Question 1

Esther has an income of $80, and she consumes pizza (P) and soda (S). The price of pizza is $10, and the price of soda is $4.
a. Graph Esther's budget constraint.
b. Graph Esther's budget constraint assuming that there is a buy-one-get-one-free pizza special.
c. Graph Esther's budget constraint assuming that there is a buy-two-get-one-free pizza special.

Accepted Answer

The answer of Esther has an income of $80, and...

Question 2

A consumer buys coffee (C) for $3 each and bagels (B) for $1.50 each. If she has income of $40, what is the equation of her budget constraint? If a tax of $0.25 were placed on the purchase of bagels, what would be the equation of her new budget constraint?

Accepted Answer

The answer of A consumer buys coffee (C) for $3...

Question 3

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 4

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 5

Nikolai consumes sandwiches in a combination of one unit of meat and two slices of cheese. Draw the Nikolai's indifference curves.

Accepted Answer

The answer of Nikolai consumes sandwiches in a combination of...

Question 6

The utility function for a consumer is U = min{X, Y}. If the price of X is $10, the price of Y is $15, and the consumer has $200, this consumer will purchase _____units of X and _____units of Y in equilibrium.

Accepted Answer

The answer of The utility function for a consumer is...

Question 7

Mark's utility function over football tickets (F) and baseball tickets (B) can be expressed as U(F,B) = F + 5B. a. What is his marginal utility of football tickets? b. What is his marginal utility of baseball tickets? c. What is his marginal rate of substitution MRS_FB?

Accepted Answer

The answer of Mark's utility function over football tickets (F)...

Question 8

David's utility is U = 10S + T, where S is rounds of sporting clays and T is rounds of trap (sporting clays and trap are both shotgun sports).
a. Graph David's indifference curve for U = 10.
b. What type of goods are sporting clays and trap?

Accepted Answer

The answer of David's utility is U = 10S +...

Question 9

Manu wants to achieve a utility level of 100. His utility function is U = XY, where MU_X = Y and MU_Y = X. What is the least amount of money (M) that Manu can spend to achieve a utility level of 100? Manu's budget constraint is M = 8X + 2Y.

Accepted Answer

The answer of Manu wants to achieve a utility level...

Question 10

Darius's utility function is U = 6XY, where the MU_X = 6Y and MU_Y = 6X. The prices of good X and good Y are $12 and $15, respectively. Suppose that Darius's indifference curve is tangent to his budget constraint, where he is consuming 20 units of good X. How many units of good Y must Darius be consuming?

Accepted Answer

The answer of Darius's utility function is U = 6XY,...

Question 11

Mark's utility function over football tickets (F) and baseball tickets (B) can be expressed as U(F,B) = F + 5B.
a. Use calculus to argue whether Mark's preferences also can be represented by U(F,B) = 5FB.
b. If Mark's utility function is U(F,B) = F + 5B, is the Lagrangian approach an appropriate way to solve for his optimal quantities? Explain why or why not.
c. If Mark's utility function is U(F,B) = 5FB, is the Lagrangian approach an appropriate way to solve for his optimal quantities? Explain why or why not.

Accepted Answer

The answer of Mark's utility function over football tickets (F)...

Question 12

Suppose that Ken cares only about bathing suits (B) and flip-flops (F). His utility function is U = B^0.8F^0.2. The price of bathing suits is $30, and the price of flip-flops is $2. Ken has a budget of $150. a. What Lagrangian equation can be used to solve Ken's utility maximization problem? b. Derive the first-order conditions for the maximization problem. c. What is the solution to Ken's maximization problem?

Accepted Answer

The answer of Suppose that Ken cares only about bathing...

Question 13

Ivy claims that if a consumer is maximizing utility and happens to be purchasing equal quantities of good X and good Y, the MRS_XY must equal 1. Prove this claim incorrect by drawing an appropriate budget constraint and indifference curve.

Accepted Answer

The answer of Ivy claims that if a consumer is...

Question 14

A consumer's utility function is U(X,Y) = min(2X,3Y). Will the Lagrangian approach be relevant for solving for the consumer's optimal bundle? Why or why not?

Accepted Answer

The answer of A consumer's utility function is U(X,Y) =...

Question 15

Bianca purchases coffee (C), bagels (B) and juice (J). At her current levels of consumption, her MU_C = 10, MU_B = 15, and MU_J = 20. The price of coffee is $2, the price of bagels is $3, and the price of juice is $4. Is Bianca maximizing her utility? If so, why? If not, what must she do to move her consumption toward equilibrium?

Accepted Answer

The answer of Bianca purchases coffee (C), bagels (B) and...

Question 16

Alice's utility function over toys (T) and games (G) can be expressed as U(T,G) = 2TG. a. What is her marginal utility of toys? b. What is her marginal utility of games? c. What is her marginal rate of substitution MRS_TG?

Accepted Answer

The answer of Alice's utility function over toys (T) and...

Question 17

Ines considers Titleist (T) and Callaway (C) golf balls perfect substitutes. Her utility function is U = 10T + 8C. A sleeve of Titleist is priced at $12, compared to $10 for Callaway balls. What is Ines's utility-maximizing bundle of golf balls? Assume that Ines can spend $120.

Accepted Answer

The answer of Ines considers Titleist (T) and Callaway (C)...

Question 18

Suppose that a consumer's utility function can be written U(X,Y) = XY². a. Use calculus to determine whether this consumer's marginal rate of substitution MRS_XY is increasing or decreasing in X. b. Is this consumer's marginal rate of substitution MRS_XY increasing or decreasing in Y?

Accepted Answer

The answer of Suppose that a consumer's utility function can...

Question 19

(Figure: Utility Functions I) What, if any, property of utility functions is violated if:  
a. the indifference curve goes through points A, C, and D?
b. the indifference curve goes through points B and E?
c. the indifference curve goes through points A, B, and D?

Accepted Answer

The answer of (Figure: Utility Functions I) What, if any,...

Question 20

Cashews are sold in either 8-ounce (C₈) or 16-ounce (C₁₆) cans. a. Write an equation that represents a person's utility function for C₈ and C₁₆. b. What is the MRS? (Assume that 16-ounce cans are measured on the y-axis and 8-ounce cans are measured on the x-axis.)

Accepted Answer

The answer of Cashews are sold in either 8-ounce (C₈)...

Quiz 4: Consumer Behavior

A consumer buys coffee (C) for $3 each and bagels (B) for $1.50 each. If she has income of $40, what is the equation of her budget constraint? If a tax of $0.25 were placed on the purchase of bagels, what would be the equation of her new budget constraint?

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?

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

Nikolai consumes sandwiches in a combination of one unit of meat and two slices of cheese. Draw the Nikolai's indifference curves.

The utility function for a consumer is U = min{X, Y}. If the price of X is $10, the price of Y is $15, and the consumer has $200, this consumer will purchase _units of X and _units of Y in equilibrium.

Mark's utility function over football tickets (F) and baseball tickets (B) can be expressed as U(F,B) = F + 5B. a. What is his marginal utility of football tickets? b. What is his marginal utility of baseball tickets? c. What is his marginal rate of substitution MRS_FB?

David's utility is U = 10S + T, where S is rounds of sporting clays and T is rounds of trap (sporting clays and trap are both shotgun sports). a. Graph David's indifference curve for U = 10. b. What type of goods are sporting clays and trap?

Manu wants to achieve a utility level of 100. His utility function is U = XY, where MU_X = Y and MU_Y = X. What is the least amount of money (M) that Manu can spend to achieve a utility level of 100? Manu's budget constraint is M = 8X + 2Y.

Ivy claims that if a consumer is maximizing utility and happens to be purchasing equal quantities of good X and good Y, the MRS_XY must equal 1. Prove this claim incorrect by drawing an appropriate budget constraint and indifference curve.

A consumer's utility function is U(X,Y) = min(2X,3Y). Will the Lagrangian approach be relevant for solving for the consumer's optimal bundle? Why or why not?

Alice's utility function over toys (T) and games (G) can be expressed as U(T,G) = 2TG. a. What is her marginal utility of toys? b. What is her marginal utility of games? c. What is her marginal rate of substitution MRS_TG?

Ines considers Titleist (T) and Callaway (C) golf balls perfect substitutes. Her utility function is U = 10T + 8C. A sleeve of Titleist is priced at $12, compared to $10 for Callaway balls. What is Ines's utility-maximizing bundle of golf balls? Assume that Ines can spend $120.

Suppose that a consumer's utility function can be written U(X,Y) = XY². a. Use calculus to determine whether this consumer's marginal rate of substitution MRS_XY is increasing or decreasing in X. b. Is this consumer's marginal rate of substitution MRS_XY increasing or decreasing in Y?

(Figure: Utility Functions I) What, if any, property of utility functions is violated if: a. the indifference curve goes through points A, C, and D? b. the indifference curve goes through points B and E? c. the indifference curve goes through points A, B, and D?

Cashews are sold in either 8-ounce (C₈) or 16-ounce (C₁₆) cans. a. Write an equation that represents a person's utility function for C₈ and C₁₆. b. What is the MRS? (Assume that 16-ounce cans are measured on the y-axis and 8-ounce cans are measured on the x-axis.)

Quiz 4: Consumer Behavior

A consumer buys coffee (C) for $3 each and bagels (B) for $1.50 each. If she has income of $40, what is the equation of her budget constraint? If a tax of $0.25 were placed on the purchase of bagels, what would be the equation of her new budget constraint?

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?

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

Nikolai consumes sandwiches in a combination of one unit of meat and two slices of cheese. Draw the Nikolai's indifference curves.

The utility function for a consumer is U = min{X, Y}. If the price of X is $10, the price of Y is $15, and the consumer has $200, this consumer will purchase _____units of X and _____units of Y in equilibrium.

Mark's utility function over football tickets (F) and baseball tickets (B) can be expressed as U(F,B) = F + 5B. a. What is his marginal utility of football tickets? b. What is his marginal utility of baseball tickets? c. What is his marginal rate of substitution MRSFB?

David's utility is U = 10S + T, where S is rounds of sporting clays and T is rounds of trap (sporting clays and trap are both shotgun sports). a. Graph David's indifference curve for U = 10. b. What type of goods are sporting clays and trap?

Manu wants to achieve a utility level of 100. His utility function is U = XY, where MUX = Y and MUY = X. What is the least amount of money (M) that Manu can spend to achieve a utility level of 100? Manu's budget constraint is M = 8X + 2Y.

Ivy claims that if a consumer is maximizing utility and happens to be purchasing equal quantities of good X and good Y, the MRSXY must equal 1. Prove this claim incorrect by drawing an appropriate budget constraint and indifference curve.

A consumer's utility function is U(X,Y) = min(2X,3Y). Will the Lagrangian approach be relevant for solving for the consumer's optimal bundle? Why or why not?

Alice's utility function over toys (T) and games (G) can be expressed as U(T,G) = 2TG. a. What is her marginal utility of toys? b. What is her marginal utility of games? c. What is her marginal rate of substitution MRSTG?

Ines considers Titleist (T) and Callaway (C) golf balls perfect substitutes. Her utility function is U = 10T + 8C. A sleeve of Titleist is priced at $12, compared to $10 for Callaway balls. What is Ines's utility-maximizing bundle of golf balls? Assume that Ines can spend $120.

Suppose that a consumer's utility function can be written U(X,Y) = XY2. a. Use calculus to determine whether this consumer's marginal rate of substitution MRSXY is increasing or decreasing in X. b. Is this consumer's marginal rate of substitution MRSXY increasing or decreasing in Y?

(Figure: Utility Functions I) What, if any, property of utility functions is violated if: a. the indifference curve goes through points A, C, and D? b. the indifference curve goes through points B and E? c. the indifference curve goes through points A, B, and D?

Cashews are sold in either 8-ounce (C8) or 16-ounce (C16) cans. a. Write an equation that represents a person's utility function for C8 and C16. b. What is the MRS? (Assume that 16-ounce cans are measured on the y-axis and 8-ounce cans are measured on the x-axis.)

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?

The utility function for a consumer is U = min{X, Y}. If the price of X is $10, the price of Y is $15, and the consumer has $200, this consumer will purchase _units of X and _units of Y in equilibrium.

Mark's utility function over football tickets (F) and baseball tickets (B) can be expressed as U(F,B) = F + 5B. a. What is his marginal utility of football tickets? b. What is his marginal utility of baseball tickets? c. What is his marginal rate of substitution MRS_FB?

Manu wants to achieve a utility level of 100. His utility function is U = XY, where MU_X = Y and MU_Y = X. What is the least amount of money (M) that Manu can spend to achieve a utility level of 100? Manu's budget constraint is M = 8X + 2Y.

Ivy claims that if a consumer is maximizing utility and happens to be purchasing equal quantities of good X and good Y, the MRS_XY must equal 1. Prove this claim incorrect by drawing an appropriate budget constraint and indifference curve.

Alice's utility function over toys (T) and games (G) can be expressed as U(T,G) = 2TG. a. What is her marginal utility of toys? b. What is her marginal utility of games? c. What is her marginal rate of substitution MRS_TG?

Suppose that a consumer's utility function can be written U(X,Y) = XY². a. Use calculus to determine whether this consumer's marginal rate of substitution MRS_XY is increasing or decreasing in X. b. Is this consumer's marginal rate of substitution MRS_XY increasing or decreasing in Y?

Cashews are sold in either 8-ounce (C₈) or 16-ounce (C₁₆) cans. a. Write an equation that represents a person's utility function for C₈ and C₁₆. b. What is the MRS? (Assume that 16-ounce cans are measured on the y-axis and 8-ounce cans are measured on the x-axis.)