Overview
Consumer Choice Problem Set
1. For each of the following examples, a consumer buys only two goods: x and y. Based on the information given in the following parts, sketch a plausible set of indifference curves (draw at least two curves on a set of labeled axes, and indicate the direction of higher utility with an arrow). Write down a utility function U(x,y) that is consistent with your graph. (2 points each, Total 8 points)
(a)I like both x and y.
(b)I like x, but I hate y.
(c)I like x, but I am indifferent to y.
(d)I only ever like x and y paired together.
2. Mr. Jones is deciding on what shade of white to paint his garage. He prefers eggshell white over ivory, beige and bone. At the paint store, he finds two new shades: cream and taupe. Mr. Jones prefers cream over eggshell white, taupe over eggshell white, and cream over taupe. The store is sold out of cream, so he buys taupe and paints his garage with it. Mr. Jones then goes back to the store, buys beige and repaints his garage. Does Mr. Jones have rational preferences? (5 points)
3. Louis has stable preferences (the same every year) and consumes two goods, wine and cheese. In 1994, the price of wine was $3 per glass and the price of cheese was $2 per ounce. Louis’s income was $60 and he bought 14 glasses of wine and 9 ounces of cheese. In 1995, wine costs $2 per glass and cheese costs $3 per ounce. Louis’s income is still $60.
(a) Draw both years’ budget lines. Where do they cross? (4 points)
Let w be glasses of wine, and c be ounces of cheese.
1994 budget: 3w + 2c = 60. 1995 budget: 2w + 3c = 60.
(b) What is Louis’s marginal rate of substitution of wine and cheese in 1994? The MRS of “wine for cheese” means that we treat wine as the x variable and cheese as the y variable. (4 points)
(c) Explain carefully how we know that in 1995, Louis will definitely not buy exactly 10 glasses of wine. (4 points)
4. Tickets to a Cubs playoff game are sold out and available only on a black-market basis. Sally and Mike are big Cubs fans and work together at a local bar. Mike tells Sally that he will go buy some tickets and asks her how many she wants.
Sally replies: “If the price per ticket is $150, buy one ticket for me. If the price per ticket is $100, buy two tickets for me. And, if the price per ticket is $50, buy three tickets for me.”
Mike responds: “What are you talking about? You’re saying you’re willing to pay more in total for two tickets than for three. You are behaving irrationally.”
Evaluate Mike’s statement. Is Sally behaving irrationally? (5 points)
5. Andy purchases two goods, apples (a) and kumquats (k). He has income of $40 and can buy apples at $2 per pound and kumquats at $4 per pound. His utility function is U(a, k) = 3a + 5k.
a. What is his marginal utility for apples and his marginal utility for kumquats? (5 points)
b. What bundle of apples and kumquats should he purchase to maximize