Consumer Choice, Demand Functions, And Welfare Analysis: A Case Study Of Jellybear Park And Transportation Modes

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Consumer Choice, Demand Functions, and Welfare Analysis: A Case Study of Jellybear Park andTransportation Modes1.(a) What is the formula for his demand functions for x1 and x2 (see lecture on 1-29-13)?u =𝑥10.33∗𝑥20.67We derived then theutility function by x1 and x2 :𝜕𝑢𝜕𝑥1=0.33𝑥1−0.67𝑥20.67𝜕𝑢𝜕𝑥2=0.67𝑥10.33𝑥2−0.33Let P1 and P2 the prices of x1 and c2, and M the income.We have :𝜕𝑢𝜕𝑥1𝑃1=𝜕𝑢𝜕𝑥2𝑃2And we have the following budget constraint :𝑥1𝑃1+𝑥2𝑃2=𝑀Hence :0.33𝑥1−0.67𝑥20.67𝑃2=0.67𝑥10.33𝑥2−0.33𝑃1𝑃2=2𝑥1𝑥2𝑃1Then :𝑥1𝑃1+2𝑥1𝑃1=𝑀𝑥1=𝑀3𝑃1And𝑥2=2𝑀3𝑃2(b) What is the income elasticity of demand for x1 with this demand function? (Hint: if incomeincreases by 10%, say, by how much does the demand for x1 increase?)

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