1. Suppose you can hire your mechanic for up to six hours. The total benefit and total cost functions areB(H) = 654H- 40H2andC(H) = 110H+ 120H2. The corresponding formulas for marginal benefit and marginal cost areMB(H) = 654 - 80HandMC(H) = 110 + 240H. What is your best choice?
2. Suppose you can hire your mechanic for up to six hours. The total benefit and total cost functions are and C(H) = 100H. The corresponding formulas for marginal benefit and marginal cost are and MC(H) = 100. What is your best choice?
3. Suppose there are two types of food, meat and bread. Draw indifference curves for the following consumers.
a. Ed likes variety and prefers to eat meat and bread together.
b. Francis dislikes variety; she likes to eat the same thing all the time.
c. Mia is a vegetarian who doesn't care (one way or the other) about meat.
d. Taka, a sumo wrestler, cares only about the number of calories he consumes; he wants to consume as many calories as possible.
e. Larry loves to eat and enjoys variety, but he also wants to lose weight. He therefore thinks that food is a good at low quantities, and
a bad at high quantities.
4. John's MRS for reading books with watching movies is three movies per book regardless of the amounts consumed. Would he rather read two books and watch no movies, or read no books and watch two movies? What is the formula for his family of indifference curves? What do these curves look like? In this example, are movies and books perfect substitutes, perfect complements, or neither?
5. Kate has 25 Smarties and Antonio has 10 Gummies. Suppose Kate's MRS for Gummies with Smarties is four regardless of what she consumes, and that Antonio's is three regardless of what he consumes. Kate and Antonio trade until there is no further opportunity for mutual gain. Can you say anything about what they've traded (how many Smarties for how many Gummies)?
6. The price of bread is $6 per kilogram and Aaron's income is $180. He buys 15 kilograms of bread, 10 kilograms of butter, and nothing else. What is the price of butter? Draw Aaron's budget constraint and identify his chosen consumption bundle.
7. Olivia has received a $15 gift certificate that is redeemable only for roasted peanuts. Bags of roasted peanuts come in two sizes, regular and jumbo. A regular bag contains 30 peanuts and a jumbo bag contains 50. If a regular bag costs 50 cents and a jumbo bag costs 75 cents, how many of each will Olivia purchase? What if the jumbo bag costs $1? In each case, draw a budget line that shows her available choices, and indicate her best choice by adding indifference curves. Assume that Olivia cares only about the number of peanuts, and not about the size of the bag.
8. Given income of $400 and concert and movie ticket prices of $25 and $10 respectively, Elena is considering whether to attend 10 concerts and 15 movies. If Elena's MRSCFis equal to F/C would she maximize utility with this choice? If not, how many movies and concerts should she attend?
9. Regular- and extra-strength pain killers are perfect substitutes; one extra-strength tablet is equivalent to two regular-strength tablets. In each of the following cases, show graphically the effect of a compensated increase in the price of regular-strength tablets. Does this change alter the consumption of regular- or extra-strength tablets? What do your answers tell you about the size of the substitution effects resulting from increases in the price of regular-strength tablets?
10. Sam currently earns $30,000 a year. The government is considering a policy that would increase Sam's income by 12 percent, but raise all prices by 8 percent. What isSam's compensating variation for the proposed policy? Can you compute it without knowing his preferences? Why or why not?