EC 203 PS: CH 6FALL 2005
1.A consumer has the utility function U(x, y) = min{x, 2y}. If the price of good x is zero and the price of good y is p, then the consumer's demand function for good y is m/2p. True or false? False
2.When other variables are held fixed, the demand for a Giffen good rises when income increases.FALSE
3.If preferences are homothetic, then the slope of the Engel curve for any good will decrease as income increases. False
4.Ms. Trinity's preferences between golf and tennis are represented by U(g, t) = gt, where g is the number of rounds of golf and t is the number of tennis matches she plays per week. She has $24 per week to spend on these sports. A round of golf and a tennis match each cost $4. She used to maximize her utility subject to this budget. She decided to limit the time she spends on these sports to 16 hours a week.A round of golf takes 4 hours. A tennis match takes 2 hours. As a result of this additional constraint on her choice,
a. she plays 1 less round of golf and 1 more tennis match each week.
b. she plays more golf and less tennis, but can't say how much.
c. her choices and her utility are unchanged.
d. she plays 2 less rounds of golf and 3 more rounds of tennis per week.
e. there is too little information to tell about her choices.A
5.Neo insists on consuming 2 units of whey per 1 unit of curds. If the price of curds is $5 and the price of whey is $6, then if Neo's income is m, his demand for curds will be
a. 5c + 6w = m.
b. 6m/5.
c. 5m.
d. m/5.
e. m/17.E
6.Morpheus has a utility function U(x1,x2)=40x11/2+x2, wherex1 is his consumption of nuts and x2 is his consumption of berries. His income is $115, the price of nuts is $5, and the price of berries is $1. How many units of berries will Morpheus demand? 35
7. Agent Smith's utility function is U(x, y) = min{4x + y, 2x + 2y, x + 4y}. Agent Smith is consuming 12 units of x and 6 units of y.
a. Draw the indifference curve through this point. At what points does this indifference curve have kinks?
b. The price of good x is $1. What is the highest possible price for y? What is the lowest possible price for y?
a. Indifference curve is a broken line extending from (36, 0) to (12, 6) to (6, 12) to (0, 36).(soldan saga sırayla: -4x, -x, -x/4)b. The price of y must be between $1 and $4.
8. With some services, e.g., checking accounts, phone service, or pay TV, a consumer is offered a choice of two or more payment plans. One can either pay a high entry fee and get a low price per unit of service or pay a low entry fee and a high price per unit of service. Suppose you have an income of 100YTL. There are two plans. Plan A has an entry fee of 20YTL with a price of 2YTL per unit. Plan B has an entry fee of40YTL with a price of 1YTL per unit for using the service. Let x be expenditure on other goods and y be consumption of the service.
a. Write down the budget equation that you would have after you paid the entry fee for each of the two plans.
b. If your utility function is xy, how much y would you choose in each case?
c. Which plan would you prefer? Explain.
a. x + 2y = 80, x + y = 60. b. 20, 30.
c. Plan B. The utility of the bundle chosen with A is 20(40) = 800 and the utility from the Plan B bundle is 30(30) = 900.
9.Oracle has the utility function U = min{4x, 2y}. Write down her demand function for x as a function of the variables m, px , and py , where m is income, px is the price of x, and py is the price of y.
x = m/(px + 2py).