EC 203.01PS: CH 5FALL 2006
1. Serkan’s utility function is U(x, y) = (x + 2)(y + 1). If his consumption of both x and y are doubled, then his marginal rate of substitution between x and y remains constant.
2.Hüseyin’s utility function is U(x, y) = min{x + 2y, y + 2x}. He maximizes his utility subject to a budget constraint. If he chooses the bundle (5, 6), then the price of x must be exactly twice the price of y.
3.Kaya’s utility function is U(x, y) = min{x, y}. He maximizes his utility subject to a budget constraint. The price of x is the same as the price of y. If the price of x rises and the price of y and his income remain constant, then his consumption of y will certainly decrease.
4.Kerem’s utility function is min{x, 5y + 2z}. The price of x is $1, the price of y is $15, and the price of z is $7. Kerem’s income is $44. How many units of x does Kerem demand?
a. 9.78 b. 11 c. 5d. 3e. None of the above.
5. Ersan consumes tomatoes and nectarines. His indifference curves are kinky. When he is consuming more tomatoes than nectarines, he is just willing to trade 3 tomatoes for 1 nectarine. When he is consuming more nectarines than tomatoes, he is just willing to trade 4 nectarines for 1 tomato. Let P1 be the price of nectarines, and P2 the price of tomatoes. Ersan maximizes his utility subject to his budget constraint. (Hint: Sketch one of his indifference curves.)
a.When P1P2, he must consume only tomatoes.
b.When P1P2, he must consume 3 times as many tomatoes as nectarines.
c.When P1 > 3P2, he must consume only tomatoes.
d.When 4P1P2, he must consume only nectarines.
e.He must consume equal numbers of both.
6. Mehmet’s utility function is U(x, y) = x + 2y, where x is his consumption of good X and y is his consumption of good Y. His income is $2. The price of Y is $2. The cost per unit of X depends on how many units he buys. The total cost of x units of X is the square root of x.
a. The bundle () is Mehmet’s utility maximizing choice, given his budget.
b. The bundle () is Mehmet’s utility maximizing choice, given his budget.
c. Given his budget, Mehmet would maximize his utility by spending all of his income on good X.
d. Given his budget, Mehmet would maximize his utility by spending all of his income on good Y.
e. None of the above.
7. Hidayet consumes cocoa and cheese. Cocoa is sold in an unusual way. There is only one supplier, and the more cocoa you buy from him, the higher the price you have to pay per unit. In fact y units of cocoa will cost Hidayety2 dollars. Cheese is sold in the usual way at a price of 2 dollars per unit. Hidayet’s income is 20 dollars and his utility function is U(x, y) = x + 2y, where x is his consumption of cheese and y is his consumption of cocoa.
a. Sketch Hidayet’s budget set and shade it in.
b. Sketch some of his indifference curves and label the point that he chooses.
c. Calculate the amount of cheese and the amount of cocoa that Hidayet demands at these prices and this income.
8. İbrahim has a utility function U(x, y) = 2xy + 1. The prices of x and y are both $1 and İbrahim has an income of $20.
a. How much of each good will he demand?
b. A tax is placed on x so that x now costs İbrahim $2 while his income and the price of y stay the same. How much of good x does he now demand?
c. Would İbrahim be as well off as he was before the tax if when the tax was imposed, his income rose by an amount equal to $1 times the answer to part (b)?
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