Question 1

Charlie's utility function is U(x_A, x_B) = x_Ax_B. If Charlie's income is $40, the price of apples is $4, and the price of bananas is $2, how many apples are there in the best bundle that Charlie can afford? A) 10 B) 8 C) 12 D) 9 E) 5

Accepted Answer

The answer of Charlie's utility function is U(x_A, x_B) =...

Question 2

Elmer's utility function is U(x, y) = min{x, y²}. 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.

Accepted Answer

Elmer's income must be at least $220 because he must be able to afford to buy 4 units of y at $15 per unit.

Question 3

Our old friend, Edmund Stench, of Chapter 2 loves punk rock video tapes. He has no income and therefore has to accept garbage in his backyard in return for money. Each video tape cost $2 and each sack of garbage that he accepts brings him $1. His utility function is given by U(c, g) = min{ 2c, 20 - g}, where c is the number of video tapes and g is the number of sacks of garbage that he gets per month. Each month he will choose to accept
A) 20 sacks of garbage.
B) no garbage.
C) 5 sacks of garbage.
D) 10 sacks of garbage.
E) 15 sacks of garbage.

Accepted Answer

To determine the best choice for Edmund, we need to compare the utility he would receive from each option.

A) Accepting 20 sacks of garbage would give him a total of $20, but it would also reduce his utility to U(c, g) = min{ 2c, 20 - 20} = 0. This means that he would not be able to purchase any video tapes and would feel very dissatisfied.

B) Accepting no garbage would give him $0, and he would have to forgo his beloved punk rock video tapes, giving him a utility of U(c, g) = min{ 2*0, 20 - 0} = 0.

C) Accepting 5 sacks of garbage would give him $5, and he would be able to purchase 2 video tapes (c = 2). However, his remaining utility would be U(c, g) = min{ 2*2, 20 - 5} = 4, since he doesn't necessarily enjoy having a lot of garbage around.

D) Accepting 10 sacks of garbage would give him $10, and he would be able to purchase 5 video tapes (c = 5). His remaining utility would be U(c, g) = min{ 2*5, 20 - 10} = 10. This is the highest utility of all options.

E) Accepting 15 sacks of garbage would give him $15, and he would be able to purchase 7 video tapes (c = 7). However, he would only have U(c, g) = min{ 2*7, 20 - 15} = 10 utility, just like the previous option with less garbage.

Therefore, the best choice for Edmund is to accept 10 sacks of garbage per month.

Question 4

Charlie has a utility function U(x_A, x_B) = x_Ax_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

Accepted Answer

Charlie's utility function is U(x_A, x_B) = x_A * x_B, which is a Cobb-Douglas utility function. To maximize utility subject to the budget constraint, Charlie should spend equal proportions of his income on apples and bananas. Given the prices, he will spend $100 on apples and $100 on bananas. Since bananas cost $2 each, he will buy 50 bananas.

Question 5

Ambrose's utility function is U(x₁, x₂) = . If the price of nuts (good 1) is $1, the price of berries (good 2) is $6, and his income is $264, how many units of nuts will Ambrose choose? A) 20 B) 144 C) 288 D) 147 E) 72

Accepted Answer

The answer of Ambrose's utility function is U(x₁, x₂) =...

Question 6

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.

Accepted Answer

The answer of Lorenzo lives on x and y alone....

Question 7

Joseph's utility function is given by U_J = x_A+ 2x_B_,where x_A denotes his consumption of apples and x_B his consumption of bananas. Clara's utility function is given by U_C = 3x_A + 2x_B. Joseph and Clara shop at the same grocery store. A) When we observe that Joseph leaves the store with some bananas, then we can deduce that Clara also buys some bananas. B) There exist prices of apples and bananas such that both consumers buy strictly positive amounts of both goods. C) When we observe that Joseph leaves the store with some apples and some bananas, then we can deduce that Clara also buys some apples and some bananas. D) When we observe that Joseph leaves the store with some apples, then we can deduce that Clara also buys some apples. E) Apples and bananas are perfect complements for Joseph.

Accepted Answer

From Joseph's utility function, we can see that he has a positive marginal utility for bananas, i.e., consuming more bananas will increase his utility. Therefore, if Joseph leaves the store with some bananas, it is likely that he has reached a point where the marginal utility from bananas is equal to the price of bananas, and he is maximizing his utility by buying some bananas. Since Clara's utility function does not involve any interaction between the goods, we cannot deduce anything about her consumption solely from Joseph's choice of bananas.

Option A is not necessarily true since Clara may have already had bananas or may prefer a different combination of goods. Option B is also not necessarily true since it depends on the relative prices of the goods and the shapes of the indifference curves. Option C is not true either as Joseph could have bought some bananas and apples in different proportions than Clara, based on their marginal utilities and prices. Finally, option E is not true since the utility function does not exhibit a fixed proportion relationship between apples and bananas.

Question 8

Arthur's preferences are defined over two basic food groups, beer, x₁, and ice cream, x₂. His utility function is u(x₁, x₂) = x²₁ + x₂. He has $100 to spend, and each of these goods costs $10 per quart. A) Arthur will consume 5 quarts of ice cream and 5 quarts of beer. B) Arthur will find that 10 quarts of beer and no ice cream is the best bundle. C) Arthur will find that 10 quarts of ice cream and no beer is the best bundle. D) Arthur is indifferent between any two points on the line that connects (5, 5) and (10, 10). E) Arthur will spendof his income on beer andof his income on ice cream.

Accepted Answer

Since Arthur's utility function is linear in both goods, the MRS (marginal rate of substitution) is constant and equals 1. We can set up the following equation to find the optimal bundle:

MRS = Px/Py

where Px is the price of beer and Py is the price of ice cream.

We know that Px/Py = 1/1 = 1, and that Arthur has $100 to spend, so he can buy 10 quarts of beer and 10 quarts of ice cream in total.

Let's first consider point A: 5 quarts of beer and 5 quarts of ice cream. The total cost of this bundle is 5*$10 + 5*$10 = $100.

At point A, the MRS is the absolute value of the slope of the indifference curve passing through A, which is -1 (the negative of the slope of the budget line which is Px/Py = 1). This means that Arthur is willing to give up 1 quart of ice cream to get 1 more quart of beer.

Now let's consider point B: 10 quarts of beer and 0 quarts of ice cream. The total cost of this bundle is 10*$10 + 0*$10 = $100.

At point B, the MRS is also -1, because the slope of the tangent to the indifference curve passing through B equals -1.

Since the MRS is the same at points A and B and the total cost is the same, Arthur is equally well off at both points. However, point B has more of the good (beer) that he likes more, so it is the optimal bundle.

Question 9

Elmer's utility function is U(x, y) = min{x, y²}. 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.

Accepted Answer

To maximize utility, Elmer will consume x and y such that their ratio equals the slope of the indifference curve at the point of consumption. The indifference curve is L-shaped, meaning that Elmer's marginal rate of substitution is 1 if x = y, and infinite if x < y or x > y. Therefore, Elmer will consume 7 units of y and x such that x = 7, which is the lowest possible consumption of x given his preference. His utility function is then U(7, 7) = min{7, 7²} = 7. His total expenditure is $15 × 7 = $105 on y. Therefore, his total expenditure on x is $25 × 7 = $175. His income must be equal to his total expenditure, which is $105 + $175 = $280. The correct answer is D, $1,330. However, this is the total expenditure if Elmer chooses to consume equal amounts of x and y. The question asks for his income if he chooses to consume 7 units of y.

Question 10

Charlie's utility function is U(x_A_,x_B) = x_Ax_B. If Charlie's income is $40, the price of apples is $4, and the price of bananas is $2, how many apples are there in the best bundle that Charlie can afford? A) 10 B) 12 C) 8 D) 9 E) 5

Accepted Answer

Charlie's utility function is U(x_A, x_B) = x_A * x_B, which is a Cobb-Douglas utility function. The optimal consumption bundle for Cobb-Douglas preferences is found by spending a fixed proportion of income on each good. Here, the proportion of income spent on apples is equal to the price of apples divided by the sum of the prices of apples and bananas. Solving for x_A, we find that Charlie can afford 5 apples.

Question 11

Max has the utility function U(x, y) = x(y + 1). The price of x is $2 and the price of y is $1. Income is $10. How much x does Max demand? How much y? If his income doubles and prices stay unchanged, will Max's demand for both goods double?

Accepted Answer

The answer of Max has the utility function U(x, y)...

Question 12

If a consumer maximizes her preferences subject to her budget by choosing a consumption bundle where the ratio of her marginal utilities of shelter and food,  , is greater than the ratio of the prices of shelter and food,  , then she must
A) be consuming food but no shelter.
B) be consuming shelter but no food.
C) believe that shelter is a "bad."
D) be consuming both food and shelter.
E) not be spending all of her income.

Accepted Answer

The answer of If a consumer maximizes her preferences subject...

Question 13

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

Accepted Answer

The answer of Clara's utility function is U(x, Y) =...

Question 14

Mort's utility function is U(x₁, x₂) = x₁x₂. 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.

Accepted Answer

The answer of Mort's utility function is U(x₁, x₂) =...

Question 15

Charlie has a utility function U(x_A, x_B) = x_Ax_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

Accepted Answer

The answer of Charlie has a utility function U(x_A, x_B)...

Question 16

Andrew's utility function is U(x₁, x₂) = 4x²₁ + x₂. 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.

Accepted Answer

The answer of Andrew's utility function is U(x₁, x₂) =...

Question 17

Ambrose's utility function is U(x₁, x₂) = . If the price of nuts (good 1) is $1, the price of berries (good 2) is $5, and his income is $145, how many units of nuts will Ambrose choose? A) 100 B) 200 C) 9 D) 103 E) 50

Accepted Answer

The answer of Ambrose's utility function is U(x₁, x₂) =...

Question 18

Justin consumes goods x and y and has a utility function U(x, y) = x² + 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 ifexceeds his income. D) he must consume some of each good if p_x = p_y. E) he must consume some of each good if.

Accepted Answer

The answer of Justin consumes goods x and y and...

Question 19

Angela consumes only two goods, x and y. Her income doubles and the prices of the two goods remain unchanged. Assuming that she is a utility maximizer and likes both goods,
A) she will consume more of both goods.
B) the ratio of her consumption of x to y remains constant.
C) her utility doubles.
D) if her preferences are convex, she must consume more x.
E) None of the above.

Accepted Answer

The answer of Angela consumes only two goods, x and...

Question 20

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

Accepted Answer

The answer of Clara's utility function is U(x, y) =...

Quiz 4: Choice

Charlie's utility function is U(x_A, x_B) = x_Ax_B. If Charlie's income is $40, the price of apples is $4, and the price of bananas is $2, how many apples are there in the best bundle that Charlie can afford?

Elmer's utility function is U(x, y) = min{x, y²}. 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?

Charlie has a utility function U(x_A, x_B) = x_Ax_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?

Ambrose's utility function is U(x₁, x₂) = . If the price of nuts (good 1) is $1, the price of berries (good 2) is $6, and his income is $264, how many units of nuts will Ambrose choose?

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

Joseph's utility function is given by U_J = x_A+ 2x_B_,where x_A denotes his consumption of apples and x_B his consumption of bananas. Clara's utility function is given by U_C = 3x_A + 2x_B. Joseph and Clara shop at the same grocery store.

Arthur's preferences are defined over two basic food groups, beer, x₁, and ice cream, x₂. His utility function is u(x₁, x₂) = x²₁ + x₂. He has $100 to spend, and each of these goods costs $10 per quart.

Elmer's utility function is U(x, y) = min{x, y²}. 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?

Charlie's utility function is U(x_A_,x_B) = x_Ax_B. If Charlie's income is $40, the price of apples is $4, and the price of bananas is $2, how many apples are there in the best bundle that Charlie can afford?

Max has the utility function U(x, y) = x(y + 1). The price of x is $2 and the price of y is $1. Income is $10. How much x does Max demand? How much y? If his income doubles and prices stay unchanged, will Max's demand for both goods double?

If a consumer maximizes her preferences subject to her budget by choosing a consumption bundle where the ratio of her marginal utilities of shelter and food, , is greater than the ratio of the prices of shelter and food, , then she must

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?

Mort's utility function is U(x₁, x₂) = x₁x₂. 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?

Charlie has a utility function U(x_A, x_B) = x_Ax_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?

Andrew's utility function is U(x₁, x₂) = 4x²₁ + x₂. 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?)

Ambrose's utility function is U(x₁, x₂) = . If the price of nuts (good 1) is $1, the price of berries (good 2) is $5, and his income is $145, how many units of nuts will Ambrose choose?

Justin consumes goods x and y and has a utility function U(x, y) = x² + 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,

Angela consumes only two goods, x and y. Her income doubles and the prices of the two goods remain unchanged. Assuming that she is a utility maximizer and likes both goods,

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?

Quiz 4: Choice

Charlie's utility function is U(xA, xB) = xAxB. If Charlie's income is $40, the price of apples is $4, and the price of bananas is $2, how many apples are there in the best bundle that Charlie can afford?

Elmer's utility function is U(x, y) = min{x, y2}. 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?

Charlie has a utility function U(xA, xB) = xAxB, 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?

Ambrose's utility function is U(x1, x2) = . If the price of nuts (good 1) is $1, the price of berries (good 2) is $6, and his income is $264, how many units of nuts will Ambrose choose?

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

Joseph's utility function is given by UJ = xA + 2xB, where xA denotes his consumption of apples and xB his consumption of bananas. Clara's utility function is given by UC = 3xA + 2xB. Joseph and Clara shop at the same grocery store.

Arthur's preferences are defined over two basic food groups, beer, x1, and ice cream, x2. His utility function is u(x1, x2) = x21 + x2. He has $100 to spend, and each of these goods costs $10 per quart.

Elmer's utility function is U(x, y) = min{x, y2}. 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?

Charlie's utility function is U(xA, xB) = xAxB. If Charlie's income is $40, the price of apples is $4, and the price of bananas is $2, how many apples are there in the best bundle that Charlie can afford?

Max has the utility function U(x, y) = x(y + 1). The price of x is $2 and the price of y is $1. Income is $10. How much x does Max demand? How much y? If his income doubles and prices stay unchanged, will Max's demand for both goods double?

If a consumer maximizes her preferences subject to her budget by choosing a consumption bundle where the ratio of her marginal utilities of shelter and food, , is greater than the ratio of the prices of shelter and food, , then she must

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?

Mort's utility function is U(x1, x2) = x1x2. 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?

Charlie has a utility function U(xA, xB) = xAxB, 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?

Andrew's utility function is U(x1, x2) = 4x21 + x2. 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?)

Ambrose's utility function is U(x1, x2) = . If the price of nuts (good 1) is $1, the price of berries (good 2) is $5, and his income is $145, how many units of nuts will Ambrose choose?

Justin consumes goods x and y and has a utility function U(x, y) = x2 + y. The price per unit of x is px and the price per unit of y is py. He has enough money so that he can afford at least 1 unit of either good. When he chooses his best affordable bundle,

Angela consumes only two goods, x and y. Her income doubles and the prices of the two goods remain unchanged. Assuming that she is a utility maximizer and likes both goods,

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?

Charlie's utility function is U(x_A, x_B) = x_Ax_B. If Charlie's income is $40, the price of apples is $4, and the price of bananas is $2, how many apples are there in the best bundle that Charlie can afford?

Elmer's utility function is U(x, y) = min{x, y²}. 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?

Charlie has a utility function U(x_A, x_B) = x_Ax_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?

Ambrose's utility function is U(x₁, x₂) = . If the price of nuts (good 1) is $1, the price of berries (good 2) is $6, and his income is $264, how many units of nuts will Ambrose choose?

Joseph's utility function is given by U_J = x_A+ 2x_B_,where x_A denotes his consumption of apples and x_B his consumption of bananas. Clara's utility function is given by U_C = 3x_A + 2x_B. Joseph and Clara shop at the same grocery store.

Arthur's preferences are defined over two basic food groups, beer, x₁, and ice cream, x₂. His utility function is u(x₁, x₂) = x²₁ + x₂. He has $100 to spend, and each of these goods costs $10 per quart.

Elmer's utility function is U(x, y) = min{x, y²}. 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?

Charlie's utility function is U(x_A_,x_B) = x_Ax_B. If Charlie's income is $40, the price of apples is $4, and the price of bananas is $2, how many apples are there in the best bundle that Charlie can afford?

Mort's utility function is U(x₁, x₂) = x₁x₂. 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?

Charlie has a utility function U(x_A, x_B) = x_Ax_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?

Andrew's utility function is U(x₁, x₂) = 4x²₁ + x₂. 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?)

Ambrose's utility function is U(x₁, x₂) = . If the price of nuts (good 1) is $1, the price of berries (good 2) is $5, and his income is $145, how many units of nuts will Ambrose choose?

Justin consumes goods x and y and has a utility function U(x, y) = x² + 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,