Well Being
Econ 201
Homework 3
Emily Wiemers
All questions are worth 11 points—you all get one point for free.
1. The only DVD club available to you charges $4 per movie per day. If your demand curve for movie rentals is given by P=20-2Q, where P is the rental price ($/day) and Q is the quantity demanded (movies per year), what is the maximum annual membership fee you would be willing to pay to join this club? 2. Smith lives in a world with two time periods. His income in each period, is $210. If the interest rate is 0.05 (5%) draw his intertemporal budget constraint. Draw his intertemporal budget constraint when r=.20 (20%). 3. If Smith from problem 2 views current and future consumption as perfect one-for-one substitutes, find his optimal consumption bundle. 4. If Smith, from problem 2 views current and future consumption as perfect complements—that is he only enjoys current consumption if he can have the same amount of future consumption and vice versa—find his optimal consumption bundle. 5. Karen earns $75,000 in the current period and will earn $75,000 in the future. a. Assuming that these are the only two periods, and that banks will borrow and lend at rate r=0, draw her intertemporal budget constraint. b. Now draw her intertemporal budget constraint if banks will borrow and lend at 10%. 6. What is the expected value of a random toss of a dice (six sided and fair)? 7. A fair coin is flipped twice and the following payoffs are assigned to each of the four possible outcomes: Heads and Heads—Win 20, Heads and Tails—Win 9, Tails and Heads—Lose 7, Tails and Tails—Lose 16. What is the expected value of this gamble? 8. Suppose your utility function is given by U=(M)1/2 where M is your total wealth. If M has an initial value of 16, will you accept the gamble in the problem 7? 9. Suppose your current wealth M, is 100 and your utility function is given by U=M2. You have a lottery ticket that pays $10 with a
Homework 3
Emily Wiemers
All questions are worth 11 points—you all get one point for free.
1. The only DVD club available to you charges $4 per movie per day. If your demand curve for movie rentals is given by P=20-2Q, where P is the rental price ($/day) and Q is the quantity demanded (movies per year), what is the maximum annual membership fee you would be willing to pay to join this club? 2. Smith lives in a world with two time periods. His income in each period, is $210. If the interest rate is 0.05 (5%) draw his intertemporal budget constraint. Draw his intertemporal budget constraint when r=.20 (20%). 3. If Smith from problem 2 views current and future consumption as perfect one-for-one substitutes, find his optimal consumption bundle. 4. If Smith, from problem 2 views current and future consumption as perfect complements—that is he only enjoys current consumption if he can have the same amount of future consumption and vice versa—find his optimal consumption bundle. 5. Karen earns $75,000 in the current period and will earn $75,000 in the future. a. Assuming that these are the only two periods, and that banks will borrow and lend at rate r=0, draw her intertemporal budget constraint. b. Now draw her intertemporal budget constraint if banks will borrow and lend at 10%. 6. What is the expected value of a random toss of a dice (six sided and fair)? 7. A fair coin is flipped twice and the following payoffs are assigned to each of the four possible outcomes: Heads and Heads—Win 20, Heads and Tails—Win 9, Tails and Heads—Lose 7, Tails and Tails—Lose 16. What is the expected value of this gamble? 8. Suppose your utility function is given by U=(M)1/2 where M is your total wealth. If M has an initial value of 16, will you accept the gamble in the problem 7? 9. Suppose your current wealth M, is 100 and your utility function is given by U=M2. You have a lottery ticket that pays $10 with a