Home / Questions / Andrew’s utility function is U(x1, x2) ? 4x21 ? x2. Andrew’s income is $32, the price of g
Andrew’s utility function is U(x_{1}, x_{2}) ? 4x^{2}_{1} ? x_{2}. Andrew’s income is $32, the price of good 1 is $16 per unit, and the price of good 2 is $1 per unit. What happens if Andrew’s income increases to $80 and prices do not change? (Hint: Does he have convex preferences?)
a.He will consume 48 more units of good 2 and the same number of units of good 1 as before.
b.He will increase his consumption of both goods.
c.He will reduce his consumption of good 2.
d.He will consume the same number of units of good 2 and 3 more units of good 1 as before.
e.None of the above.
32.Lorenzo lives on x and y alone. His utility function is U(x, y) ? min?3x ? 4y, 7y?. The prices of both goods are positive. He will
a.never buy more x than y.
b.buy equal amounts of the two goods.
c.always buy more y than x.
d.always buy more x than y.
e.More than one of the above is true.
33.Mort’s utility function is U(x_{1}, x_{2}) ? x_{1}x_{2}. His income is $100. The price of good 2 is $10. Good 1 is priced as follows. The first 6 units cost $10 per unit and any additional units cost $5 per unit. What consumption bundle does Mort choose?
a.(5, 5)
b.(7, 3.5)
c.(9, 3)
d.(6, 4)
e.None of the above.
34.Clara’s utility function is U(x, y) ? (x ? 2)(y ? 1). If her marginal rate of substitution is −4 and she is consuming 14 units of good x, how many units of good y must she be consuming?
a.30
b.68
c.18
d.63
e.9
35.Clara’s utility function is U(x, Y) ? (x ? 2)(Y ? 1). If her marginal rate of substitution is −3 and she is consuming 12 units of good x, how many units of good Y must she be consuming?
a.15
b.46
c.24
d.41
e.7
36.Elmer’s utility function is U(x, y) ? min?x, y^{2}?. If the price of x is $25 and the price of y is $15 and if Elmer chooses to consume 7 units of y, what must his income be?
a.$2,660
b.$280
c.$1,430
d.$1,330
e.There is not enough information to determine his income.
37.Elmer’s utility function is U(x, y) ? min?x, y^{2}?. If the price of x is $10 and the price of y is $15 and if Elmer chooses to consume 4 units of y, what must his income be?
a.$220
b.$100
c.$320
d.$440
e.There is not enough information to determine his income.
38.Justin consumes goods x and y and has a utility function U(x, y) ? x^{2} ? y. The price per unit of x is p_{x} and the price per unit of y is p_{y}. He has enough money so that he can afford at least 1 unit of either good. When he chooses his best affordable bundle,
a.his budget line must be tangent to the indifference curve passing through this bundle.
b.he must consume only x.
c.he must consume only y if p^{2}_{x} / p_{y} exceeds his income.
d.he must consume some of each good if p_{x} ? p_{y}.
e.he must consume some of each good if p_{y} ? p_{x }/2.
39.Charlie has a utility function U(x_{A}, x_{B}) ? x_{A}x_{B}, the price of apples is $1, and the price of bananas is $2. If Charlie’s income were $120, how many units of bananas would he consume if he chose the bundle that maximized his utility subject to his budget constraint?
a.30
b.15
c.60
d.6
e.90
40.Charlie has a utility function U(x_{A}, x_{B}) ? x_{A}x_{B}, the price of apples is $1, and the price of bananas is $2. If Charlie’s income were $200, how many units of bananas would he consume if he chose the bundle that maximized his utility subject to his budget constraint?
a.25
b.50
c.10
d.100
e.150
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