EC 203.01 PS: CH 4 FALL 2006
1. With quasilinear preferences, the slope of indifference curves is constant along all rays through the origin. FALSE
2. Dr. Jack Shepard consumes only two goods and hates them both. His utility function is U(x, y) = 2max{x, y}. Dr. Shepard has (weakly) convex preferences. TRUE
3. Kate’s utility function is U(x, y) = x + y 2 – y. If we draw her indifference curves with x on the horizontal axis and y on the vertical axis, then these indifference curves are everywhere downward sloping and get flatter as one moves from left to right. FALSE
4. Hurley’s utility function is U(x, y) = 32xy. He has 10 units of good x and 8 units of good y. Sayed’s utility function for the same two goods is U(x, y) = 3x + 5y. Sayed has 9 units of x and 13 units of y.
a. Sayed prefers Hurley’s bundle to his own, but Hurley prefers his own bundle to Sayed’s.
b. Each prefers the other’s bundle to his own.
c. Neither prefers the other’s bundle to his own.
d. Hurley prefers Sayed’s bundle to his own bundle, but Sayed prefers his own bundle to Hurley’s.
e. Since they have different preferences, there is not enough information to determine who envies whom. D
5. Sawyer’s utility function is U(x, y) = max{ 2x – y, 2y – x}.
a. Sawyer’s preferences are quasilinear.
b. If Sawyer has more x than y, any increase in his consumption of y would lower his utility.
c. If Sawyer has more x than y, a decrease in his consumption of y would raise his utility.
d. Sawyer always prefers more of each good to less.
e. Goods x and y are perfect substitutes. B
6. Charlie consumes only goods 1 and 2. His utility function is U(x1, x2) = x1 + x2 + min{x1, x2}. Each of Charlie’s indifference curves is
a. L-shaped.
b. made up of three line segments with slopes –2, –1, and –.
c. made up of two line segments with slopes –2 and –.
d. is smooth and has no kinks.
e. is a diamond-shaped figure consisting of four line segments. C
7. John likes to have the same amount of x as he has of y. His utility function is U(x, y) = min{2x– y, 2y– x}.
a. Draw the indifference curve for John that passes through the bundle (0, 0) and the indifference curve that passes through (4, 4). (Hint: Each indifference curve is the intersection of two line segments.)
b. If John has a bundle that he likes better than (0, 0) and his consumption of both goods is doubled, is John better off?
c. Does John always prefer more of either good to less?
a. John’s indifference curves are V-shaped. The one through the origin consists of the two rays y = 2x and x = 2y. The one through (2, 2) has two rays going out from (2, 2), one with slope and theother with slope 2.
b. Yes.
c. No. If x > y, then an increase in x by itself makes John worse off, and if y > x, an increase in y by itself makes him worse off.
8. A consumer has a utility function of the form U(x, y) =x a + y b, where both a and b are nonnegative. What additional restrictions on the values of the parameters a and b are imposed by each of the following assumptions?
a. Preferences are quasilinear and convex, and x is a normal good.
b. Preferences are homothetic.
c. Preferences are homothetic and convex.
d. Goods x and y are perfect substitutes.
a. a = 1 and b is between 0 and 1.
b. a = b.
c. a = b and a is between 0 and 1.
d. a = b = 1.
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