class so they can draw accurate diagrams.
Questions for Review
1. It is often said that a good theory is one that can be refuted by an empirical, data-oriented
study. Explain why a theory that cannot be evaluated empirically is not a good theory.
A theory is useful only if it succeeds in explaining and predicting the phenomena it was intended to
explain. If a theory cannot be evaluated or tested by comparing its predictions to known facts and
data, then we have no idea whether the theory is valid. If we cannot validate the theory, we cannot
have any confidence in its predictions, and it is of little use.
1 The CPI and PPI are reported by the Bureau of Labor Statistics (www.bls.gov). The PCE Price Index is compiled
by the Bureau of Economic Analysis in the Commerce Department (www.bea.gov).
Preliminaries
Teaching Notes
Chapter 1 covers basic concepts students first saw in their introductory course but could bear some
repeating. Since most students will not have read this chapter before the first class, it is a good time to get
them talking about some of the concepts presented. You might start by asking for a definition of economics.
Make sure to emphasize scarcity and trade-offs. Remind students that the objective of economics is to
explain observed phenomena and predict behavior of consumers and firms as economic conditions change.
Ask about the differences (and similarities) between microeconomics and macroeconomics and the
difference between positive and normative analysis. Review the concept of a market and the role prices
play in allocating resources. Discussions of economic theories and models may be a bit abstract at this
point in the course, but you can lay the groundwork for a deeper discussion that might take place when
you cover consumer behavior in Chapter 3.
Section 1.3 considers real and nominal prices. Given the reliance on dollar prices in the economy, students
must understand the difference between real and nominal prices and how to compute real prices. Most
students know about the Consumer Price Index, so you might also mention other price indexes such as the
Producer Price Index and the Personal Consumption Expenditures (PCE) Price Index, which is the Fed’s
preferred inflation measure.1 It is very useful to go over some numerical examples using goods that are in
the news and/or that students often purchase such as cell phones, food, textbooks, and a college education.
In general, the first class is a good time to pique student interest in the course. It is also a good time to tell
students that they need to work hard to learn how to do economic analysis, and that memorization alone
will not get them through the course. Students must learn to think like economists, so encourage them to
work lots of problems. Also encourage them to draw graphs neatly and large enough to make them easy to
interpret. It always amazes me to see the tiny, poorly drawn graphs some students produce. It is no wonder
their answers are often incorrect. You might even suggest they bring a small ruler and colored pencils to
class so they can draw accurate diagrams.
Questions for Review
1. It is often said that a good theory is one that can be refuted by an empirical, data-oriented
study. Explain why a theory that cannot be evaluated empirically is not a good theory.
A theory is useful only if it succeeds in explaining and predicting the phenomena it was intended to
explain. If a theory cannot be evaluated or tested by comparing its predictions to known facts and
data, then we have no idea whether the theory is valid. If we cannot validate the theory, we cannot
have any confidence in its predictions, and it is of little use.
1 The CPI and PPI are reported by the Bureau of Labor Statistics (www.bls.gov). The PCE Price Index is compiled
by the Bureau of Economic Analysis in the Commerce Department (www.bea.gov).
Loading page 5...
Chapter 1 Preliminaries 3
3
2. Which of the following two statements involves positive economic analysis and which normative?
How do the two kinds of analysis differ?
a. Gasoline rationing (allocating to each individual a maximum amount of gasoline that can be
purchased each year) is poor social policy because it interferes with the workings of the
competitive market system.
Positive economic analysis is concerned with explaining what is and predicting what will be.
Normative economic analysis describes what ought to be. Statement (a) is primarily normative
because it makes the normative assertion (i.e., a value judgment) that gasoline rationing is “poor
social policy.” There is also a positive element to statement (a), because it claims that gasoline
rationing “interferes with the workings of the competitive market system.” This is a prediction
that a constraint placed on demand will change the market equilibrium.
b. Gasoline rationing is a policy under which more people are made worse off than are made
better off.
Statement (b) is positive because it predicts how gasoline rationing affects people without
making a value judgment about the desirability of the rationing policy.
3. Suppose the price of regular-octane gasoline were 20 cents per gallon higher in New Jersey than
in Oklahoma. Do you think there would be an opportunity for arbitrage (i.e., that firms could
buy gas in Oklahoma and then sell it at a profit in New Jersey)? Why or why not?
Oklahoma and New Jersey represent separate geographic markets for gasoline because of high
transportation costs, so arbitrage is unlikely. There would be an opportunity for arbitrage only if
transportation costs were less than 20 cents per gallon. Then arbitrageurs could make a profit by
purchasing gasoline in Oklahoma, paying to transport it to New Jersey and selling it in New Jersey. If
the transportation costs were 20 cents or higher, however, no arbitrage would take place.
4. In Example 1.3, what economic forces explain why the real price of eggs has fallen while the
real price of a college education has increased? How have these changes affected consumer
choices?
The price and quantity of goods such as eggs and services, like a college education, are determined
by the interaction of supply and demand. The real price of eggs fell from 1970 to 2016 because of
either a reduction in demand (e.g., consumers switched to lower-cholesterol food), an increase in
supply due perhaps to a reduction in production costs (e.g., improvements in egg production
technology), or both. In response, the price of eggs relative to other foods decreased. The real price of
a college education rose because of either an increase in demand (e.g., the perceived value of a college
education increased, population increased), a decrease in supply due to an increase in the cost of
providing an education (increases in faculty salaries, costs of complying with new regulations, etc.),
or both.
5. Suppose that the Japanese yen rises against the U.S. dollar—that is, it will take more dollars to
buy a given amount of Japanese yen. Explain why this increase simultaneously increases the
real price of Japanese cars for U.S. consumers and lowers the real price of U.S. automobiles for
Japanese consumers.
As the value of the yen grows relative to the dollar, it takes more dollars to purchase a yen, and it
takes fewer yen to purchase a dollar. Assume that the costs of production for both Japanese and U.S.
automobiles remain unchanged. Then using the new exchange rate, the purchase of a Japanese
automobile priced in yen requires more dollars, so for U.S. consumers the real price of Japanese cars
3
2. Which of the following two statements involves positive economic analysis and which normative?
How do the two kinds of analysis differ?
a. Gasoline rationing (allocating to each individual a maximum amount of gasoline that can be
purchased each year) is poor social policy because it interferes with the workings of the
competitive market system.
Positive economic analysis is concerned with explaining what is and predicting what will be.
Normative economic analysis describes what ought to be. Statement (a) is primarily normative
because it makes the normative assertion (i.e., a value judgment) that gasoline rationing is “poor
social policy.” There is also a positive element to statement (a), because it claims that gasoline
rationing “interferes with the workings of the competitive market system.” This is a prediction
that a constraint placed on demand will change the market equilibrium.
b. Gasoline rationing is a policy under which more people are made worse off than are made
better off.
Statement (b) is positive because it predicts how gasoline rationing affects people without
making a value judgment about the desirability of the rationing policy.
3. Suppose the price of regular-octane gasoline were 20 cents per gallon higher in New Jersey than
in Oklahoma. Do you think there would be an opportunity for arbitrage (i.e., that firms could
buy gas in Oklahoma and then sell it at a profit in New Jersey)? Why or why not?
Oklahoma and New Jersey represent separate geographic markets for gasoline because of high
transportation costs, so arbitrage is unlikely. There would be an opportunity for arbitrage only if
transportation costs were less than 20 cents per gallon. Then arbitrageurs could make a profit by
purchasing gasoline in Oklahoma, paying to transport it to New Jersey and selling it in New Jersey. If
the transportation costs were 20 cents or higher, however, no arbitrage would take place.
4. In Example 1.3, what economic forces explain why the real price of eggs has fallen while the
real price of a college education has increased? How have these changes affected consumer
choices?
The price and quantity of goods such as eggs and services, like a college education, are determined
by the interaction of supply and demand. The real price of eggs fell from 1970 to 2016 because of
either a reduction in demand (e.g., consumers switched to lower-cholesterol food), an increase in
supply due perhaps to a reduction in production costs (e.g., improvements in egg production
technology), or both. In response, the price of eggs relative to other foods decreased. The real price of
a college education rose because of either an increase in demand (e.g., the perceived value of a college
education increased, population increased), a decrease in supply due to an increase in the cost of
providing an education (increases in faculty salaries, costs of complying with new regulations, etc.),
or both.
5. Suppose that the Japanese yen rises against the U.S. dollar—that is, it will take more dollars to
buy a given amount of Japanese yen. Explain why this increase simultaneously increases the
real price of Japanese cars for U.S. consumers and lowers the real price of U.S. automobiles for
Japanese consumers.
As the value of the yen grows relative to the dollar, it takes more dollars to purchase a yen, and it
takes fewer yen to purchase a dollar. Assume that the costs of production for both Japanese and U.S.
automobiles remain unchanged. Then using the new exchange rate, the purchase of a Japanese
automobile priced in yen requires more dollars, so for U.S. consumers the real price of Japanese cars
Loading page 6...
Pindyck/Rubinfeld, Microeconomics, Ninth Edition
4
in dollars increases. Similarly, the purchase of a U.S. automobile priced in dollars requires fewer yen,
and thus for Japanese consumers the real price of a U.S. automobile in yen decreases.
6. The price of long-distance telephone service fell from 40 cents per minute in 1996 to 22 cents
per minute in 1999, a 45% (18 cents/40 cents) decrease. The Consumer Price Index increased
by 10% over this period. What happened to the real price of telephone service?
Let the CPI for 1996 equal 100 and the CPI for 1999 equal 110, which reflects a 10% increase in the
overall price level. Now let’s find the real price of telephone service (in 1996 dollars) in each year.
The real price in 1996 is simply 40 cents. To find the real price in 1999, divide CPI1996 by CPI1999
and multiply the result by the nominal price in 1999. The result is (100/110) 22 20 cents. The real
price therefore fell from 40 to 20 cents, a 50% decline.
Exercises
1. Decide whether each of the following statements is true or false and explain why:
a. Fast-food chains like McDonald’s, Burger King, and Wendy’s operate all over the United
States. Therefore the market for fast food is a national market.
This statement is false. People generally buy fast food locally and do not travel large distances
across the United States just to buy a cheaper fast-food meal. Because there is little potential for
arbitrage between fast-food restaurants that are located some distance from each other, there are
likely to be multiple fast-food markets across the country.
b. People generally buy clothing in the city in which they live. Therefore there is a clothing
market in, say, Atlanta that is distinct from the clothing market in Los Angeles.
This statement is mostly false. Although consumers are unlikely to travel across the country to
buy clothing, they can purchase many items online. In this way, clothing retailers in different
cities compete with each other and with online stores such as Amazon, L.L. Bean and
Zappos.com. Also, suppliers can easily move clothing from one part of the country to another.
Thus, if clothing is more expensive in Atlanta than Los Angeles, clothing companies can shift
supplies to Atlanta, which would reduce the price in Atlanta. Occasionally, there may be a
market for a specific clothing item in a faraway market that results in a great opportunity for
arbitrage, such as the market for blue jeans in the old Soviet Union.
c. Some consumers strongly prefer Pepsi and some strongly prefer Coke. Therefore there is
no single market for colas.
This statement is false. Although some people have strong preferences for a particular brand of
cola, the different brands are similar enough that they constitute one market. There are consumers
who do not have strong preferences for one type of cola, and there are consumers who may have
a preference, but who will also be influenced by price. Given these possibilities, the price of cola
drinks will not tend to differ by very much, particularly for Coke and Pepsi.
2. The following table shows the average retail price of butter and the Consumer Price Index from
1980 to 2010, scaled so that the CPI 100 in 1980.
4
in dollars increases. Similarly, the purchase of a U.S. automobile priced in dollars requires fewer yen,
and thus for Japanese consumers the real price of a U.S. automobile in yen decreases.
6. The price of long-distance telephone service fell from 40 cents per minute in 1996 to 22 cents
per minute in 1999, a 45% (18 cents/40 cents) decrease. The Consumer Price Index increased
by 10% over this period. What happened to the real price of telephone service?
Let the CPI for 1996 equal 100 and the CPI for 1999 equal 110, which reflects a 10% increase in the
overall price level. Now let’s find the real price of telephone service (in 1996 dollars) in each year.
The real price in 1996 is simply 40 cents. To find the real price in 1999, divide CPI1996 by CPI1999
and multiply the result by the nominal price in 1999. The result is (100/110) 22 20 cents. The real
price therefore fell from 40 to 20 cents, a 50% decline.
Exercises
1. Decide whether each of the following statements is true or false and explain why:
a. Fast-food chains like McDonald’s, Burger King, and Wendy’s operate all over the United
States. Therefore the market for fast food is a national market.
This statement is false. People generally buy fast food locally and do not travel large distances
across the United States just to buy a cheaper fast-food meal. Because there is little potential for
arbitrage between fast-food restaurants that are located some distance from each other, there are
likely to be multiple fast-food markets across the country.
b. People generally buy clothing in the city in which they live. Therefore there is a clothing
market in, say, Atlanta that is distinct from the clothing market in Los Angeles.
This statement is mostly false. Although consumers are unlikely to travel across the country to
buy clothing, they can purchase many items online. In this way, clothing retailers in different
cities compete with each other and with online stores such as Amazon, L.L. Bean and
Zappos.com. Also, suppliers can easily move clothing from one part of the country to another.
Thus, if clothing is more expensive in Atlanta than Los Angeles, clothing companies can shift
supplies to Atlanta, which would reduce the price in Atlanta. Occasionally, there may be a
market for a specific clothing item in a faraway market that results in a great opportunity for
arbitrage, such as the market for blue jeans in the old Soviet Union.
c. Some consumers strongly prefer Pepsi and some strongly prefer Coke. Therefore there is
no single market for colas.
This statement is false. Although some people have strong preferences for a particular brand of
cola, the different brands are similar enough that they constitute one market. There are consumers
who do not have strong preferences for one type of cola, and there are consumers who may have
a preference, but who will also be influenced by price. Given these possibilities, the price of cola
drinks will not tend to differ by very much, particularly for Coke and Pepsi.
2. The following table shows the average retail price of butter and the Consumer Price Index from
1980 to 2010, scaled so that the CPI 100 in 1980.
Loading page 7...
Chapter 1 Preliminaries 5
5
1980 1990 2000 2010
CPI 100 158.56 208.98 218.06
Retail price of butter
(salted, grade AA, per lb.) $1.88 $1.99 $2.52 $2.88
5
1980 1990 2000 2010
CPI 100 158.56 208.98 218.06
Retail price of butter
(salted, grade AA, per lb.) $1.88 $1.99 $2.52 $2.88
Loading page 8...
Pindyck/Rubinfeld, Microeconomics, Ninth Edition
6
a. Calculate the real price of butter in 1980 dollars. Has the real price increased/decreased/
stayed the same from 1980 to 2000? From 1980 to 2010?
Real price of butter in year t 1980
t
CPI
CPI nominal price of butter in year t.
1980 1990 2000 2010
Real price of butter (1980 $) $1.88 $1.26 $1.21 $1.32
The real price of butter decreased from $1.88 in 1980 to $1.21 in 2000, and it decreased from
$1.88 in 1980 to $1.32 in 2010, although it did increase between 2000 and 2010.
b. What is the percentage change in the real price (1980 dollars) from 1980 to 2000? From
1980 to 2010?
Real price decreased by $0.67 (1.88 1.21 0.67) between 1980 and 2000. The percentage
change in real price from 1980 to 2000 was therefore (0.67/1.88) 100% 35.6%. The
decrease was $0.56 between 1980 and 2010 which, in percentage terms, is (0.56/1.88)
100% 29.8%.
c. Convert the CPI into 1990 100 and determine the real price of butter in 1990 dollars.
To convert the CPI so that 1990 100, divide the CPI for each year by the CPI for 1990 and
multiply that result by 100. Use the formula from answer (a) and the new CPI numbers below to
find the real price of butter in 1990 dollars.
1980 1990 2000 2010
New CPI 63.07 100 131.80 137.53
Real price of butter (1990 $) $2.98 $1.99 $1.91 $2.09
d. What is the percentage change in the real price (1990 dollars) from 1980 to 2000? Compare
this with your answer in (b). What do you notice? Explain.
Real price decreased by $1.07 (2.98 1.91 1.07). The percentage change in real price from
1980 to 2000 was therefore (1.07/2.98) 100% 35.9%. This answer is the same (except for
rounding error) as in (b). It does not matter which year is chosen as the base year when
calculating percentage changes in real prices.
3. At the time this book went to print, the minimum wage was $7.25. To find the current value of
the CPI, go to http://www.bls.gov/cpi/home.htm. Click on “CPI Tables,” which is found on the
left side of the website. Then, click on “Table Containing History of CPI-U U.S. All Items
Indexes and Annual Percent Changes from 1913 to Present.” This will give you the CPI from
1913 to the present.
a. With these values, calculate the current real minimum wage in 1990 dollars.
The last CPI value available when these answers were prepared was October 2016. Thus, all
calculations are as of that date. You should update the CPI value for your answers.
Real minimum wage in October 2016
2016
1990
CPI
CPI minimum wage 729.241
7.130 $7.25 $3.92.
So, as of October 2016, the real minimum wage in 1990 dollars was $3.92.
6
a. Calculate the real price of butter in 1980 dollars. Has the real price increased/decreased/
stayed the same from 1980 to 2000? From 1980 to 2010?
Real price of butter in year t 1980
t
CPI
CPI nominal price of butter in year t.
1980 1990 2000 2010
Real price of butter (1980 $) $1.88 $1.26 $1.21 $1.32
The real price of butter decreased from $1.88 in 1980 to $1.21 in 2000, and it decreased from
$1.88 in 1980 to $1.32 in 2010, although it did increase between 2000 and 2010.
b. What is the percentage change in the real price (1980 dollars) from 1980 to 2000? From
1980 to 2010?
Real price decreased by $0.67 (1.88 1.21 0.67) between 1980 and 2000. The percentage
change in real price from 1980 to 2000 was therefore (0.67/1.88) 100% 35.6%. The
decrease was $0.56 between 1980 and 2010 which, in percentage terms, is (0.56/1.88)
100% 29.8%.
c. Convert the CPI into 1990 100 and determine the real price of butter in 1990 dollars.
To convert the CPI so that 1990 100, divide the CPI for each year by the CPI for 1990 and
multiply that result by 100. Use the formula from answer (a) and the new CPI numbers below to
find the real price of butter in 1990 dollars.
1980 1990 2000 2010
New CPI 63.07 100 131.80 137.53
Real price of butter (1990 $) $2.98 $1.99 $1.91 $2.09
d. What is the percentage change in the real price (1990 dollars) from 1980 to 2000? Compare
this with your answer in (b). What do you notice? Explain.
Real price decreased by $1.07 (2.98 1.91 1.07). The percentage change in real price from
1980 to 2000 was therefore (1.07/2.98) 100% 35.9%. This answer is the same (except for
rounding error) as in (b). It does not matter which year is chosen as the base year when
calculating percentage changes in real prices.
3. At the time this book went to print, the minimum wage was $7.25. To find the current value of
the CPI, go to http://www.bls.gov/cpi/home.htm. Click on “CPI Tables,” which is found on the
left side of the website. Then, click on “Table Containing History of CPI-U U.S. All Items
Indexes and Annual Percent Changes from 1913 to Present.” This will give you the CPI from
1913 to the present.
a. With these values, calculate the current real minimum wage in 1990 dollars.
The last CPI value available when these answers were prepared was October 2016. Thus, all
calculations are as of that date. You should update the CPI value for your answers.
Real minimum wage in October 2016
2016
1990
CPI
CPI minimum wage 729.241
7.130 $7.25 $3.92.
So, as of October 2016, the real minimum wage in 1990 dollars was $3.92.
Loading page 9...
Chapter 1 Preliminaries 7
7
b. Stated in real 1990 dollars, what is the percentage change in the real minimum wage from
1985 to the present?
The minimum wage in 1985 was $3.35. You can get a complete listing of historical minimum
wage rates from the Department of Labor, Wage and Hour Division at http://www.dol.gov/
whd/minwage/chart.htm.
Real minimum wage in 1985 1990
1985
CPI
CPI $3.35 130.7
107.6 $3.35 $4.07 in 1990 dollars.
The real minimum wage (in 1990 dollars) therefore decreased slightly from $4.07 in 1985 to
$3.92 in 2016. This is a decrease of $4.07 3.92 $0.15, so the percentage change
is (0.15/4.07) 100% 3.69%.
7
b. Stated in real 1990 dollars, what is the percentage change in the real minimum wage from
1985 to the present?
The minimum wage in 1985 was $3.35. You can get a complete listing of historical minimum
wage rates from the Department of Labor, Wage and Hour Division at http://www.dol.gov/
whd/minwage/chart.htm.
Real minimum wage in 1985 1990
1985
CPI
CPI $3.35 130.7
107.6 $3.35 $4.07 in 1990 dollars.
The real minimum wage (in 1990 dollars) therefore decreased slightly from $4.07 in 1985 to
$3.92 in 2016. This is a decrease of $4.07 3.92 $0.15, so the percentage change
is (0.15/4.07) 100% 3.69%.
Loading page 10...
Chapter 2
The Basics of Supply and Demand
Teaching Notes
This chapter reviews the basics of supply and demand that students should be familiar with from their
introductory economics courses. You may choose to spend more or less time on this chapter depending
on how much review your students require. Chapter 2 departs from the standard treatment of supply and
demand basics found in most other intermediate microeconomics textbooks by discussing many real-world
markets (copper, office space in New York City, wheat, gasoline, natural gas, coffee, and others) and
teaching students how to analyze these markets with the tools of supply and demand. The real-world
applications are intended to show students the relevance of supply and demand analysis, and you may
find it helpful to refer to these examples during class.
One of the most common problems students have in supply/demand analysis is confusion between a
movement along a supply or demand curve and a shift in the curve. You should stress the ceteris paribus
assumption, and explain that all variables except price are held constant along a supply or demand curve.
So movements along the demand curve occur only with changes in price. When one of the omitted factors
changes, the entire supply or demand curve shifts. You might find it useful to make up a simple linear
demand function with quantity demanded on the left and the good’s price, a competing good’s price and
income on the right. This gives you a chance to discuss substitutes and complements and also normal and
inferior goods. Plug in values for the competing good’s price and income and plot the demand curve. Then
change, say, the other good’s price and plot the demand curve again to show that it shifts. This demonstration
helps students understand that the other variables are actually in the demand function and are merely
lumped into the intercept term when we draw a demand curve. The same, of course, applies to supply
curves as well.
It is important to make the distinction between quantity demanded as a function of price, QD D(P), and
the inverse demand function, P D 1(QD), where price is a function of the quantity demanded. Since we
plot price on the vertical axis, the inverse demand function is very useful. You can demonstrate this if you
use an example as suggested above and plot the resulting demand curves. And, of course, there are
“regular” and inverse supply curves as well.
Students also can have difficulties understanding how a market adjusts to a new equilibrium. They often
think that the supply and/or demand curves shift as part of the equilibrium process. For example, suppose
demand increases. Students typically recognize that price must increase, but some go on to say that supply
will also have to increase to satisfy the increased level of demand. This may be a case of confusing an
increase in quantity supplied with an increase in supply, but I have seen many students draw a shift in
supply, so I try to get this cleared up as soon as possible.
The concept of elasticity, introduced in Section 2.4, is another source of problems. It is important to stress
the fact that any elasticity is the ratio of two percentages. So, for example, if a firm’s product has a price
elasticity of demand of 2, the firm can determine that a 5% increase in price will result in a 10% drop in
sales. Use lots of concrete examples to convince students that firms and governments can make important
The Basics of Supply and Demand
Teaching Notes
This chapter reviews the basics of supply and demand that students should be familiar with from their
introductory economics courses. You may choose to spend more or less time on this chapter depending
on how much review your students require. Chapter 2 departs from the standard treatment of supply and
demand basics found in most other intermediate microeconomics textbooks by discussing many real-world
markets (copper, office space in New York City, wheat, gasoline, natural gas, coffee, and others) and
teaching students how to analyze these markets with the tools of supply and demand. The real-world
applications are intended to show students the relevance of supply and demand analysis, and you may
find it helpful to refer to these examples during class.
One of the most common problems students have in supply/demand analysis is confusion between a
movement along a supply or demand curve and a shift in the curve. You should stress the ceteris paribus
assumption, and explain that all variables except price are held constant along a supply or demand curve.
So movements along the demand curve occur only with changes in price. When one of the omitted factors
changes, the entire supply or demand curve shifts. You might find it useful to make up a simple linear
demand function with quantity demanded on the left and the good’s price, a competing good’s price and
income on the right. This gives you a chance to discuss substitutes and complements and also normal and
inferior goods. Plug in values for the competing good’s price and income and plot the demand curve. Then
change, say, the other good’s price and plot the demand curve again to show that it shifts. This demonstration
helps students understand that the other variables are actually in the demand function and are merely
lumped into the intercept term when we draw a demand curve. The same, of course, applies to supply
curves as well.
It is important to make the distinction between quantity demanded as a function of price, QD D(P), and
the inverse demand function, P D 1(QD), where price is a function of the quantity demanded. Since we
plot price on the vertical axis, the inverse demand function is very useful. You can demonstrate this if you
use an example as suggested above and plot the resulting demand curves. And, of course, there are
“regular” and inverse supply curves as well.
Students also can have difficulties understanding how a market adjusts to a new equilibrium. They often
think that the supply and/or demand curves shift as part of the equilibrium process. For example, suppose
demand increases. Students typically recognize that price must increase, but some go on to say that supply
will also have to increase to satisfy the increased level of demand. This may be a case of confusing an
increase in quantity supplied with an increase in supply, but I have seen many students draw a shift in
supply, so I try to get this cleared up as soon as possible.
The concept of elasticity, introduced in Section 2.4, is another source of problems. It is important to stress
the fact that any elasticity is the ratio of two percentages. So, for example, if a firm’s product has a price
elasticity of demand of 2, the firm can determine that a 5% increase in price will result in a 10% drop in
sales. Use lots of concrete examples to convince students that firms and governments can make important
Loading page 11...
Chapter 2 The Basics of Supply and Demand 9
use of elasticity information. A common source of confusion is the negative value for the price elasticity
of demand. We often talk about it as if it were a positive number. The book is careful in referring to the
“magnitude” of the price elasticity, by which it means the absolute value of the price elasticity, but students
may not pick this up on their own. I warn students that I will speak of price elasticities as if they were
positive numbers and will say that a good whose elasticity is 2 is more elastic (or greater) than one whose
elasticity is 1, even though the mathematically inclined may cringe.
Section 2.6 brings a lot of this material together because elasticities are used to derive demand and supply
curves, market equilibria are computed, curves are shifted, and new equilibria are determined. This shows
students how we can estimate the quantitative (not just the qualitative) effects of, say, a disruption in oil
supply as in Example 2.9. Unfortunately, this section takes some time to cover, especially if your students’
algebra is rusty. You’ll have to decide whether the benefits outweigh the costs.
Price controls are introduced in Section 2.7. Students usually don’t realize the full effects of price controls.
They think only of the initial effect on prices without realizing that shortages or surpluses are created, so
this is an important topic. However, the coverage here is quite brief. Chapter 9 examines the effects of
price controls and other forms of government intervention in much greater detail, so you may want to
defer this topic until then.
Questions for Review
1. Suppose that unusually hot weather causes the demand curve for ice cream to shift to the right.
Why will the price of ice cream rise to a new market-clearing level?
Suppose the supply of ice cream is completely inelastic in the short run, so the supply curve is
vertical as shown below. The initial equilibrium is at price P1. The unusually hot weather causes the
demand curve for ice cream to shift from D1 to D2, creating short-run excess demand (i.e., a temporary
shortage) at the current price. Consumers will bid against each other for the ice cream, putting
upward pressure on the price, and ice cream sellers will react by raising price. The price of ice cream
will rise until the quantity demanded and the quantity supplied are equal, which occurs at price P2.
use of elasticity information. A common source of confusion is the negative value for the price elasticity
of demand. We often talk about it as if it were a positive number. The book is careful in referring to the
“magnitude” of the price elasticity, by which it means the absolute value of the price elasticity, but students
may not pick this up on their own. I warn students that I will speak of price elasticities as if they were
positive numbers and will say that a good whose elasticity is 2 is more elastic (or greater) than one whose
elasticity is 1, even though the mathematically inclined may cringe.
Section 2.6 brings a lot of this material together because elasticities are used to derive demand and supply
curves, market equilibria are computed, curves are shifted, and new equilibria are determined. This shows
students how we can estimate the quantitative (not just the qualitative) effects of, say, a disruption in oil
supply as in Example 2.9. Unfortunately, this section takes some time to cover, especially if your students’
algebra is rusty. You’ll have to decide whether the benefits outweigh the costs.
Price controls are introduced in Section 2.7. Students usually don’t realize the full effects of price controls.
They think only of the initial effect on prices without realizing that shortages or surpluses are created, so
this is an important topic. However, the coverage here is quite brief. Chapter 9 examines the effects of
price controls and other forms of government intervention in much greater detail, so you may want to
defer this topic until then.
Questions for Review
1. Suppose that unusually hot weather causes the demand curve for ice cream to shift to the right.
Why will the price of ice cream rise to a new market-clearing level?
Suppose the supply of ice cream is completely inelastic in the short run, so the supply curve is
vertical as shown below. The initial equilibrium is at price P1. The unusually hot weather causes the
demand curve for ice cream to shift from D1 to D2, creating short-run excess demand (i.e., a temporary
shortage) at the current price. Consumers will bid against each other for the ice cream, putting
upward pressure on the price, and ice cream sellers will react by raising price. The price of ice cream
will rise until the quantity demanded and the quantity supplied are equal, which occurs at price P2.
Loading page 12...
10 Pindyck/Rubinfeld, Microeconomics, Ninth Edition
2. Use supply and demand curves to illustrate how each of the following events would affect the
price of butter and the quantity of butter bought and sold:
a. An increase in the price of margarine.
Butter and margarine are substitute goods for most people. Therefore, an increase in the price of
margarine will cause people to increase their consumption of butter, thereby shifting the demand
curve for butter out from D1 to D2 in Figure 2.2.a. This shift in demand causes the equilibrium
price of butter to rise from P1 to P2 and the equilibrium quantity to increase from Q1 to Q2.
Figure 2.2.a
b. An increase in the price of milk.
Milk is the main ingredient in butter. An increase in the price of milk increases the cost of
producing butter, which reduces the supply of butter. The supply curve for butter shifts from
S1 to S2 in Figure 2.2.b, resulting in a higher equilibrium price, P2 and a lower equilibrium
quantity, Q2, for butter.
Figure 2.2.b
2. Use supply and demand curves to illustrate how each of the following events would affect the
price of butter and the quantity of butter bought and sold:
a. An increase in the price of margarine.
Butter and margarine are substitute goods for most people. Therefore, an increase in the price of
margarine will cause people to increase their consumption of butter, thereby shifting the demand
curve for butter out from D1 to D2 in Figure 2.2.a. This shift in demand causes the equilibrium
price of butter to rise from P1 to P2 and the equilibrium quantity to increase from Q1 to Q2.
Figure 2.2.a
b. An increase in the price of milk.
Milk is the main ingredient in butter. An increase in the price of milk increases the cost of
producing butter, which reduces the supply of butter. The supply curve for butter shifts from
S1 to S2 in Figure 2.2.b, resulting in a higher equilibrium price, P2 and a lower equilibrium
quantity, Q2, for butter.
Figure 2.2.b
Loading page 13...
Chapter 2 The Basics of Supply and Demand 11
Note: Butter is in fact made from the fat that is skimmed from milk; thus butter and milk are joint
products, and this complicates things. If you take account of this relationship, your answer might
change, but it depends on why the price of milk increased. If the increase were caused by an
increase in the demand for milk, the equilibrium quantity of milk supplied would increase. With
more milk being produced, there would be more milk fat available to make butter, and the price
of milk fat would fall. This would shift the supply curve for butter to the right, resulting in a drop
in the price of butter and an increase in the quantity of butter supplied.
c. A decrease in average income levels.
Assuming that butter is a normal good, a decrease in average income will cause the demand
curve for butter to decrease (i.e., shift from D1 to D2). This will result in a decline in the
equilibrium price from P1 to P2, and a decline in the equilibrium quantity from Q1 to Q2. See
Figure 2.2.c.
Figure 2.2.c
3. If a 3% increase in the price of corn flakes causes a 6% decline in the quantity demanded, what
is the elasticity of demand?
The elasticity of demand is the percentage change in the quantity demanded divided by the
percentage change in the price. The elasticity of demand for corn flakes is therefore
% 6 2.
% 3
D
P
Q
E P
4. Explain the difference between a shift in the supply curve and a movement along the supply
curve.
A movement along the supply curve occurs when the price of the good changes. A shift of the supply
curve is caused by a change in something other than the good’s price that results in a change in the
quantity supplied at the current price. Some examples are a change in the price of an input, a change
in technology that reduces the cost of production, and an increase in the number of firms supplying
the product.
Note: Butter is in fact made from the fat that is skimmed from milk; thus butter and milk are joint
products, and this complicates things. If you take account of this relationship, your answer might
change, but it depends on why the price of milk increased. If the increase were caused by an
increase in the demand for milk, the equilibrium quantity of milk supplied would increase. With
more milk being produced, there would be more milk fat available to make butter, and the price
of milk fat would fall. This would shift the supply curve for butter to the right, resulting in a drop
in the price of butter and an increase in the quantity of butter supplied.
c. A decrease in average income levels.
Assuming that butter is a normal good, a decrease in average income will cause the demand
curve for butter to decrease (i.e., shift from D1 to D2). This will result in a decline in the
equilibrium price from P1 to P2, and a decline in the equilibrium quantity from Q1 to Q2. See
Figure 2.2.c.
Figure 2.2.c
3. If a 3% increase in the price of corn flakes causes a 6% decline in the quantity demanded, what
is the elasticity of demand?
The elasticity of demand is the percentage change in the quantity demanded divided by the
percentage change in the price. The elasticity of demand for corn flakes is therefore
% 6 2.
% 3
D
P
Q
E P
4. Explain the difference between a shift in the supply curve and a movement along the supply
curve.
A movement along the supply curve occurs when the price of the good changes. A shift of the supply
curve is caused by a change in something other than the good’s price that results in a change in the
quantity supplied at the current price. Some examples are a change in the price of an input, a change
in technology that reduces the cost of production, and an increase in the number of firms supplying
the product.
Loading page 14...
12 Pindyck/Rubinfeld, Microeconomics, Ninth Edition
5. Explain why for many goods, the long-run price elasticity of supply is larger than the short-run
elasticity.
The price elasticity of supply is the percentage change in the quantity supplied divided by the
percentage change in price. In the short run, an increase in price induces firms to produce more by
using their facilities more hours per week, paying workers to work overtime and hiring new workers.
Nevertheless, there is a limit to how much firms can produce because they face capacity constraints
in the short run. In the long run, however, firms can expand capacity by building new plants and
hiring new permanent workers. Also, new firms can enter the market and add their output to total
supply. Hence a greater change in quantity supplied is possible in the long run, and thus the price
elasticity of supply is larger in the long run than in the short run.
6. Why do long-run elasticities of demand differ from short-run elasticities? Consider two goods:
paper towels and televisions. Which is a durable good? Would you expect the price elasticity of
demand for paper towels to be larger in the short run or in the long run? Why? What about the
price elasticity of demand for televisions?
Long-run and short-run elasticities differ based on how rapidly consumers respond to price changes
and how many substitutes are available. If the price of paper towels, a nondurable good, were to
increase, consumers might react only minimally in the short run because it takes time for people to
change their consumption habits. In the long run, however, consumers might learn to use other
products such as sponges or kitchen towels instead of paper towels. Thus, the price elasticity would
be larger in the long run than in the short run. In contrast, the quantity demanded of durable goods,
such as televisions, might change dramatically in the short run. For example, the initial result of a
price increase for televisions would cause consumers to delay purchases because they could keep
on using their current TVs longer. Eventually consumers would replace their televisions as they wore
out or became obsolete. Therefore, we expect the demand for durables to be more elastic in the short
run than in the long run.
7. Are the following statements true or false? Explain your answers.
a. The elasticity of demand is the same as the slope of the demand curve.
False. Elasticity of demand is the percentage change in quantity demanded divided by the
percentage change in the price of the product. In contrast, the slope of the demand curve is the
change in quantity demanded (in units) divided by the change in price (typically in dollars).
The difference is that elasticity uses percentage changes while the slope is based on changes
in the number of units and number of dollars.
b. The cross-price elasticity will always be positive.
False. The cross-price elasticity measures the percentage change in the quantity demanded of
one good due to a 1% change in the price of another good. This elasticity will be positive for
substitutes (an increase in the price of hot dogs is likely to cause an increase in the quantity
demanded of hamburgers) and negative for complements (an increase in the price of hot dogs is
likely to cause a decrease in the quantity demanded of hot dog buns).
c. The supply of apartments is more inelastic in the short run than the long run.
True. In the short run it is difficult to change the supply of apartments in response to a change in
price. Increasing the supply requires constructing new apartment buildings, which can take a year
or more. Therefore, the elasticity of supply is more inelastic in the short run than in the long run.
5. Explain why for many goods, the long-run price elasticity of supply is larger than the short-run
elasticity.
The price elasticity of supply is the percentage change in the quantity supplied divided by the
percentage change in price. In the short run, an increase in price induces firms to produce more by
using their facilities more hours per week, paying workers to work overtime and hiring new workers.
Nevertheless, there is a limit to how much firms can produce because they face capacity constraints
in the short run. In the long run, however, firms can expand capacity by building new plants and
hiring new permanent workers. Also, new firms can enter the market and add their output to total
supply. Hence a greater change in quantity supplied is possible in the long run, and thus the price
elasticity of supply is larger in the long run than in the short run.
6. Why do long-run elasticities of demand differ from short-run elasticities? Consider two goods:
paper towels and televisions. Which is a durable good? Would you expect the price elasticity of
demand for paper towels to be larger in the short run or in the long run? Why? What about the
price elasticity of demand for televisions?
Long-run and short-run elasticities differ based on how rapidly consumers respond to price changes
and how many substitutes are available. If the price of paper towels, a nondurable good, were to
increase, consumers might react only minimally in the short run because it takes time for people to
change their consumption habits. In the long run, however, consumers might learn to use other
products such as sponges or kitchen towels instead of paper towels. Thus, the price elasticity would
be larger in the long run than in the short run. In contrast, the quantity demanded of durable goods,
such as televisions, might change dramatically in the short run. For example, the initial result of a
price increase for televisions would cause consumers to delay purchases because they could keep
on using their current TVs longer. Eventually consumers would replace their televisions as they wore
out or became obsolete. Therefore, we expect the demand for durables to be more elastic in the short
run than in the long run.
7. Are the following statements true or false? Explain your answers.
a. The elasticity of demand is the same as the slope of the demand curve.
False. Elasticity of demand is the percentage change in quantity demanded divided by the
percentage change in the price of the product. In contrast, the slope of the demand curve is the
change in quantity demanded (in units) divided by the change in price (typically in dollars).
The difference is that elasticity uses percentage changes while the slope is based on changes
in the number of units and number of dollars.
b. The cross-price elasticity will always be positive.
False. The cross-price elasticity measures the percentage change in the quantity demanded of
one good due to a 1% change in the price of another good. This elasticity will be positive for
substitutes (an increase in the price of hot dogs is likely to cause an increase in the quantity
demanded of hamburgers) and negative for complements (an increase in the price of hot dogs is
likely to cause a decrease in the quantity demanded of hot dog buns).
c. The supply of apartments is more inelastic in the short run than the long run.
True. In the short run it is difficult to change the supply of apartments in response to a change in
price. Increasing the supply requires constructing new apartment buildings, which can take a year
or more. Therefore, the elasticity of supply is more inelastic in the short run than in the long run.
Loading page 15...
Chapter 2 The Basics of Supply and Demand 13
8. Suppose the government regulates the prices of beef and chicken and sets them below their
market-clearing levels. Explain why shortages of these goods will develop and what factors will
determine the sizes of the shortages. What will happen to the price of pork? Explain briefly.
If the price of a commodity is set below its market-clearing level, the quantity that firms are willing to
supply is less than the quantity that consumers wish to purchase. The extent of the resulting shortage
depends on the elasticities of demand and supply as well as the amount by which the regulated price
is set below the market-clearing price. For instance, if both supply and demand are elastic, the shortage
is larger than if both are inelastic, and if the regulated price is substantially below the market-clearing
price, the shortage is larger than if the regulated price is only slightly below the market-clearing price.
Factors such as the willingness of consumers to eat less meat and the ability of farmers to reduce the
size of their herds/flocks will determine the relevant elasticities. Customers whose demands for
beef and chicken are not met because of the shortages will want to purchase substitutes like pork.
This increases the demand for pork (i.e., shifts demand to the right), which results in a higher price
for pork.
9. The city council of a small college town decides to regulate rents in order to reduce student
living expenses. Suppose the average annual market-clearing rent for a two-bedroom apartment
had been $700 per month and that rents were expected to increase to $900 within a year. The
city council limits rents to their current $700-per-month level.
a. Draw a supply and demand graph to illustrate what will happen to the rental price of an
apartment after the imposition of rent controls.
Initially demand is D1 and supply is S, so the equilibrium rent is $700 and Q1 apartments are
rented. Without regulation, demand was expected to increase to D2, which would have raised
rent to $900 and resulted in Q2 apartment rentals. Under the city council regulation, however,
the rental price stays at the old equilibrium level of $700 per month. After demand increases to
D2, only Q1 apartments will be supplied while Q3 will be demanded. There will be a shortage of
Q3 Q1 apartments.
a. Do you think this policy will benefit all students? Why or why not?
No. It will benefit those students who get an apartment, although these students may find that the
cost of searching for an apartment is higher given the shortage of apartments. Those students who
do not get an apartment may face higher costs as a result of having to live outside the college
town. Their rent may be higher and their transportation costs will be higher, so they will be worse
off as a result of the policy.
8. Suppose the government regulates the prices of beef and chicken and sets them below their
market-clearing levels. Explain why shortages of these goods will develop and what factors will
determine the sizes of the shortages. What will happen to the price of pork? Explain briefly.
If the price of a commodity is set below its market-clearing level, the quantity that firms are willing to
supply is less than the quantity that consumers wish to purchase. The extent of the resulting shortage
depends on the elasticities of demand and supply as well as the amount by which the regulated price
is set below the market-clearing price. For instance, if both supply and demand are elastic, the shortage
is larger than if both are inelastic, and if the regulated price is substantially below the market-clearing
price, the shortage is larger than if the regulated price is only slightly below the market-clearing price.
Factors such as the willingness of consumers to eat less meat and the ability of farmers to reduce the
size of their herds/flocks will determine the relevant elasticities. Customers whose demands for
beef and chicken are not met because of the shortages will want to purchase substitutes like pork.
This increases the demand for pork (i.e., shifts demand to the right), which results in a higher price
for pork.
9. The city council of a small college town decides to regulate rents in order to reduce student
living expenses. Suppose the average annual market-clearing rent for a two-bedroom apartment
had been $700 per month and that rents were expected to increase to $900 within a year. The
city council limits rents to their current $700-per-month level.
a. Draw a supply and demand graph to illustrate what will happen to the rental price of an
apartment after the imposition of rent controls.
Initially demand is D1 and supply is S, so the equilibrium rent is $700 and Q1 apartments are
rented. Without regulation, demand was expected to increase to D2, which would have raised
rent to $900 and resulted in Q2 apartment rentals. Under the city council regulation, however,
the rental price stays at the old equilibrium level of $700 per month. After demand increases to
D2, only Q1 apartments will be supplied while Q3 will be demanded. There will be a shortage of
Q3 Q1 apartments.
a. Do you think this policy will benefit all students? Why or why not?
No. It will benefit those students who get an apartment, although these students may find that the
cost of searching for an apartment is higher given the shortage of apartments. Those students who
do not get an apartment may face higher costs as a result of having to live outside the college
town. Their rent may be higher and their transportation costs will be higher, so they will be worse
off as a result of the policy.
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14 Pindyck/Rubinfeld, Microeconomics, Ninth Edition
10. In a discussion of tuition rates, a university official argues that the demand for admission is
completely price inelastic. As evidence, she notes that while the university has doubled its
tuition (in real terms) over the past 15 years, neither the number nor quality of students
applying has decreased. Would you accept this argument? Explain briefly. (Hint: The official
makes an assertion about the demand for admission, but does she actually observe a demand
curve? What else could be going on?)
I would not accept this argument. The university official assumes that demand has remained stable
(i.e., the demand curve has not shifted) over the 15-year period. This seems very unlikely. Demand
for college educations has increased over the years for many reasons—real incomes have increased,
population has increased, the perceived value of a college degree has increased, etc. What has
probably happened is that tuition doubled from T1 to T2, but demand also increased from D1 to D2
over the 15 years, and the two effects have offset each other. The result is that the quantity (and
quality) of applications has remained steady at A. The demand curve is not perfectly inelastic as
the official asserts.
11. Suppose the demand curve for a product is given by Q 10 2P PS, where P is the price of
the product and PS is the price of a substitute good. The price of the substitute good is $2.00.
a. Suppose P $1.00. What is the price elasticity of demand? What is the cross-price elasticity
of demand?
Find quantity demanded when P $1.00 and PS $2.00. Q 10 2(1) 2 10.
Price elasticity of demand 1 2
( 2) 0.2.
10 10
P Q
Q P
Cross-price elasticity of demand 2 (1) 0.2.
10
s
s
P Q
Q P
b. Suppose the price of the good, P, goes to $2.00. Now what is the price elasticity of demand?
What is the cross-price elasticity of demand?
When P $2.00, Q 10 2(2) 2 8.
Price elasticity of demand 2 4
( 2) 0.5.
8 8
P Q
Q P
Cross-price elasticity of demand 2 (1) 0.25.
8
s
s
P Q
Q P
10. In a discussion of tuition rates, a university official argues that the demand for admission is
completely price inelastic. As evidence, she notes that while the university has doubled its
tuition (in real terms) over the past 15 years, neither the number nor quality of students
applying has decreased. Would you accept this argument? Explain briefly. (Hint: The official
makes an assertion about the demand for admission, but does she actually observe a demand
curve? What else could be going on?)
I would not accept this argument. The university official assumes that demand has remained stable
(i.e., the demand curve has not shifted) over the 15-year period. This seems very unlikely. Demand
for college educations has increased over the years for many reasons—real incomes have increased,
population has increased, the perceived value of a college degree has increased, etc. What has
probably happened is that tuition doubled from T1 to T2, but demand also increased from D1 to D2
over the 15 years, and the two effects have offset each other. The result is that the quantity (and
quality) of applications has remained steady at A. The demand curve is not perfectly inelastic as
the official asserts.
11. Suppose the demand curve for a product is given by Q 10 2P PS, where P is the price of
the product and PS is the price of a substitute good. The price of the substitute good is $2.00.
a. Suppose P $1.00. What is the price elasticity of demand? What is the cross-price elasticity
of demand?
Find quantity demanded when P $1.00 and PS $2.00. Q 10 2(1) 2 10.
Price elasticity of demand 1 2
( 2) 0.2.
10 10
P Q
Q P
Cross-price elasticity of demand 2 (1) 0.2.
10
s
s
P Q
Q P
b. Suppose the price of the good, P, goes to $2.00. Now what is the price elasticity of demand?
What is the cross-price elasticity of demand?
When P $2.00, Q 10 2(2) 2 8.
Price elasticity of demand 2 4
( 2) 0.5.
8 8
P Q
Q P
Cross-price elasticity of demand 2 (1) 0.25.
8
s
s
P Q
Q P
Loading page 17...
Chapter 2 The Basics of Supply and Demand 15
12. Suppose that rather than the declining demand assumed in Example 2.8, a decrease in the cost
of copper production causes the supply curve to shift to the right by 40%. How will the price of
copper change?
If the supply curve shifts to the right by 40% then the new quantity supplied will be 140% of the old
quantity supplied at every price. The new supply curve is therefore the old supply curve multiplied
by 1.4.
QS 1.4 (9 9P) 12.6 12.6P. To find the new equilibrium price of copper, set the new supply
equal to demand. Thus, –12.6 12.6P 27 3P. Solving for price results in P $2.54 per pound for
the new equilibrium price. The price decreased by 46 cents per pound, from $3.00 to $2.54, a drop of
about 15.3%.
13. Suppose the demand for natural gas is perfectly inelastic. What would be the effect, if any, of
natural gas price controls?
If the demand for natural gas is perfectly inelastic, the demand curve is vertical. Consumers will
demand the same quantity regardless of price. In this case, price controls will have no effect on the
quantity demanded, but they will still cause a shortage if the supply curve is upward sloping and the
regulated price is set below the market-clearing price, because suppliers will produce less natural gas
than consumers wish to purchase.
Exercises
1. Suppose the demand curve for a product is given by Q 300 2P 4I, where I is average
income measured in thousands of dollars. The supply curve is Q 3P 50.
a. If I 25, find the market-clearing price and quantity for the product.
Given I 25, the demand curve becomes Q 300 − 2P 4(25), or Q 400 − 2P. Set demand
equal to supply and solve for P and then Q:
400 2P 3P 50
P 90
Q 400 2(90) 220.
b. If I 50, find the market-clearing price and quantity for the product.
Given I 50, the demand curve becomes Q 300 2P 4(50), or Q 500 2P. Setting demand
equal to supply, solve for P and then Q:
500 2P 3P 50
P 110
Q 500 2(110) 280.
c. Draw a graph to illustrate your answers.
It is easier to draw the demand and supply curves if you first solve for the inverse demand and
supply functions, i.e., solve the functions for P. Demand in part a is P 200 0.5Q and supply
is P 16.67 0.333Q. These are shown on the graph as Da and S. Equilibrium price and quantity
are found at the intersection of these demand and supply curves. When the income level increases
12. Suppose that rather than the declining demand assumed in Example 2.8, a decrease in the cost
of copper production causes the supply curve to shift to the right by 40%. How will the price of
copper change?
If the supply curve shifts to the right by 40% then the new quantity supplied will be 140% of the old
quantity supplied at every price. The new supply curve is therefore the old supply curve multiplied
by 1.4.
QS 1.4 (9 9P) 12.6 12.6P. To find the new equilibrium price of copper, set the new supply
equal to demand. Thus, –12.6 12.6P 27 3P. Solving for price results in P $2.54 per pound for
the new equilibrium price. The price decreased by 46 cents per pound, from $3.00 to $2.54, a drop of
about 15.3%.
13. Suppose the demand for natural gas is perfectly inelastic. What would be the effect, if any, of
natural gas price controls?
If the demand for natural gas is perfectly inelastic, the demand curve is vertical. Consumers will
demand the same quantity regardless of price. In this case, price controls will have no effect on the
quantity demanded, but they will still cause a shortage if the supply curve is upward sloping and the
regulated price is set below the market-clearing price, because suppliers will produce less natural gas
than consumers wish to purchase.
Exercises
1. Suppose the demand curve for a product is given by Q 300 2P 4I, where I is average
income measured in thousands of dollars. The supply curve is Q 3P 50.
a. If I 25, find the market-clearing price and quantity for the product.
Given I 25, the demand curve becomes Q 300 − 2P 4(25), or Q 400 − 2P. Set demand
equal to supply and solve for P and then Q:
400 2P 3P 50
P 90
Q 400 2(90) 220.
b. If I 50, find the market-clearing price and quantity for the product.
Given I 50, the demand curve becomes Q 300 2P 4(50), or Q 500 2P. Setting demand
equal to supply, solve for P and then Q:
500 2P 3P 50
P 110
Q 500 2(110) 280.
c. Draw a graph to illustrate your answers.
It is easier to draw the demand and supply curves if you first solve for the inverse demand and
supply functions, i.e., solve the functions for P. Demand in part a is P 200 0.5Q and supply
is P 16.67 0.333Q. These are shown on the graph as Da and S. Equilibrium price and quantity
are found at the intersection of these demand and supply curves. When the income level increases
Loading page 18...
16 Pindyck/Rubinfeld, Microeconomics, Ninth Edition
in part b, the demand curve shifts up and to the right. Inverse demand is P 250 0.5Q and is
labeled Db. The intersection of the new demand curve and original supply curve is the new
equilibrium point.
2. Consider a competitive market for which the quantities demanded and supplied (per year) at
various prices are given as follows:
Price (Dollars) Demand (Millions) Supply (Millions)
60 22 14
80 20 16
100 18 18
120 16 20
a. Calculate the price elasticity of demand when the price is $80 and when the price is $100.
.
D
D D
D
D
Q
Q QP
E P Q P
P
With each price increase of $20, the quantity demanded decreases by 2 million. Therefore,
2 0.1.
20
DQ
P
At P 80, quantity demanded is 20 million and thus
80 ( 0.1) 0.40.
20
DE
Similarly, at P 100, quantity demanded equals 18 million and
100 ( 0.1) 0.56.
18
DE
in part b, the demand curve shifts up and to the right. Inverse demand is P 250 0.5Q and is
labeled Db. The intersection of the new demand curve and original supply curve is the new
equilibrium point.
2. Consider a competitive market for which the quantities demanded and supplied (per year) at
various prices are given as follows:
Price (Dollars) Demand (Millions) Supply (Millions)
60 22 14
80 20 16
100 18 18
120 16 20
a. Calculate the price elasticity of demand when the price is $80 and when the price is $100.
.
D
D D
D
D
Q
Q QP
E P Q P
P
With each price increase of $20, the quantity demanded decreases by 2 million. Therefore,
2 0.1.
20
DQ
P
At P 80, quantity demanded is 20 million and thus
80 ( 0.1) 0.40.
20
DE
Similarly, at P 100, quantity demanded equals 18 million and
100 ( 0.1) 0.56.
18
DE
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Chapter 2 The Basics of Supply and Demand 17
b. Calculate the price elasticity of supply when the price is $80 and when the price is $100.
.
S
S S
S
S
Q
Q QP
E P Q P
P
With each price increase of $20, quantity supplied increases by 2 million. Therefore,
2 0.1.
20
SQ
P
At P 80, quantity supplied is 16 million and
80 (0.1) 0.5.
16
SE
Similarly, at P 100, quantity supplied equals 18 million and
100 (0.1) 0.56.
18
SE
c. What are the equilibrium price and quantity?
The equilibrium price is the price at which the quantity supplied equals the quantity demanded.
Using the table, the equilibrium price is P* $100 and the equilibrium quantity is Q* 18 million.
d. Suppose the government sets a price ceiling of $80. Will there be a shortage, and if so, how
large will it be?
With a price ceiling of $80, price cannot be above $80, so the market cannot reach its equilibrium
price of $100. At $80, consumers would like to buy 20 million, but producers will supply only
16 million. This will result in a shortage of 4 million units.
3. Refer to Example 2.5 (page 37) on the market for wheat. In 1998, the total demand for U.S.
wheat was Q 3244 283P and the domestic supply was QS 1944 207P. At the end of 1998,
both Brazil and Indonesia opened their wheat markets to U.S. farmers. Suppose that these new
markets add 200 million bushels to U.S. wheat demand. What will be the free-market price of
wheat and what quantity will be produced and sold by U.S. farmers?
If Brazil and Indonesia add 200 million bushels of wheat to U.S. wheat demand, the new demand
curve will be Q 200, or
QD (3244 283P) 200 3444 283P.
Equate supply and the new demand to find the new equilibrium price.
1944 207P 3444 283P, or
490P 1500, and thus P $3.06 per bushel.
To find the equilibrium quantity, substitute the price into either the supply or demand equation.
Using demand,
QD 3444 283(3.06) 2578 million bushels.
b. Calculate the price elasticity of supply when the price is $80 and when the price is $100.
.
S
S S
S
S
Q
Q QP
E P Q P
P
With each price increase of $20, quantity supplied increases by 2 million. Therefore,
2 0.1.
20
SQ
P
At P 80, quantity supplied is 16 million and
80 (0.1) 0.5.
16
SE
Similarly, at P 100, quantity supplied equals 18 million and
100 (0.1) 0.56.
18
SE
c. What are the equilibrium price and quantity?
The equilibrium price is the price at which the quantity supplied equals the quantity demanded.
Using the table, the equilibrium price is P* $100 and the equilibrium quantity is Q* 18 million.
d. Suppose the government sets a price ceiling of $80. Will there be a shortage, and if so, how
large will it be?
With a price ceiling of $80, price cannot be above $80, so the market cannot reach its equilibrium
price of $100. At $80, consumers would like to buy 20 million, but producers will supply only
16 million. This will result in a shortage of 4 million units.
3. Refer to Example 2.5 (page 37) on the market for wheat. In 1998, the total demand for U.S.
wheat was Q 3244 283P and the domestic supply was QS 1944 207P. At the end of 1998,
both Brazil and Indonesia opened their wheat markets to U.S. farmers. Suppose that these new
markets add 200 million bushels to U.S. wheat demand. What will be the free-market price of
wheat and what quantity will be produced and sold by U.S. farmers?
If Brazil and Indonesia add 200 million bushels of wheat to U.S. wheat demand, the new demand
curve will be Q 200, or
QD (3244 283P) 200 3444 283P.
Equate supply and the new demand to find the new equilibrium price.
1944 207P 3444 283P, or
490P 1500, and thus P $3.06 per bushel.
To find the equilibrium quantity, substitute the price into either the supply or demand equation.
Using demand,
QD 3444 283(3.06) 2578 million bushels.
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18 Pindyck/Rubinfeld, Microeconomics, Ninth Edition
4. A vegetable fiber is traded in a competitive world market, and the world price is $9 per pound.
Unlimited quantities are available for import into the United States at this price. The U.S.
domestic supply and demand for various price levels are shown as follows:
Price
U.S. Supply
(Million LBS)
U.S. Demand
(Million LBS)
3 2 34
6 4 28
9 6 22
12 8 16
15 10 10
18 12 4
a. What is the equation for demand? What is the equation for supply?
The equation for demand is of the form Q a bP. First find the slope, which is
6 2 .
3
Q b
P
You can figure this out by noticing that every time price increases by 3,
quantity demanded falls by 6 million pounds. Demand is now Q a 2P. To find a, plug in any
of the price and quantity demanded points from the table. For example: Q 34 a 2(3) so that
a 40 and demand is therefore Q 40 2P.
The equation for supply is of the form Q c dP. First find the slope, which is 2 .
3
Q d
P
You can figure this out by noticing that every time price increases by 3, quantity supplied
increases by 2 million pounds. Supply is now 2 .
3
Q c P To find c, plug in any of the price
and quantity supplied points from the table. For example: 2
2 (3)
3
Q c so that c 0 and
supply is 2 .
3
Q P
b. At a price of $9, what is the price elasticity of demand? What is it at a price of $12?
Elasticity of demand at P 9 is 9 18
( 2) 0.82.
22 22
P Q
Q P
Elasticity of demand at P 12 is 12 24
( 2) 1.5.
16 16
P Q
Q P
c. What is the price elasticity of supply at $9? At $12?
Elasticity of supply at P 9 is 9 2 18 1.0.
6 3 18
P Q
Q P
Elasticity of supply at P 12 is 12 2 24 1.0.
8 3 24
P Q
Q P
4. A vegetable fiber is traded in a competitive world market, and the world price is $9 per pound.
Unlimited quantities are available for import into the United States at this price. The U.S.
domestic supply and demand for various price levels are shown as follows:
Price
U.S. Supply
(Million LBS)
U.S. Demand
(Million LBS)
3 2 34
6 4 28
9 6 22
12 8 16
15 10 10
18 12 4
a. What is the equation for demand? What is the equation for supply?
The equation for demand is of the form Q a bP. First find the slope, which is
6 2 .
3
Q b
P
You can figure this out by noticing that every time price increases by 3,
quantity demanded falls by 6 million pounds. Demand is now Q a 2P. To find a, plug in any
of the price and quantity demanded points from the table. For example: Q 34 a 2(3) so that
a 40 and demand is therefore Q 40 2P.
The equation for supply is of the form Q c dP. First find the slope, which is 2 .
3
Q d
P
You can figure this out by noticing that every time price increases by 3, quantity supplied
increases by 2 million pounds. Supply is now 2 .
3
Q c P To find c, plug in any of the price
and quantity supplied points from the table. For example: 2
2 (3)
3
Q c so that c 0 and
supply is 2 .
3
Q P
b. At a price of $9, what is the price elasticity of demand? What is it at a price of $12?
Elasticity of demand at P 9 is 9 18
( 2) 0.82.
22 22
P Q
Q P
Elasticity of demand at P 12 is 12 24
( 2) 1.5.
16 16
P Q
Q P
c. What is the price elasticity of supply at $9? At $12?
Elasticity of supply at P 9 is 9 2 18 1.0.
6 3 18
P Q
Q P
Elasticity of supply at P 12 is 12 2 24 1.0.
8 3 24
P Q
Q P
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Chapter 2 The Basics of Supply and Demand 19
d. In a free market, what will be the U.S. price and level of fiber imports?
With no restrictions on trade, the price in the United States will be the same as the world price,
so P $9. At this price, the domestic supply is 6 million lbs., while the domestic demand is
22 million lbs. Imports make up the difference and are thus 22 6 = 16 million lbs.
5. Much of the demand for U.S. agricultural output has come from other countries. In 1998, the
total demand for wheat was Q 3244 283P. Of this, total domestic demand was QD 1700
107P, and domestic supply was QS 1944 207P. Suppose the export demand for wheat falls
by 40%.
a. U.S. farmers are concerned about this drop in export demand. What happens to the free-
market price of wheat in the United States? Do farmers have much reason to worry?
Before the drop in export demand, the market equilibrium price is found by setting total demand
equal to domestic supply:
3244 283P 1944 207P, or
P $2.65.
Export demand is the difference between total demand and domestic demand: Q 3244 283P
minus QD 1700 107P. So export demand is originally Qe 1544 176P. After the 40% drop,
export demand is only 60% of the original export demand. The new export demand is therefore,
Q′e 0.6Qe 0.6(1544 176P) 926.4 105.6P. Graphically, export demand has pivoted
inward as illustrated in the figure below.
The new total demand becomes
Q′ QD Q′e (1700 107P) (926.4 105.6P) 2626.4 212.6P.
Equating total supply and the new total demand,
1944 207P 2626.4 212.6P, or
P $1.63,
which is a significant drop from the original market-clearing price of $2.65 per bushel. At this
price, the market-clearing quantity is about Q 2281 million bushels. Total revenue has
decreased from about $6609 million to $3718 million, so farmers have a lot to worry about.
d. In a free market, what will be the U.S. price and level of fiber imports?
With no restrictions on trade, the price in the United States will be the same as the world price,
so P $9. At this price, the domestic supply is 6 million lbs., while the domestic demand is
22 million lbs. Imports make up the difference and are thus 22 6 = 16 million lbs.
5. Much of the demand for U.S. agricultural output has come from other countries. In 1998, the
total demand for wheat was Q 3244 283P. Of this, total domestic demand was QD 1700
107P, and domestic supply was QS 1944 207P. Suppose the export demand for wheat falls
by 40%.
a. U.S. farmers are concerned about this drop in export demand. What happens to the free-
market price of wheat in the United States? Do farmers have much reason to worry?
Before the drop in export demand, the market equilibrium price is found by setting total demand
equal to domestic supply:
3244 283P 1944 207P, or
P $2.65.
Export demand is the difference between total demand and domestic demand: Q 3244 283P
minus QD 1700 107P. So export demand is originally Qe 1544 176P. After the 40% drop,
export demand is only 60% of the original export demand. The new export demand is therefore,
Q′e 0.6Qe 0.6(1544 176P) 926.4 105.6P. Graphically, export demand has pivoted
inward as illustrated in the figure below.
The new total demand becomes
Q′ QD Q′e (1700 107P) (926.4 105.6P) 2626.4 212.6P.
Equating total supply and the new total demand,
1944 207P 2626.4 212.6P, or
P $1.63,
which is a significant drop from the original market-clearing price of $2.65 per bushel. At this
price, the market-clearing quantity is about Q 2281 million bushels. Total revenue has
decreased from about $6609 million to $3718 million, so farmers have a lot to worry about.
Loading page 22...
20 Pindyck/Rubinfeld, Microeconomics, Ninth Edition
b. Now suppose the U.S. government wants to buy enough wheat to raise the price to $3.50 per
bushel. With the drop in export demand, how much wheat would the government have to
buy? How much would this cost the government?
With a price of $3.50, the market is not in equilibrium. Quantity demanded and supplied are
Q′ 2626.4 212.6(3.50) 1882.3, and
QS 1944 207(3.50) 2668.5.
Excess supply is therefore 2668.5 1882.3 786.2 million bushels. The government must
purchase this amount to support a price of $3.50, and will have to spend $3.50(786.2 million)
$2751.7 million.
6. The rent control agency of New York City has found that aggregate demand is QD 160 8P.
Quantity is measured in tens of thousands of apartments. Price, the average monthly rental
rate, is measured in hundreds of dollars. The agency also noted that the increase in Q at lower P
results from more three-person families coming into the city from Long Island and demanding
apartments. The city’s board of realtors acknowledges that this is a good demand estimate and
has shown that supply is QS 70 7P.
a. If both the agency and the board are right about demand and supply, what is the free-
market price? What is the change in city population if the agency sets a maximum average
monthly rent of $300 and all those who cannot find an apartment leave the city?
Set supply equal to demand to find the free-market price for apartments:
160 8P 70 7P, or P 6,
which means the rental price is $600 since price is measured in hundreds of dollars. Substituting
the equilibrium price into either the demand or supply equation to determine the equilibrium
quantity:
QD 160 8(6) 112
and
QS 70 7(6) 112.
The quantity of apartments rented is 1,120,000 since Q is measured in tens of thousands of
apartments. If the rent control agency sets the rental rate at $300, the quantity supplied would
be 910,000 (QS 70 7(3) 91), a decrease of 210,000 apartments from the free-market
equilibrium. Assuming three people per family per apartment, this would imply a loss in city
population of 630,000 people. Note: At the $300 rental rate, the demand for apartments is
1,360,000 units, and the resulting shortage is 450,000 units (1,360,000 910,000). However,
excess demand (the shortage) and lower quantity demanded are not the same concept. The
shortage of 450,000 units is the difference between the number of apartments demanded at the
new lower price (including the number demanded by new people who would have moved into
the city), and the number supplied at the lower price. But these new people will not actually
move into the city because the apartments are not available. Therefore, the city population will
fall by 630,000, which is due to the drop in the number of apartments available from 1,120,000
(the old equilibrium value) to 910,000.
b. Now suppose the U.S. government wants to buy enough wheat to raise the price to $3.50 per
bushel. With the drop in export demand, how much wheat would the government have to
buy? How much would this cost the government?
With a price of $3.50, the market is not in equilibrium. Quantity demanded and supplied are
Q′ 2626.4 212.6(3.50) 1882.3, and
QS 1944 207(3.50) 2668.5.
Excess supply is therefore 2668.5 1882.3 786.2 million bushels. The government must
purchase this amount to support a price of $3.50, and will have to spend $3.50(786.2 million)
$2751.7 million.
6. The rent control agency of New York City has found that aggregate demand is QD 160 8P.
Quantity is measured in tens of thousands of apartments. Price, the average monthly rental
rate, is measured in hundreds of dollars. The agency also noted that the increase in Q at lower P
results from more three-person families coming into the city from Long Island and demanding
apartments. The city’s board of realtors acknowledges that this is a good demand estimate and
has shown that supply is QS 70 7P.
a. If both the agency and the board are right about demand and supply, what is the free-
market price? What is the change in city population if the agency sets a maximum average
monthly rent of $300 and all those who cannot find an apartment leave the city?
Set supply equal to demand to find the free-market price for apartments:
160 8P 70 7P, or P 6,
which means the rental price is $600 since price is measured in hundreds of dollars. Substituting
the equilibrium price into either the demand or supply equation to determine the equilibrium
quantity:
QD 160 8(6) 112
and
QS 70 7(6) 112.
The quantity of apartments rented is 1,120,000 since Q is measured in tens of thousands of
apartments. If the rent control agency sets the rental rate at $300, the quantity supplied would
be 910,000 (QS 70 7(3) 91), a decrease of 210,000 apartments from the free-market
equilibrium. Assuming three people per family per apartment, this would imply a loss in city
population of 630,000 people. Note: At the $300 rental rate, the demand for apartments is
1,360,000 units, and the resulting shortage is 450,000 units (1,360,000 910,000). However,
excess demand (the shortage) and lower quantity demanded are not the same concept. The
shortage of 450,000 units is the difference between the number of apartments demanded at the
new lower price (including the number demanded by new people who would have moved into
the city), and the number supplied at the lower price. But these new people will not actually
move into the city because the apartments are not available. Therefore, the city population will
fall by 630,000, which is due to the drop in the number of apartments available from 1,120,000
(the old equilibrium value) to 910,000.
Loading page 23...
Chapter 2 The Basics of Supply and Demand 21
b. Suppose the agency bows to the wishes of the board and sets a rental of $900 per month on
all apartments to allow landlords a “fair” rate of return. If 50% of any long-run increases
in apartment offerings come from new construction, how many apartments are constructed?
At a rental rate of $900, the demand for apartments would be 160 8(9) 88, or 880,000 units,
which is 240,000 fewer apartments than the original free-market equilibrium number of
1,120,000. Therefore, no new apartments would be constructed.
7. In 2010, Americans smoked 315 billion cigarettes, or 15.75 billion packs of cigarettes. The
average retail price (including taxes) was about $5.00 per pack. Statistical studies have shown
that the price elasticity of demand is 0.4, and the price elasticity of supply is 0.5.
a. Using this information, derive linear demand and supply curves for the cigarette market.
Let the demand curve be of the form Q a bP and the supply curve be of the form Q c dP,
where a, b, c, and d are positive constants. To begin, recall the formula for the price elasticity of
demand
.D
P
P Q
E Q P
We know the demand elasticity is –0.4, P 5, and Q 15.75, which means we can solve for the
slope, −b, which is Q/P in the above formula.
5
0.4 15.75
15.75
0.4 1.26 .
5
Q
P
Q b
P
To find the constant a, substitute for Q, P, and b in the demand function to get 15.75 a 1.26(5),
so a 22.05. The equation for demand is therefore Q 22.05 1.26P. To find the supply curve,
recall the formula for the elasticity of supply and follow the same method as above:
5
0.5 15.75
15.75
0.5 1.575 .
5
S
P
P Q
E Q P
Q
P
Q d
P
To find the constant c, substitute for Q, P, and d in the supply function to get 15.75 c 1.575(5)
and c 7.875. The equation for supply is therefore Q 7.875 1.575P.
b. In 1998, Americans smoked 23.5 billion packs cigarettes, and the retail price was about
$2.00 per pack. The decline in cigarette consumption from 1998 to 2010 was due in part to
greater public awareness of the health hazards from smoking, but was also due in part to
the increase in price. Suppose that the entire decline was due to the increase in price. What
could you deduce from that about the price elasticity of demand?
Calculate the arc elasticity of demand since we have a range of prices rather than a single price.
The arc elasticity formula is
P
Q P
E P Q
b. Suppose the agency bows to the wishes of the board and sets a rental of $900 per month on
all apartments to allow landlords a “fair” rate of return. If 50% of any long-run increases
in apartment offerings come from new construction, how many apartments are constructed?
At a rental rate of $900, the demand for apartments would be 160 8(9) 88, or 880,000 units,
which is 240,000 fewer apartments than the original free-market equilibrium number of
1,120,000. Therefore, no new apartments would be constructed.
7. In 2010, Americans smoked 315 billion cigarettes, or 15.75 billion packs of cigarettes. The
average retail price (including taxes) was about $5.00 per pack. Statistical studies have shown
that the price elasticity of demand is 0.4, and the price elasticity of supply is 0.5.
a. Using this information, derive linear demand and supply curves for the cigarette market.
Let the demand curve be of the form Q a bP and the supply curve be of the form Q c dP,
where a, b, c, and d are positive constants. To begin, recall the formula for the price elasticity of
demand
.D
P
P Q
E Q P
We know the demand elasticity is –0.4, P 5, and Q 15.75, which means we can solve for the
slope, −b, which is Q/P in the above formula.
5
0.4 15.75
15.75
0.4 1.26 .
5
Q
P
Q b
P
To find the constant a, substitute for Q, P, and b in the demand function to get 15.75 a 1.26(5),
so a 22.05. The equation for demand is therefore Q 22.05 1.26P. To find the supply curve,
recall the formula for the elasticity of supply and follow the same method as above:
5
0.5 15.75
15.75
0.5 1.575 .
5
S
P
P Q
E Q P
Q
P
Q d
P
To find the constant c, substitute for Q, P, and d in the supply function to get 15.75 c 1.575(5)
and c 7.875. The equation for supply is therefore Q 7.875 1.575P.
b. In 1998, Americans smoked 23.5 billion packs cigarettes, and the retail price was about
$2.00 per pack. The decline in cigarette consumption from 1998 to 2010 was due in part to
greater public awareness of the health hazards from smoking, but was also due in part to
the increase in price. Suppose that the entire decline was due to the increase in price. What
could you deduce from that about the price elasticity of demand?
Calculate the arc elasticity of demand since we have a range of prices rather than a single price.
The arc elasticity formula is
P
Q P
E P Q
Loading page 24...
22 Pindyck/Rubinfeld, Microeconomics, Ninth Edition
where P and Q are average price and quantity, respectively. The change in quantity was
15.75 23.5 7.75, and the change in price was 5 2 3. The average price was (2 5)/2
3.50, and the average quantity was (23.5 15.75)/2 19.625. Therefore, the price elasticity of
demand, assuming that the entire decline in quantity was due solely to the price increase, was
7.75 3.50 0.46.
3 19.625
P
Q P
E P Q
8. In Example 2.8 we examined the effect of a 20% decline in copper demand on the price of
copper, using the linear supply and demand curves developed in Section 2.6. Suppose the long-
run price elasticity of copper demand was 0.75 instead of 0.5.
a. Assuming, as before, that the equilibrium price and quantity are P* $3 per pound and
Q* 18 million metric tons per year, derive the linear demand curve consistent with the
smaller elasticity.
Following the method outlined in Section 2.6, solve for a and b in the demand equation
QD a bP. Because b is the slope, we can use b rather than Q/P in the elasticity
formula. Therefore, * .
*
D
P
E b Q
Here ED 0.75 (the long-run price elasticity), P* 3
and Q* 18. Solving for b,
3
0.75 ,
18
b
or b 0.75(6) 4.5.
To find the intercept, we substitute for b, QD ( Q*), and P ( P*) in the demand equation:
18 a 4.5(3), or a 31.5.
The linear demand equation is therefore
QD 31.5 4.5P.
b. Using this demand curve, recalculate the effect of a 55% decline in copper demand on the
price of copper.
The new demand is 55% below the original (using our convention that quantity demanded is
reduced by 55% at every price); therefore, multiply demand by 0.45 because the new demand is
only 45% of the original demand:
Equating this to supply,
14.175 2.025P 9 9P, so
P $2.10.
With the 55% decline in demand, the price of copper falls from $3.00 to $2.10 per pound. The
decrease in demand therefore leads to a drop in price of 90 cents per pound, a 30% decline.
where P and Q are average price and quantity, respectively. The change in quantity was
15.75 23.5 7.75, and the change in price was 5 2 3. The average price was (2 5)/2
3.50, and the average quantity was (23.5 15.75)/2 19.625. Therefore, the price elasticity of
demand, assuming that the entire decline in quantity was due solely to the price increase, was
7.75 3.50 0.46.
3 19.625
P
Q P
E P Q
8. In Example 2.8 we examined the effect of a 20% decline in copper demand on the price of
copper, using the linear supply and demand curves developed in Section 2.6. Suppose the long-
run price elasticity of copper demand was 0.75 instead of 0.5.
a. Assuming, as before, that the equilibrium price and quantity are P* $3 per pound and
Q* 18 million metric tons per year, derive the linear demand curve consistent with the
smaller elasticity.
Following the method outlined in Section 2.6, solve for a and b in the demand equation
QD a bP. Because b is the slope, we can use b rather than Q/P in the elasticity
formula. Therefore, * .
*
D
P
E b Q
Here ED 0.75 (the long-run price elasticity), P* 3
and Q* 18. Solving for b,
3
0.75 ,
18
b
or b 0.75(6) 4.5.
To find the intercept, we substitute for b, QD ( Q*), and P ( P*) in the demand equation:
18 a 4.5(3), or a 31.5.
The linear demand equation is therefore
QD 31.5 4.5P.
b. Using this demand curve, recalculate the effect of a 55% decline in copper demand on the
price of copper.
The new demand is 55% below the original (using our convention that quantity demanded is
reduced by 55% at every price); therefore, multiply demand by 0.45 because the new demand is
only 45% of the original demand:
Equating this to supply,
14.175 2.025P 9 9P, so
P $2.10.
With the 55% decline in demand, the price of copper falls from $3.00 to $2.10 per pound. The
decrease in demand therefore leads to a drop in price of 90 cents per pound, a 30% decline.
Loading page 25...
Chapter 2 The Basics of Supply and Demand 23
9. In Example 2.8 (page 52), we discussed the recent decline in world demand for copper, due in
part to China’s decreasing consumption. What would happen, however, if China’s demand
were increasing?
a. Using the original elasticities of demand and supply (i.e., ES 1.5 and ED 0.5), calculate
the effect of a 20% increase in copper demand on the price of copper.
The original demand is Q 27 3P and supply is Q 9 9P as shown on page 51. The
20% increase in demand means that the new demand is 120% of the original demand, so the
new demand is QD 1.2Q. QD (1.2)(27 3P) 32.4 3.6P. The new equilibrium is where
QD equals the original supply:
32.4 3.6P 9 9P.
The new equilibrium price is P* $3.29 per pound. An increase in demand of 20%, therefore,
entails an increase in price of 29 cents per pound, or 9.7%.
b. Now calculate the effect of this increase in demand on the equilibrium quantity, Q*.
Using the new price of $3.29 in the supply curve, the new equilibrium quantity is Q* 9
9(3.29) 20.61 million metric tons per year, an increase of 2.61 million metric tons (mmt)
per year. Except for rounding, you get the same result by plugging the new price of $3.29 into
the new demand curve. So an increase in demand of 20% entails an increase in quantity
of 2.61 mmt per year, or 14.5%.
c. As we discussed in Example 2.8, the U.S. production of copper declined between 2000 and
2003. Calculate the effect on the equilibrium price and quantity of both a 20% increase in
copper demand (as you just did in part a) and of a 20% decline in copper supply.
The new supply of copper falls (shifts to the left) to 80% of the original, so QS 0.8Q
(0.8)(9 9P) 7.2 7.2P. The new equilibrium is where QD QS.
32.4 3.6P 7.2 7.2P
The new equilibrium price is P* $3.67 per pound. Plugging this price into the new supply
equation, the new equilibrium quantity is Q* 7.2 7.2(3.67) 19.22 million metric tons
per year. Except for rounding, you get the same result if you substitute the new price into the
new demand equation. The combined effect of a 20% increase in demand and a 20% decrease
in supply is that price increases by 67 cents per pound, or 22%, and quantity increases by 1.22
mmt per year, or 6.8%, compared to the original equilibrium.
10. Example 2.9 (page 54) analyzes the world oil market. Using the data given in that example:
a. Show that the short-run demand and competitive supply curves are indeed given by
D 36.75 0.035P
SC 21.85 0.023P.
The competitive (non-OPEC) quantity supplied is Sc Q* 23. The general form for the linear
competitive supply equation is SC c dP. We can write the short-run supply elasticity as
ES d(P*/Q*). Since ES 0.05, P* $50, and Q* 23, 0.05 d(50/23). Hence d 0.023.
Substituting for d, Sc, and P in the supply equation, c 21.85, and the short-run competitive
supply equation is Sc 21.85 0.023P.
9. In Example 2.8 (page 52), we discussed the recent decline in world demand for copper, due in
part to China’s decreasing consumption. What would happen, however, if China’s demand
were increasing?
a. Using the original elasticities of demand and supply (i.e., ES 1.5 and ED 0.5), calculate
the effect of a 20% increase in copper demand on the price of copper.
The original demand is Q 27 3P and supply is Q 9 9P as shown on page 51. The
20% increase in demand means that the new demand is 120% of the original demand, so the
new demand is QD 1.2Q. QD (1.2)(27 3P) 32.4 3.6P. The new equilibrium is where
QD equals the original supply:
32.4 3.6P 9 9P.
The new equilibrium price is P* $3.29 per pound. An increase in demand of 20%, therefore,
entails an increase in price of 29 cents per pound, or 9.7%.
b. Now calculate the effect of this increase in demand on the equilibrium quantity, Q*.
Using the new price of $3.29 in the supply curve, the new equilibrium quantity is Q* 9
9(3.29) 20.61 million metric tons per year, an increase of 2.61 million metric tons (mmt)
per year. Except for rounding, you get the same result by plugging the new price of $3.29 into
the new demand curve. So an increase in demand of 20% entails an increase in quantity
of 2.61 mmt per year, or 14.5%.
c. As we discussed in Example 2.8, the U.S. production of copper declined between 2000 and
2003. Calculate the effect on the equilibrium price and quantity of both a 20% increase in
copper demand (as you just did in part a) and of a 20% decline in copper supply.
The new supply of copper falls (shifts to the left) to 80% of the original, so QS 0.8Q
(0.8)(9 9P) 7.2 7.2P. The new equilibrium is where QD QS.
32.4 3.6P 7.2 7.2P
The new equilibrium price is P* $3.67 per pound. Plugging this price into the new supply
equation, the new equilibrium quantity is Q* 7.2 7.2(3.67) 19.22 million metric tons
per year. Except for rounding, you get the same result if you substitute the new price into the
new demand equation. The combined effect of a 20% increase in demand and a 20% decrease
in supply is that price increases by 67 cents per pound, or 22%, and quantity increases by 1.22
mmt per year, or 6.8%, compared to the original equilibrium.
10. Example 2.9 (page 54) analyzes the world oil market. Using the data given in that example:
a. Show that the short-run demand and competitive supply curves are indeed given by
D 36.75 0.035P
SC 21.85 0.023P.
The competitive (non-OPEC) quantity supplied is Sc Q* 23. The general form for the linear
competitive supply equation is SC c dP. We can write the short-run supply elasticity as
ES d(P*/Q*). Since ES 0.05, P* $50, and Q* 23, 0.05 d(50/23). Hence d 0.023.
Substituting for d, Sc, and P in the supply equation, c 21.85, and the short-run competitive
supply equation is Sc 21.85 0.023P.
Loading page 26...
24 Pindyck/Rubinfeld, Microeconomics, Ninth Edition
Similarly, world demand is D a bP, and the short-run demand elasticity is ED b(P*/Q*),
where Q* is total world demand of 35. Therefore, 0.05 b(50/35), and b 0.035. Substituting
b 0.035, D 35, and P 50 in the demand equation gives 35 a 0.035(50), so that a 36.75.
Hence the short-run world demand equation is D 36.75 0.035P.
b. Show that the long-run demand and competitive supply curves are indeed given by
D 45.5 0.210P
SC 16.1 0.138P.
Do the same calculations as above but now using the long-run elasticities, ES 0.30 and ED
0.30: ES d(P*/Q*) and ED b(P*/Q*), implying 0.30 d(50/23) and 0.30 b(50/35).
So d 0.138 and b 0.210.
Next solve for c and a: Sc c dP and D a bP, implying 23 c 0.138(50) and 35
a 0.210(50). So c 16.1 and a 45.5.
c. In Example 2.9 we examined the impact on price of a disruption of oil from Saudi Arabia.
Suppose that instead of a decline in supply, OPEC production increases by 2 billion barrels
per year (bb/yr) because the Saudis open large new oil fields. Calculate the effect of this
increase in production on the supply of oil in both the short run and the long run.
OPEC’s supply increases from 12 bb/yr to 14 bb/yr as a result. Add 14 bb/yr to the short-run
and long-run competitive supply equations. The new total supply equations are:
Short-run: ST
14 Sc 14 21.85 0.023P 35.85 0.023P, and
Long-run: ST
14 Sc 14 16.1 0.138P 30.1 0.138P.
These are equated with short-run and long-run demand, so that:
35.85 0.023P 36.75 0.035P, implying that P $15.52 in the short run, and
30.1 0.138P 45.5 0.210P, implying that P $44.25 in the long run.
In the short run, total supply is 35.85 0.023(15.52) 36.21 bb/yr. In the long run, total supply
remains the same at 30.1 0.138(44.25) 36.21 bb/yr. Compared to current total supply of 35
bb/yr, supply increases by 1.21 bb/yr.
11. Refer to Example 2.10 (page 59), which analyzes the effects of price controls on natural gas.
a. Using the data in the example, show that the following supply and demand curves describe
the market for natural gas in 2005–2007:
Supply: Q 15.90 0.72PG 0.05PO
Demand: Q 0.02 1.8PG 0.69PO
Also, verify that if the price of oil is $50, these curves imply a free-market price of $6.40 for
natural gas.
To solve this problem, apply the analysis of Section 2.6 using the definition of cross-price
elasticity of demand given in Section 2.4. For example, the cross-price elasticity of demand
for natural gas with respect to the price of oil is:
.G O
GO
O G
Q P
E P Q
Similarly, world demand is D a bP, and the short-run demand elasticity is ED b(P*/Q*),
where Q* is total world demand of 35. Therefore, 0.05 b(50/35), and b 0.035. Substituting
b 0.035, D 35, and P 50 in the demand equation gives 35 a 0.035(50), so that a 36.75.
Hence the short-run world demand equation is D 36.75 0.035P.
b. Show that the long-run demand and competitive supply curves are indeed given by
D 45.5 0.210P
SC 16.1 0.138P.
Do the same calculations as above but now using the long-run elasticities, ES 0.30 and ED
0.30: ES d(P*/Q*) and ED b(P*/Q*), implying 0.30 d(50/23) and 0.30 b(50/35).
So d 0.138 and b 0.210.
Next solve for c and a: Sc c dP and D a bP, implying 23 c 0.138(50) and 35
a 0.210(50). So c 16.1 and a 45.5.
c. In Example 2.9 we examined the impact on price of a disruption of oil from Saudi Arabia.
Suppose that instead of a decline in supply, OPEC production increases by 2 billion barrels
per year (bb/yr) because the Saudis open large new oil fields. Calculate the effect of this
increase in production on the supply of oil in both the short run and the long run.
OPEC’s supply increases from 12 bb/yr to 14 bb/yr as a result. Add 14 bb/yr to the short-run
and long-run competitive supply equations. The new total supply equations are:
Short-run: ST
14 Sc 14 21.85 0.023P 35.85 0.023P, and
Long-run: ST
14 Sc 14 16.1 0.138P 30.1 0.138P.
These are equated with short-run and long-run demand, so that:
35.85 0.023P 36.75 0.035P, implying that P $15.52 in the short run, and
30.1 0.138P 45.5 0.210P, implying that P $44.25 in the long run.
In the short run, total supply is 35.85 0.023(15.52) 36.21 bb/yr. In the long run, total supply
remains the same at 30.1 0.138(44.25) 36.21 bb/yr. Compared to current total supply of 35
bb/yr, supply increases by 1.21 bb/yr.
11. Refer to Example 2.10 (page 59), which analyzes the effects of price controls on natural gas.
a. Using the data in the example, show that the following supply and demand curves describe
the market for natural gas in 2005–2007:
Supply: Q 15.90 0.72PG 0.05PO
Demand: Q 0.02 1.8PG 0.69PO
Also, verify that if the price of oil is $50, these curves imply a free-market price of $6.40 for
natural gas.
To solve this problem, apply the analysis of Section 2.6 using the definition of cross-price
elasticity of demand given in Section 2.4. For example, the cross-price elasticity of demand
for natural gas with respect to the price of oil is:
.G O
GO
O G
Q P
E P Q
Loading page 27...
Chapter 2 The Basics of Supply and Demand 25
G
O
Q
P
is the change in the quantity of natural gas demanded because of a small change in
the price of oil, and for linear demand equations, it is constant. If we represent demand as
–G G OQ a bP eP (notice that income is held constant), then .G
O
Q e
P
Substituting this into
the cross-price elasticity, *
* ,O
GO
G
P
E e Q
where *
OP and *
GQ are the equilibrium price and quantity.
We know that * $50oP and * 23GQ trillion cubic feet (Tcf). Solving for e,
50
1.5 ,
23
e
or e 0.69.
Similarly, representing the supply equation as ,G G OQ c dP gP the cross-price elasticity of
supply is *
* ,O
G
P
g Q
which we know to be 0.1. Solving for g,
23
50
1.0 g , or g 0.5 rounded to
one decimal place.
We know that ES 0.2, PG* 6.40, and Q* 23. Therefore,
23
40.6
2.0 d , or d 0.72. Also,
ED 0.5, so
23
40.6
5.0 b , and thus b 1.8.
By substituting these values for d, g, b, and e into our linear supply and demand equations, we
may solve for c and a:
23 c 0.72(6.40) 0.05(50), so c 15.9, and
23 a 1.8(6.40) 0.69(50), so that a 0.02.
Therefore, the supply and demand curves for natural gas are as given. If the price of oil is $50,
these curves imply a free-market price of $6.40 for natural gas as shown below. Substitute the
price of oil in the supply and demand equations. Then set supply equal to demand and solve for
the price of gas.
15.9 0.72PG 0.05(50) 0.02 1.8PG 0.69(50)
18.4 0.72PG 34.52 1.8PG
PG $6.40.
b. Suppose the regulated price of gas were $4.50 per thousand cubic feet instead of $3.00. How
much excess demand would there have been?
With a regulated price of $4.50 for natural gas and the price of oil equal to $50 per barrel,
Demand: QD 0.02 − 1.8(4.50) 0.69(50) 26.4, and
Supply: QS 15.9 0.72(4.50) 0.05(50) 21.6
With a demand of 26.4 Tcf and a supply of 21.6 Tcf, there would be an excess demand (i.e., a
shortage) of 4.8 Tcf.
G
O
Q
P
is the change in the quantity of natural gas demanded because of a small change in
the price of oil, and for linear demand equations, it is constant. If we represent demand as
–G G OQ a bP eP (notice that income is held constant), then .G
O
Q e
P
Substituting this into
the cross-price elasticity, *
* ,O
GO
G
P
E e Q
where *
OP and *
GQ are the equilibrium price and quantity.
We know that * $50oP and * 23GQ trillion cubic feet (Tcf). Solving for e,
50
1.5 ,
23
e
or e 0.69.
Similarly, representing the supply equation as ,G G OQ c dP gP the cross-price elasticity of
supply is *
* ,O
G
P
g Q
which we know to be 0.1. Solving for g,
23
50
1.0 g , or g 0.5 rounded to
one decimal place.
We know that ES 0.2, PG* 6.40, and Q* 23. Therefore,
23
40.6
2.0 d , or d 0.72. Also,
ED 0.5, so
23
40.6
5.0 b , and thus b 1.8.
By substituting these values for d, g, b, and e into our linear supply and demand equations, we
may solve for c and a:
23 c 0.72(6.40) 0.05(50), so c 15.9, and
23 a 1.8(6.40) 0.69(50), so that a 0.02.
Therefore, the supply and demand curves for natural gas are as given. If the price of oil is $50,
these curves imply a free-market price of $6.40 for natural gas as shown below. Substitute the
price of oil in the supply and demand equations. Then set supply equal to demand and solve for
the price of gas.
15.9 0.72PG 0.05(50) 0.02 1.8PG 0.69(50)
18.4 0.72PG 34.52 1.8PG
PG $6.40.
b. Suppose the regulated price of gas were $4.50 per thousand cubic feet instead of $3.00. How
much excess demand would there have been?
With a regulated price of $4.50 for natural gas and the price of oil equal to $50 per barrel,
Demand: QD 0.02 − 1.8(4.50) 0.69(50) 26.4, and
Supply: QS 15.9 0.72(4.50) 0.05(50) 21.6
With a demand of 26.4 Tcf and a supply of 21.6 Tcf, there would be an excess demand (i.e., a
shortage) of 4.8 Tcf.
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26 Pindyck/Rubinfeld, Microeconomics, Ninth Edition
c. Suppose that the market for natural gas remained unregulated. If the price of oil had
increased from $50 to $100, what would have happened to the free-market price of
natural gas?
In this case
Demand: QD 0.02 1.8PG 0.69(100) 69.02 1.8PG, and
Supply: QS 15.9 0.72PG 0.05(100) 20.9 0.72PG.
Equating supply and demand and solving for the equilibrium price,
20.9 0.72PG 69.02 – 1.8PG, or PG $19.10.
The free-market price of natural gas would have almost tripled from $6.40 to $19.10.
12. The table below shows the retail price and sales for instant coffee and roasted coffee for two
years.
Year
Retail Price of
Instant Coffee
($/LB)
Sales of Instant
Coffee
(Million LBs)
Retail Price of
Roasted Coffee
($/LB)
Sales of
Roasted Coffee
(Million LBs)
Year 1 10.35 75 4.11 820
Year 2 10.48 70 3.76 850
a. Using these data alone, estimate the short-run price elasticity of demand for roasted coffee.
Derive a linear demand curve for roasted coffee.
To find elasticity, first estimate the slope of the demand curve:
820 850 30 85.7
4.11 3.76 0.35
Q
P
Given the slope, we can now estimate elasticity using the price and quantity data from the above
table. Assuming the demand curve is linear, the elasticity will differ between the two years
because price and quantity are different. We can calculate the elasticities at both points and also
find the arc elasticity at the average point between the two years:
1
2
4.11( 85.7) 0.043
820
3.76 ( 85.7) 0.038
850
3.935 ( 85.7) 0.040.
835
P
P
ARC
P
P Q
E Q P
P Q
E Q P
P Q
E Q P
To derive the demand curve for roasted coffee, Q a bP, note that the slope of the demand
curve is 85.7 b. To find the coefficient a, use either of the data points from the table above
so that 820 a 85.7(4.11) or 850 a 85.7(3.76). In either case, a 1172.2. The equation for
the demand curve is therefore
Q 1172.2 85.7P.
c. Suppose that the market for natural gas remained unregulated. If the price of oil had
increased from $50 to $100, what would have happened to the free-market price of
natural gas?
In this case
Demand: QD 0.02 1.8PG 0.69(100) 69.02 1.8PG, and
Supply: QS 15.9 0.72PG 0.05(100) 20.9 0.72PG.
Equating supply and demand and solving for the equilibrium price,
20.9 0.72PG 69.02 – 1.8PG, or PG $19.10.
The free-market price of natural gas would have almost tripled from $6.40 to $19.10.
12. The table below shows the retail price and sales for instant coffee and roasted coffee for two
years.
Year
Retail Price of
Instant Coffee
($/LB)
Sales of Instant
Coffee
(Million LBs)
Retail Price of
Roasted Coffee
($/LB)
Sales of
Roasted Coffee
(Million LBs)
Year 1 10.35 75 4.11 820
Year 2 10.48 70 3.76 850
a. Using these data alone, estimate the short-run price elasticity of demand for roasted coffee.
Derive a linear demand curve for roasted coffee.
To find elasticity, first estimate the slope of the demand curve:
820 850 30 85.7
4.11 3.76 0.35
Q
P
Given the slope, we can now estimate elasticity using the price and quantity data from the above
table. Assuming the demand curve is linear, the elasticity will differ between the two years
because price and quantity are different. We can calculate the elasticities at both points and also
find the arc elasticity at the average point between the two years:
1
2
4.11( 85.7) 0.043
820
3.76 ( 85.7) 0.038
850
3.935 ( 85.7) 0.040.
835
P
P
ARC
P
P Q
E Q P
P Q
E Q P
P Q
E Q P
To derive the demand curve for roasted coffee, Q a bP, note that the slope of the demand
curve is 85.7 b. To find the coefficient a, use either of the data points from the table above
so that 820 a 85.7(4.11) or 850 a 85.7(3.76). In either case, a 1172.2. The equation for
the demand curve is therefore
Q 1172.2 85.7P.
Loading page 29...
Chapter 2 The Basics of Supply and Demand 27
b. Now estimate the short-run price elasticity of demand for instant coffee. Derive a linear
demand curve for instant coffee.
To find elasticity, first estimate the slope of the demand curve:
75 70 5 38.5
10.35 10.48 0.13
Q
P
Given the slope, we can now estimate elasticity using the price and quantity data from the above
table. Assuming demand is of the form Q a − bP, the elasticity will differ in the two years
because price and quantity are different. The elasticities at both points and at the average point
between the two years are:
1
2
10.35 ( 38.5) 5.31
75
10.48 ( 38.5) 5.76
70
10.415 ( 38.5) 5.53.
72.5
P
P
ARC
P
P Q
E Q P
P Q
E Q P
P Q
E Q P
To derive the demand curve for instant coffee, note that the slope of the demand curve
is 38.5 b. To find the coefficient a, use either of the data points from the table above
so that a 75 38.5(10.35) 473.5 or a 70 38.5(10.48) 473.5. The equation for the
demand curve is therefore
Q 473.5 38.5P.
c. Which coffee has the higher short-run price elasticity of demand? Why do you think this is
the case?
Instant coffee is significantly more elastic than roasted coffee. In fact, the demand for roasted
coffee is inelastic and the demand for instant coffee is highly elastic. Roasted coffee may have
an inelastic demand in the short run because many people think of coffee as a necessary good.
Changes in the price of roasted coffee will not drastically affect the quantity demanded because
people want their roasted coffee. Many people, on the other hand, may view instant coffee as a
convenient, though imperfect and somewhat inferior, substitute for roasted coffee. So if the price
of instant coffee rises, the quantity demanded will fall by a large percentage because many
people will decide to switch to roasted coffee instead of paying more for a lower quality
substitute.
b. Now estimate the short-run price elasticity of demand for instant coffee. Derive a linear
demand curve for instant coffee.
To find elasticity, first estimate the slope of the demand curve:
75 70 5 38.5
10.35 10.48 0.13
Q
P
Given the slope, we can now estimate elasticity using the price and quantity data from the above
table. Assuming demand is of the form Q a − bP, the elasticity will differ in the two years
because price and quantity are different. The elasticities at both points and at the average point
between the two years are:
1
2
10.35 ( 38.5) 5.31
75
10.48 ( 38.5) 5.76
70
10.415 ( 38.5) 5.53.
72.5
P
P
ARC
P
P Q
E Q P
P Q
E Q P
P Q
E Q P
To derive the demand curve for instant coffee, note that the slope of the demand curve
is 38.5 b. To find the coefficient a, use either of the data points from the table above
so that a 75 38.5(10.35) 473.5 or a 70 38.5(10.48) 473.5. The equation for the
demand curve is therefore
Q 473.5 38.5P.
c. Which coffee has the higher short-run price elasticity of demand? Why do you think this is
the case?
Instant coffee is significantly more elastic than roasted coffee. In fact, the demand for roasted
coffee is inelastic and the demand for instant coffee is highly elastic. Roasted coffee may have
an inelastic demand in the short run because many people think of coffee as a necessary good.
Changes in the price of roasted coffee will not drastically affect the quantity demanded because
people want their roasted coffee. Many people, on the other hand, may view instant coffee as a
convenient, though imperfect and somewhat inferior, substitute for roasted coffee. So if the price
of instant coffee rises, the quantity demanded will fall by a large percentage because many
people will decide to switch to roasted coffee instead of paying more for a lower quality
substitute.
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PART TWO
Producers, Consumers,
and Competitive Markets
Producers, Consumers,
and Competitive Markets
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Subject
Economics