1.) If two goods are both desirable and preferences are strictly convex, then: a
ID: 1137494 • Letter: 1
Question
1.) If two goods are both desirable and preferences are strictly convex, then:
a. there must be a kink in the indifference curves.
b. indifference curves must be straight lines.
c. if two bundles are indifferent, then an average of the two bundles is worse than either one.
d. the marginal rate of substitution is not constant along indifference curves.
e. None of the above.
2) Preferences are said to be monotonic if
a. all goods must be consumed in fixed proportions.
b. all goods are perfect substitutes.
c. there is a diminishing marginal rate of substitution.
d. more is always preferred to less.
e. all of the above.
3) Charlie’s indifference curves have the equation xB = c/xA where larger constant c denote better indifference curves. Charlie strictly prefers the bundle (10, 17) to
a. the bundle (11, 16).
b. the bundle (17, 10).
c. the bundle (11, 15).
d. more than one of these bundles.
e. none of these bundles.
4) Mary’s utility function is U(x, y) = 25xy. She has 12 units of good x and 8 units of good y. Ben’s utility function for the same two goods is U(x, y) = 4x + 4y. Ben has 9 units of x and 13 units of y.
a. Mary prefers Ben’s bundle to her own bundle, but Ben prefers his own bundle to Mary’s.
b. Ben prefers Mary’s bundle to his own, but Mary prefers her own bundle to Ben’s.
c. Each prefers the other’s bundle to his/her own.
d. Neither prefers the other’s bundle to his/her own.
e. Since they have different preferences, there is not enough information to determine who envies whom.
5) Martha has preferences represented by the utility function U(x, y) = 10x + 5y. She consumes 10 units of good x and 9 units of good y. If her consumption of good x is lowered to 1, how many units of y must she have in order to be exactly as well off as before?
a. 20
b. 30
c. 27
d. 18
e. None of the above.
6) Henry’s utility function is x 2 + 16xw + 64w 2 , where x is his consumption of x and w is his consumption of w. Set the utility function equal to a constant, say k and then try to solve one in terms of the other.
a. Henry’s preferences are nonconvex.
b. Henry’s indifference curves are straight lines.
c. Henry has a bliss point.
d. Henry’s indifference curves are hyperbolas.
e. None of the above.
7) Alex’s utility function is U(x1, x2) = x1x2. His income is 100 dollars. The price of good 2 is p2 = 4. Good 1 is priced as follows. The first 15 units cost 4 dollars per unit and any additional units cost 2 dollars per unit. What consumption bundle does Alex choose?
a. (12.5, 12.5)
b. (25,12.5)
c. (12.5, 25)
d. (15, 10)
e. None of the above.
Answer the following question. 1) Draw graphs with quantities of pepperoni pizza on the horizontal axis and quantities of anchovy pizza on the vertical axis to illustrate the following situations. In each case draw two different indifference curves and make a little arrow pointing in the direction of greater preference. a. John loves pepperoni pizza and hates anchovy pizza. b. Jerry hates anchovy pizza and is completely indifferent about pepperoni pizza.
Explanation / Answer
1) d is correct
for strictly convex preferences, indifference curve is convex. The slope of indifference curve is marginal rate of substitution. For convex indifference curves, marginal rate of substitution decreases as one goes down along the indifference curve.
2) d is correct
Preferences are said to be monotonic if consumers always prefer more of both goods to bundles with less goods.
3) a is correct
Xb = C/Xa
C = Xa.Xb
with Xa= 10 and Xb=17
C= 10*17= 170
So any bundle which gives C greater than 170 are preferred.
when Xa is 11 and Xb is 16, C = 11*16= 176
this gives higher C
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