Annie plans to buy a convertible this weekend. Her two favorite cars are the BMW Z3, which would give
her 150,000 utils of satisfaction, and the Mitsubishi Eclipse Spyder GS-T, which would give her only
124,000 utils of satisfaction. The BMW Z3 that she wants sells for $37,220, while the Mitsubishi sells for
$28,200. She can afford either car.
a. Which car will she buy in order to maximize her utility?
b. To what price will her second choice have to fall to get her to make it her first choice?
5. Ryan King just stopped at the Exxon station on the way to campus and bought four Butterfinger candy bars,
two 20-ounce bottles of grape-watermelon Snapple, and 10 gallons of gas. His marginal-utility-to-price
ratios are 3.21 for the Butterfingers, 4.8 for the Snapples, and 5.7 for the gas. Explain why this set of
purchases did not maximize Ryan’s utility and how he could have increased his utility.
6. Show, using utility theory, why a consumer who is initially maximizing her utility will alter her
consumption pattern in response to a change in the price of a good.
14. Assume f is a differentiable function, where the signs of f'(x) are as follows: f'(x) > 0 on (-0,-5) U (4,00) and f'(x) ,2, 0 on (-0,-5) U (4,00) and f(x)Apr 20 2021
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