Question 1

Suppose that U = min{2X, 0.5Y}, where X is units of good X and Y is units of good Y. The price of good X is $1 and the price of good Y is $2. What is the minimum expenditure necessary to achieve a utility level of 100?
A) $333.33
B) $550
C) $1,200
D) $450

Accepted Answer

The answer of Suppose that U = min{2X, 0.5Y}, where...

Question 2

Suppose that MU_X = Y and MU_Y = X. The prices of good X and good Y are $5 and $4, respectively. How many units of good X does the consumer buy if she has $410 of income? A) 15 B) 41 C) 25 D) 33

Accepted Answer

The answer of Suppose that MU_X = Y and MU_Y...

Question 3

The consumer's budget constraint is $6 = 0.50G + P, where G is packs of gum and P is bags of pretzels. The marginal utility of pretzels is MU_P = G^0.5, and the marginal utility of gum is MU_G = 0.5G^-^0.5P. The consumer's utility function is U = G^0.5P. the utility-maximizing bundle consists of _____ packs of gum and _____ bags of pretzels. A) 8; 2 B) 4; 4 C) 2; 5 D) 6; 3

Accepted Answer

To maximize utility, the consumer should equate the marginal rate of substitution (MRS) to the price ratio. The MRS is MU_G/MU_P = (0.5G^(-0.5)P)/(G^0.5) = 0.5P/G. The price ratio is 0.50/1. Setting MRS = price ratio gives 0.5P/G = 0.50/1, which simplifies to P = G. Substituting P = G into the budget constraint 6 = 0.50G + P gives 6 = 0.50G + G, which simplifies to 6 = 1.5G, so G = 4 and P = 4.

Question 4

If a consumer's budget constraint has a slope that is less than -1:
A) the consumer gets more utility from good X than from good Y.
B) the price of good X is less than the price of good Y.
C) the consumer gets less utility from good X than from good Y.
D) the price of good X is greater than the price of good Y.

Accepted Answer

The slope of a consumer's budget constraint is given by the negative ratio of the prices of the two goods (-Px/Py). If the slope is less than -1, it means that the price of good X (Px) is greater than the price of good Y (Py).

Question 5

Use the following to answer question:
Figure 4.16 
-(Figure 4.16) To maximize utility, this consumer will buy _____ hockey tickets and _____ soccer tickets.
A) 5; 3
B) 3; 5
C) 8; 0
D) 0; 8

Accepted Answer

The consumer will buy 5 hockey tickets and 3 soccer tickets because at that point, the budget line is tangent to the highest possible indifference curve (IC3). This is the point where the consumer's marginal rate of substitution (MRS) (the slope of the indifference curve) equals the price ratio of hockey tickets to soccer tickets. Any other combination of hockey and soccer tickets would result in a lower level of utility.

Question 6

Draw an indifference curve for the utility function U = 0.5XY when utility equals 5. Identify four consumption bundles on the indifference curve along with their respective values of X and Y.

Accepted Answer

The answer of Draw an indifference curve for the utility...

Question 7

List the four properties of utility functions, giving an example of each property.

Accepted Answer

The answer of List the four properties of utility functions,...

Question 8

The utility function for Morris is U = min{4M, T}, where M is pints of milk and T is cans of tuna. Morris has $90 to spend on tuna (priced at $2 per can) and milk (priced at $1 per pint). What is Morris's utility-maximizing consumption bundle?
A) M = 30 and T = 30
B) M = 40 and T = 25
C) M = 10 and T = 40
D) M = 15 and T = 65

Accepted Answer

The answer of The utility function for Morris is U...

Question 9

Larry's utility function is U = 4X + 12Y. Which property of consumer preferences does Larry's utility function violate? Explain your answer.

Accepted Answer

The answer of Larry's utility function is U = 4X...

Question 10

Use the following to answer question: Figure 4.15 -(Figure 4.15) The consumer maximizes utility by consuming: A) 7 mushrooms and no spinach. B) 8 units of spinach and no mushrooms. C) on indifference curve U₂. D) approximately 4 mushrooms and 4 units of spinach.

Accepted Answer

The consumer maximizes utility at the point where the budget constraint is tangent to the highest possible indifference curve (i.e. where MRS = price ratio). This occurs at a point approximately 4 mushrooms and 4 units of spinach, as shown in the graph. Therefore, choice D is the best choice.

Question 11

Suppose that MU_Y = 15, MU_X = 10, P_Y = $2, and P_X = $1. Which of the following statements is TRUE? A) The consumer is maximizing utility. B) The consumer could increase utility by giving up 1 unit of good Y for 2 units of good X. C) The consumer could increase utility by giving up 2 units of good X for 1 unit of good Y. D) The consumer is receiving more marginal utility per dollar from good Y than from good X.

Accepted Answer

To determine if the consumer is maximizing utility, we need to compare the marginal utility per dollar of each good.

MU1U1B1YS1U1B0/ PS1U1B1YS1U1B0 = 15/2 = 7.5
MU1U1B1XS1U1B0/ PS1U1B1XS1U1B0 = 10/1 = 10

Since the marginal utility per dollar for good X is higher than for good Y, the consumer is not currently maximizing their utility.

To increase utility, the consumer should give up some good Y for more good X. Option B suggests trading 1 unit of good Y for 2 units of good X, which would result in the following new marginal utility per dollar calculations:

MU1U1B1YS1U1B0/ PS1U1B1YS1U1B0 = 14/2 = 7
MU1U1B1XS1U1B0/ PS1U1B1XS1U1B0 = 12/3 = 4

The marginal utility per dollar for good Y has decreased, but the marginal utility per dollar for good X has also decreased by a larger amount. Therefore, the consumer would not want to give up 2 units of good X for 1 unit of good Y (option C). Option B, on the other hand, increases the marginal utility per dollar for both goods and would result in a higher level of utility for the consumer.

Question 12

Nancy's ratio of marginal utility for coffee and lipstick is 3:1, while the price ratio of coffee to lipstick is 1.5:1. Which of the following statements is (are) TRUE? 
A) IV only
B) I and II
C) I and III
D) III only

Accepted Answer

The answer of Nancy's ratio of marginal utility for coffee...

Question 13

Peter's utility function is U = 5X + 2Y. What is Peter's marginal utility of good X and good Y? Interpret your answer.

Accepted Answer

The answer of Peter's utility function is U = 5X...

Question 14

Jimi's utility function for guitars (G) and haircuts (H) is U = 1.05GH. Eddie's utility function for guitars and haircuts is U = GH + H^0.5. Does Jimi or Eddie receive more satisfaction from consuming 10 guitars and 9 haircuts?

Accepted Answer

The answer of Jimi's utility function for guitars (G) and...

Question 15

Frank's utility function is U = 10X + 6Y. Frank has a budget of $60 to spend on goods X and Y. The price of good X is $3 and the price of good Y is $2. How many units of good X and good Y does Frank purchase?
A) X = 20 and Y = 0
B) X = 0 and Y = 10
C) X = 15 and Y = 5
D) X = 10 and Y = 20

Accepted Answer

Frank maximizes his utility by spending his entire budget on the good that provides the highest marginal utility per dollar. The marginal utility per dollar for X is 10/3 and for Y is 6/2 = 3.33. Since 10/3 > 3.33, Frank spends all $60 on X, buying 20 units (60/3 = 20).

Question 16

Parker consumes goods X and Y. Her utility function is U = XY, which means that MU_X = Y and MU_Y = X. Prove that Parker's utility function satisfies all four assumptions of consumer preferences.

Accepted Answer

The answer of Parker consumes goods X and Y. Her...

Question 17

Billy is maximizing utility subject to his limited income. As a result, which of the following statements is TRUE? A) The slope of the indifference curve is twice the slope of the budget constraint. B) The indifference curve intersects the budget constraint at precisely two points. C) The budget constraint is tangent to the indifference curve. D) The MRS_XY = P_XP_Y.

Accepted Answer

When maximizing utility subject to limited income, the budget constraint is tangent to the highest possible indifference curve. This creates the highest possible level of utility given the constraints of income and price. Therefore, choice C is true. Choices A and B are not necessarily true for all situations, and choice D is irrelevant.

Question 18

Bertha's utility function for soccer balls (S) and tennis balls (T) is U = ST + 5S. Find five consumption bundles that give Bertha exactly 100 units of utility.

Accepted Answer

The answer of Bertha's utility function for soccer balls (S)...

Question 19

Missy's utility increases with the size of her apartment. However, Missy is willing to sacrifice some apartment space if she can live closer to the beach. Draw Missy's indifference curves.

Accepted Answer

The answer of Missy's utility increases with the size of...

Question 20

A consumer spends his limited income on three goods such that the MU_X = 4, MU_Y = 4, MU_Z = 4; and P_X = 4, P_Y = 2, P_Z = 1. Which of the following statements is (are) TRUE? A) I B) II C) III D) II and III

Accepted Answer

I. The marginal utility per dollar of X is equal to 1 since MU_X / P_X = 4/4 = 1. II. The consumer is currently not spending his income in the most efficient way since the marginal utility per dollar of Y is higher than the marginal utility per dollar of X or Z. MU_Y / P_Y = 4/2 = 2 and MU_Z / P_Z = 4/1 = 4. III. It is not possible to determine whether the consumer is spending all of his income since we do not know the total amount of income he has available to spend.

Quiz 4: Consumer Behavior

Suppose that U = min{2X, 0.5Y}, where X is units of good X and Y is units of good Y. The price of good X is $1 and the price of good Y is $2. What is the minimum expenditure necessary to achieve a utility level of 100?

Suppose that MU_X = Y and MU_Y = X. The prices of good X and good Y are $5 and $4, respectively. How many units of good X does the consumer buy if she has $410 of income?

If a consumer's budget constraint has a slope that is less than -1:

Use the following to answer question: Figure 4.16 -(Figure 4.16) To maximize utility, this consumer will buy _ hockey tickets and _ soccer tickets.

Draw an indifference curve for the utility function U = 0.5XY when utility equals 5. Identify four consumption bundles on the indifference curve along with their respective values of X and Y.

List the four properties of utility functions, giving an example of each property.

The utility function for Morris is U = min{4M, T}, where M is pints of milk and T is cans of tuna. Morris has $90 to spend on tuna (priced at $2 per can) and milk (priced at $1 per pint) . What is Morris's utility-maximizing consumption bundle?

Larry's utility function is U = 4X + 12Y. Which property of consumer preferences does Larry's utility function violate? Explain your answer.

Use the following to answer question: Figure 4.15 -(Figure 4.15) The consumer maximizes utility by consuming:

Suppose that MU_Y = 15, MU_X = 10, P_Y = $2, and P_X = $1. Which of the following statements is TRUE?

Nancy's ratio of marginal utility for coffee and lipstick is 3:1, while the price ratio of coffee to lipstick is 1.5:1. Which of the following statements is (are) TRUE?

Peter's utility function is U = 5X + 2Y. What is Peter's marginal utility of good X and good Y? Interpret your answer.

Jimi's utility function for guitars (G) and haircuts (H) is U = 1.05GH. Eddie's utility function for guitars and haircuts is U = GH + H^0.5. Does Jimi or Eddie receive more satisfaction from consuming 10 guitars and 9 haircuts?

Frank's utility function is U = 10X + 6Y. Frank has a budget of $60 to spend on goods X and Y. The price of good X is $3 and the price of good Y is $2. How many units of good X and good Y does Frank purchase?

Parker consumes goods X and Y. Her utility function is U = XY, which means that MU_X = Y and MU_Y = X. Prove that Parker's utility function satisfies all four assumptions of consumer preferences.

Billy is maximizing utility subject to his limited income. As a result, which of the following statements is TRUE?

Bertha's utility function for soccer balls (S) and tennis balls (T) is U = ST + 5S. Find five consumption bundles that give Bertha exactly 100 units of utility.

Missy's utility increases with the size of her apartment. However, Missy is willing to sacrifice some apartment space if she can live closer to the beach. Draw Missy's indifference curves.

A consumer spends his limited income on three goods such that the MU_X = 4, MU_Y = 4, MU_Z = 4; and P_X = 4, P_Y = 2, P_Z = 1. Which of the following statements is (are) TRUE?

Quiz 4: Consumer Behavior

Suppose that U = min{2X, 0.5Y}, where X is units of good X and Y is units of good Y. The price of good X is $1 and the price of good Y is $2. What is the minimum expenditure necessary to achieve a utility level of 100?

Suppose that MUX = Y and MUY = X. The prices of good X and good Y are $5 and $4, respectively. How many units of good X does the consumer buy if she has $410 of income?

If a consumer's budget constraint has a slope that is less than -1:

Use the following to answer question: Figure 4.16 -(Figure 4.16) To maximize utility, this consumer will buy _____ hockey tickets and _____ soccer tickets.

Draw an indifference curve for the utility function U = 0.5XY when utility equals 5. Identify four consumption bundles on the indifference curve along with their respective values of X and Y.

List the four properties of utility functions, giving an example of each property.

The utility function for Morris is U = min{4M, T}, where M is pints of milk and T is cans of tuna. Morris has $90 to spend on tuna (priced at $2 per can) and milk (priced at $1 per pint) . What is Morris's utility-maximizing consumption bundle?

Larry's utility function is U = 4X + 12Y. Which property of consumer preferences does Larry's utility function violate? Explain your answer.

Use the following to answer question: Figure 4.15 -(Figure 4.15) The consumer maximizes utility by consuming:

Suppose that MUY = 15, MUX = 10, PY = $2, and PX = $1. Which of the following statements is TRUE?

Nancy's ratio of marginal utility for coffee and lipstick is 3:1, while the price ratio of coffee to lipstick is 1.5:1. Which of the following statements is (are) TRUE?

Peter's utility function is U = 5X + 2Y. What is Peter's marginal utility of good X and good Y? Interpret your answer.

Jimi's utility function for guitars (G) and haircuts (H) is U = 1.05GH. Eddie's utility function for guitars and haircuts is U = GH + H0.5. Does Jimi or Eddie receive more satisfaction from consuming 10 guitars and 9 haircuts?

Frank's utility function is U = 10X + 6Y. Frank has a budget of $60 to spend on goods X and Y. The price of good X is $3 and the price of good Y is $2. How many units of good X and good Y does Frank purchase?

Parker consumes goods X and Y. Her utility function is U = XY, which means that MUX = Y and MUY = X. Prove that Parker's utility function satisfies all four assumptions of consumer preferences.

Billy is maximizing utility subject to his limited income. As a result, which of the following statements is TRUE?

Bertha's utility function for soccer balls (S) and tennis balls (T) is U = ST + 5S. Find five consumption bundles that give Bertha exactly 100 units of utility.

Missy's utility increases with the size of her apartment. However, Missy is willing to sacrifice some apartment space if she can live closer to the beach. Draw Missy's indifference curves.

A consumer spends his limited income on three goods such that the MUX = 4, MUY = 4, MUZ = 4; and PX = 4, PY = 2, PZ = 1. Which of the following statements is (are) TRUE?

Suppose that MU_X = Y and MU_Y = X. The prices of good X and good Y are $5 and $4, respectively. How many units of good X does the consumer buy if she has $410 of income?

Use the following to answer question: Figure 4.16 -(Figure 4.16) To maximize utility, this consumer will buy _ hockey tickets and _ soccer tickets.

Suppose that MU_Y = 15, MU_X = 10, P_Y = $2, and P_X = $1. Which of the following statements is TRUE?

Jimi's utility function for guitars (G) and haircuts (H) is U = 1.05GH. Eddie's utility function for guitars and haircuts is U = GH + H^0.5. Does Jimi or Eddie receive more satisfaction from consuming 10 guitars and 9 haircuts?

Parker consumes goods X and Y. Her utility function is U = XY, which means that MU_X = Y and MU_Y = X. Prove that Parker's utility function satisfies all four assumptions of consumer preferences.

A consumer spends his limited income on three goods such that the MU_X = 4, MU_Y = 4, MU_Z = 4; and P_X = 4, P_Y = 2, P_Z = 1. Which of the following statements is (are) TRUE?