Quiz 4: Consumer Behavior

Sonia says she prefers two theater tickets and one bottle of French wine to three games of bowling and one pitcher of draft beer. In this example, Sonia is demonstrating the _____ assumption of consumer behavior. A) more is better than less B) completeness and rankability C) transitivity D) diminishing marginal utility

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.

(Figure: Good Y and Good X IV) Which of the following changes could have rotated the budget constraint in the direction indicated by the arrow in the graph? A) an increase in the price of good X B) a decrease in the price of good Y C) a decrease in income D) an increase in the price of good Y

Randy likes baseball more than football, football more than basketball, and basketball more than baseball. Which assumption about consumer preferences does this violate? A) completeness and rankability B) more is better C) transitivity D) The more a consumer has of a particular good, the less she is willing to give up of something else to get even more of that good.

(Figure: Tomatoes and Carrots IV) Which of these indifference curves is convex to the origin? A) U₁ B) U₂ C) U₃ D) U₄

Martha loves to eat chili, especially an award-winning chili recipe that calls for using 2 tablespoons of chili powder for every 1 pound of ground buffalo. Which of the following utility functions could represent Martha's preferences, where U is a function of tablespoons of chili powder (P) and pounds of ground buffalo (B)? A) U = min{2B, P} B) U = min{0.50B, P} C) U = 2P + B D) U = 2PB

(Figure: Good Y and Good X III) The indifference curve _____ indicates that the two goods, X and Y, are relatively poor substitutes for one another, whereas the indifference curve _____ indicates that the two goods are close substitutes for one another. A) U₁; U₃ B) U₃; U₂ C) U₂; U₁ D) U₃; U₁

(Figure: Tomatoes and Carrots III) This figure violates the assumption: A) of convex indifference curves. B) of transitivity. C) of rankability. D) that the more you have of a good, the less you are willing to give up to get even more of it.

Kalini spends all of her income on movie tickets and groceries. Suppose Kalini is presented with two options: A and B. Option A gives her a voucher of $X that she can only spend on groceries. Option B gives her $X that she can spend on either or both of the goods (a transfer of cash). Assuming Kalini prefers Option B to Option A and purchases positive values of movie tickets and groceries, which of the following is correct? A) Kalini values the choice that the cash transfer offers. B) Kalini does not gain any utility by consuming groceries. C) Kalini does not value the choice that the cash transfer offers. D) Kalini does not gain any utility by consuming movie tickets.

(Figure: Coats and Sweaters I) Which of the following statements is FALSE? I. At point A, the consumer is willing to give up three winter coats for one wool sweater. II) At point B, the consumer is willing to give up one winter coat for four wool sweaters. III) At point A, the consumer is willing to give up three wool sweaters for one winter coat. IV) At point B, the consumer is willing to give up four wool sweaters for one winter coat. A) I only B) I and II C) III D) IV

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.

For the utility function U(X,Y) = 10X + 4Y, the marginal utility of X is: A) 10X. B) 10. C) 10X + 4Y. D) 10 + 4Y.

Mika spends all of her income on pizza and gasoline. Suppose Mika is presented with two options: A and B. Option A will subsidize gasoline by decreasing its price by 50%. Option B will increase Mika's income by the cost of the subsidy in Option A. Which of the following must be true? A) Mika will always strictly prefer Option A to Option B. B) Mika will always strictly prefer Option B to Option A. C) Mika will never prefer Option A to Option B. D) Mike will never prefer Option B to Option A.

Suppose that MRS_XY = Y/X. As X increases: A) MRS_XY increases. B) MRS_XY decreases. C) MRS_XY remains constant. D) MRS_XY increases and then decreases.

The equation for the marginal rate of substitution of good X for good Y (that is, MRS_XY) is given by: A) ΔU(X,Y)/ΔX. B) -ΔY/ΔX. C) ΔY × ΔX. D) -X/Y.

Hideki spends all of his money on movie tickets and groceries. Suppose Hideki is presented with two options: A and B. Option A gives him a voucher of $X that he can only spend on groceries. Option B gives him $X that he can spend on either or both of the goods. Which of the following is correct? A) Hideki always prefers Option A to Option B. B) Hideki can never be indifferent between Option A and Option B. C) Hideki is always indifferent between Option A and Option B. D) Hideki can prefer Option B to Option A but cannot prefer Option A to Option B.

Rohan 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.

Veronika's utility function for regular-flavored toothpaste (R) and mint-flavored toothpaste (M) is given by U = 2R + 4M. Which of the following statements is TRUE? A) MRS_MR = 2M/R. B) Veronika's indifference curves are vertical. C) Veronika's indifference curves are horizontal. D) Veronika is willing to give up two tubes of regular-flavored toothpaste for one tube of mint-flavored toothpaste.

(Figure: Mushrooms and Spinach I) 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.

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? I) Because the marginal utilities of all three goods are equal, the consumer is maximizing utility. II) The consumer receives the most bang for the buck from good Z. III) The marginal utility per dollar spent is not equal across all three goods, so the consumer is not maximizing utility. A) I B) II C) III D) II and III

Sofia spends all of her income on pizza and gasoline. Suppose Sophia is presented with two options: A and B. Option A will subsidize gasoline by decreasing its price by 50%. Option B will increase Sophia's income by the cost of the subsidy in Option A. Assuming Sophia strictly prefers Option B to Option A, which of the following must be true? A) Sophia consumes at least some of each good. B) Sophia gains more utility from pizza than gasoline. C) Sophia gains more utility from gasoline than pizza. D) Sophia only consumes gasoline.

For the utility function U(X,Y) = X^0.75Y^0.25, the marginal utility of Y is: A) 0.75X^0.75Y^0.25. B) 0.25X^0.75Y^0.25. C) 0.75X^-0.25Y^0.25. D) 0.25X^0.75Y^-0.75.

Mika's marginal rate of substitution of apples (A) for oranges (O) is 5 (MRS_AO = 5). This information implies that: A) Mika is willing to trade away five apples for one more orange, holding her utility constant. B) Mika will move to a higher indifference curve if she trades away five apples for one more orange. C) Mika should own five times as many apples as oranges. D) the slope of the indifference curve is five and thus upward sloping.

The utility function U = Y/X violates the assumption(s) of: A) rankability. B) completeness. C) more is better. D) rankability and completeness.

(Figure: Good Y and Good X V) For budget constraint 1, the price of good X and the price of good Y could equal _____, respectively. A) $175 and $100 B) $80 and $140 C) $160 and $140 D) $6 and $4

A graph of the utility function U = 4Y + X would reveal that goods X and Y are: A) perfect substitutes. B) near substitutes. C) perfect complements. D) near complements.

(Figure: Good Y and Good X I) Which of the following statements is TRUE? I. The consumer prefers any point on indifference curve U₂ to any point on indifference curve U₁. II) The consumer receives 20% more satisfaction from consuming along indifference curve U₂ than along indifference curve U₁. III) This consumer is not willing to give up units of good X for more units of good Y. A) I and III B) I C) II D) I and II

Ezra spends all of his income on pizza and gasoline. Suppose Ezra is presented with two options: A and B. Option A will subsidize gasoline by decreasing its price by 50%. Option B will increase Ezra's income by the cost of the subsidy in Option A. Which of the following is correct? A) Ezra will never prefer Option A to Option B. B) Ezra needs to spend all of his income on gasoline to prefer Option B. C) Ezra needs to spend all of his income on pizza to prefer Option B to Option A. D) Ezra would never be indifferent between Option A and Option B.

For the utility function U(X,Y) = X^0.5Y^0.5, the marginal rate of substitution MRS_XY is: A) 0.5Y/X. B) 0.5X/Y. C) X/Y. D) Y/X.

Suppose that the marginal utility of good Y = 2X² and the marginal utility of good X = 4XY. What is the slope of the indifference curve when Y = 7 and X = 2? Assume that good X is on the horizontal axis and good Y is on the vertical axis. A) 7 B) 0.143 C) -14 D) -0.143

Yanas ratio of marginal utility for coffee and soda is 3:1, while the price ratio of coffee to soda is 1.5:1. Which of the following statements is (are) TRUE? I) Coffee provides Yana with 3 times the marginal utility of soda. II) Yana could increase utility by decreasing her consumption of coffee by 3 units and increasing her consumption of soda by 1.5 units. III) Yana could increase utility by decreasing her consumption of soda by 3 units and increasing her consumption of coffee by 2 units. IV) Yana could increase utility by decreasing her consumption of coffee by 1 unit and increasing her consumption of soda by 3 units. A) IV only B) I and II C) I and III D) III only

For the utility function U(X,Y) = 6X + Y^0.5, the marginal utility of Y is: A) 6X + 0.5Y^-0.5. B) 6 + 0.5Y^-0.5. C) Y^-0.5. D) 0.5Y^-0.5.

The consumer's utility function for goods X and Y is U = 3X + 15Y. Good X is placed on the x-axis and good Y is placed on the y-axis. Which of the following statements is TRUE? I) The marginal utility of good Y is 15. II) The MRS_XY = 5. III) The consumer is always willing to trade away 5 units of good X for 1 unit of good Y. A) I and II B) II only C) I and III D) I, II, and III

Ahmed spends all of his money on movie tickets and groceries. Suppose Ahmed is presented with two options: A and B. Option A gives him a voucher of $X that he can only spend on groceries. Option B gives him $X that he can spend on either or both of the goods. Which of the following is correct assuming Ahmed is indifferent between the two options? A) Ahmed spends at least $X on groceries. B) Ahmed spends less than $X on groceries. C) Ahmed must be indifferent between movie tickets and groceries. D) Ahmed spends his entire income on movie tickets.

Suppose that U = U(P, M), where P and M are peanuts and marshmallows. The marginal utility of marshmallows, MU_M, is given by: A) P + M. B) P/M. C) ΔU(P, M)/ΔM. D) ΔU(P, M) × ΔM.

Gael's utility function for trout (T) and salmon (S) is given by U = ST, where the MU_T = S and MU_S = T. Which pair of consumption bundles lies on the same indifference curve? A) bundles of (S = 2 and T = 4) and (S = 3 and T = 3) B) bundles of (S = 5 and T = 5) and (S = 25 and T = 1) C) bundles of (S = 10 and T = 2) and (S = 5 and T = 1) D) bundles of (S = 8 and T = 6) and (S = 7 and T = 10)

Suppose that Maria cares only about shoes and clothes. Her utility function is U = S^0.5C^0.5, where S is the number of pairs of shoes and C is the number of clothing items that she owns. The price of shoes is $80, and the price of clothes is $100. Suppose that Maria must have 1,000 units of utility and wants to achieve this level of utility with the lowest possible expenditure. How can Maria's expenditure minimization problem be expressed as a Lagrangian equation? A) B) C) D)

(Figure: Good Y and Good X II) What type of good is good X, assuming a person increases the level of happiness when consuming more of good Y? A) perfect substitute B) perfect complement C) bad D) neutral good

Sofia's utility is a function of golf (G) and music lessons (M), where MU_G = 1/G and MU_M = 1/M. What is MRS_GM when M = 10 and G = 4? A) 2.5 B) 14 C) 0.4 D) 6

Louis's utility function is U = 10X + 6Y. Louis 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 Louis purchase? A) X = 20 and Y = 0 B) X = 0 and Y = 10 C) X = 30 and Y = 0 D) X = 10 and Y = 20

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

Sofia's utility is a function of golf (G) and music lessons (M), where MU_G = 1/G and MU_M = 1/M. What is the equation for the marginal rate of substitution of music lessons for golf (MRS_GM)? A) GM B) M/G C) G/M D) M - G

Juanita spends all of her income on movie tickets and groceries. Suppose Juanita is presented with two options: A and B. Option A gives her a voucher of $X that she can only spend on groceries. Option B gives her $X that she can spend on either or both of the goods. Assuming Juanita prefers Option B to Option A, which of the following is correct? A) Juanita spends her entire income on groceries. B) Juanita spends less than $X on groceries. C) Juanita spends more than $X on groceries, but still buys some movie tickets. D) Juanita would never prefer Option B to Option A.

Suppose that Arthur cares only about video games and coffee. His utility function is U = VC, where V is the number of video games that he plays and C is the number of cups of coffee that he drinks. The price of video games is $50, and the price of coffee is $3. Arthur has a budget of $800. Which levels of V and C maximize Arthur's utility? A) V = 10 and C = 100 B) V = 13 and C = 50 C) V = 16 and C = 0 D) V = 8 and C = 133.33

(Figure: Good Y and Good X V) Suppose the budget constraint shifted from constraint 2 to constraint 1. What could have caused this change? A) a decrease in income B) a decrease in the price of good X relative to that of good Y C) a decrease in income and an increase in the price of good X relative to that of good Y D) an increase in the price of good X and no change in the price of Y

Which of the following is NOT a result of completeness and rankability? I) A person prefers one consumption bundle to another. II) A person is indifferent between two consumption bundles. III) A person likes jelly beans more than hamburgers. A) I B) II C) III D) None of the above

Beth has $400 of income to spend on e-books (E), priced at $20 per book, and exercise classes called Zumba (Z), priced at $16 per class. Which of the following consumption bundles is infeasible? A) E = 20 and Z = 0 B) E = 2 and Z = 22 C) E = 10 and Z = 13 D) E = 8 and Z = 15

(Figure: Video Games and Guitars I) _____ is willing to give up a lot guitars for a small number of video games, and _____ is willing to give up a lot of video games for a small number of guitars. A) John; Paul B) Paul; John C) Paul; Paul D) John; John

(Figure: Tomatoes and Carrots I) Joanne's utility function is U = TC, where T is baskets of tomatoes and C is bags of carrots. One of Joanne's indifference curves will go through points: A) A, B, and F. B) B, D, and E. C) A, D, and E. D) B, C, and F.

(Figure: Pineapples and Oranges I) This figure shows the level of happiness that Sam receives when consuming pineapples and oranges. Sam's grandmother, who is visiting from Florida, gives Sam 10 oranges and 1 pineapple. According to his levels of happiness in consuming pineapples and oranges, Sam will be willing to: A) trade away more than one orange for an additional pineapple. B) trade lots of pineapples for an additional orange. C) trade his only pineapple for one more orange. D) give up all of his oranges for four more pineapples.

Maggie prefers cheese to crayons, and she prefers crayons to coconuts. To satisfy the assumption of _____, Maggie must also prefer _____. A) rankability; cheese to coconuts B) transitivity; cheese to coconuts C) transitivity; coconuts to cheese D) rankability; coconuts to cheese

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

Suppose a consumer spends all income on goods X and Y. Suppose the price of good Y increases and the consumer's income decreases. Which of the following must be true? A) The amount of good Y that the consumer can purchase increases. B) The amount of good X that the consumer can purchase increases. C) The amount of good X that the consumer can purchase decreases and the amount of good Y that the consumer can purchase increases. D) The amounts of good X and good Y that the consumer can purchase decrease.

(Figure: Coats and Sweaters II) What is the marginal rate of substitution between points A and B? A) 4 B) 6 C) 2 D) 8

(Figure: Coats and Sweaters II) Suppose that the consumer moves from point A to point B along her indifference curve. If the marginal utility of winter coats is 25, the marginal utility of wool sweaters is: A) 12.5. B) 2. C) 16. D) 50.

Suppose a consumer spends all income on goods X and Y. Suppose the price of good X decreases and the consumer's income decreases. Which of the following must be true? A) The amount of good Y that the consumer can purchase decreases. B) The amount of good X that the consumer can purchase decreases. C) Both A and B. D) None of the above.

Joaquim has new babies at home, so he cares only about diapers and wipes. Joaquim's preferences are represented by U(D,W) = DW, where D is the number of diapers and W is the number of wipes that Joaquim purchases. Joaquim's preferences can also be represented by this utility function: A) U(D,W) = D^0.5W^0.5 B) U(D,W) = D^0.5 + W^0.5 C) U(D,W) = D + W D) U(D,W) = 0.5D + 0.5W

Kyle's utility function is U = 4X + 3.7Y, where X is units of good X and Y is units of good Y. What is the marginal utility of good X? A) 4X + 3.7 B) 4 C) 0.3X D) U/4

Suppose that Lloyd cares only about shoes and clothes. Lloyd's utility function is U = S^0.5C^0.5, where S is the number of pairs of shoes and C is the number of clothing items that Lloyd owns. The price of shoes is $80, and the price of clothes is $100. Lloyd has a budget of $3200. Which levels of S and C maximize Lloyd's utility? A) S = 40 and C = 0 B) S = 16 and C = 20 C) S = 20 and C = 16 D) S = 10 and C = 24

Lars spends all of his income on pizza and gasoline. Suppose Lars is presented with two options: A and B. Option A will subsidize gasoline by decreasing its price by 50%. Option B will increase Lars's income by the cost of the subsidy in Option A. Assuming Lars is indifferent between Option A and Option B, which of the following is correct? A) Lars gains more utility from Option A than Option B. B) Lars purchases at least some pizza and at least some gasoline. C) Lars gains more utility from Option B than Option A. D) Lars must spend all of his money on gasoline.

(Figure: Good Y and Good X V) For budget constraint 2, suppose that the price of good Y is $90 per unit. What is the price of good X? A) $92 B) $88 C) $81 D) $102.24

Suppose that Eugene cares only about action figures and ice cream. His utility function is U = A^0.33C^0.67, where A is the number of action figures he owns and C is the number of scoops of ice cream he eats. The price of action figures is $10, and the price of ice cream is $4. Eugene has a budget of $100. How can Eugene's utility maximization problem be expressed as a Lagrangian equation? A) B) C) D)

Suppose a consumer spends all income on goods X and Y. Suppose the price of good X increases and the consumer's income increases. Which of the following must be true? A) The amount of good X that the consumer can purchase increases. B) The amount of good Y that the consumer can purchase increases. C) Both A and B. D) None of the above.

Sarinda consumes crab cakes and tuna. Sarinda's utility increases with the consumption of crab cakes, but her utility neither increases nor decreases with the consumption of tuna. Assuming tuna is on the x-axis and crab cake is on the y-axis, what do Sarinda's indifference curves look like? A) horizontal lines B) vertical lines C) upward-sloping lines from the origin D) downward-sloping lines

Which assumption(s) allow(s) us to draw indifference curves? A) cardinal measurement and cardinal ranking B) rankability and completeness C) that the more we have of a good, the less we are willing to give up to get even more of it D) free disposal and more is better

Suppose that Arthur cares only about video games and coffee. His utility function is U = VC, where V is the number of video games that he plays and C is the number of cups of coffee that he drinks. The price of video games is $50, and the price of coffee is $3. Arthur has a budget of $800. What is the Lagrangian equation that can be used to solve Arthur's utility maximization problem? A) B) C) D)

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

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

(Figure: Tomatoes and Carrots II) Which of the following statements is FALSE given the two goods tomatoes and carrots? A) Indifference curve U₂ provides a higher level of utility than indifference curve U₁. B) Bundle C is preferred to bundle D. C) Bundle A is preferred to bundle C. D) The consumer is indifferent between bundle A and bundle D.

Suppose that Eugene cares only about action figures and ice cream. His utility function is U = A^0.33C^0.67, where A is the number of action figures he owns and C is the number of scoops of ice cream he eats. The price of action figures is $10, and the price of ice cream is $4. Eugene has a budget of $100. Which levels of A and C maximize Eugene's utility? A) A = 6.66 and C = 8.33 B) A = 3.33 and C = 16.66 C) A = 10 and C = 0 D) A = 6 and C = 10

(Figure: Left Shoes and Right Shoes I) Nikolai enjoys eating sandwiches that have one slice of meat and two slices of cheese. His indifference curves are presented in Figure 4.12. Based on the shape of Nikolai's indifference curves, meat and cheese are: A) perfect substitutes. B) perfect complements. C) consumed in changing proportions. D) neither perfect substitutes nor perfect complements.

Which of the following statements is FALSE? A) Utility is the difference between the consumer's assets and her liabilities. B) One person's utility cannot be compared to another person's utility. C) A utility function gives the relationship between a consumer's well-being and the quantity of goods consumed. D) Inputs into a utility function may include wool socks, DVD rentals, roller coaster rides, asparagus, and Sunday church services.

The additional utility obtained from consuming an extra unit of a good is called: A) marginal utility. B) marginal rate of substitution. C) disutility. D) population-averaged utility.

Nikolai enjoys eating sandwiches that have one slice of meat and two slices of cheese. Which set of market bundles provides Nikolai with the highest level of utility? A) 4 slices of meat and 4 slices of cheese B) 3 slices of meat and 6 slices of cheese C) 2 slices of meat and 2 slices of cheese D) 1 slice of meat and 2 slices of cheese

For the utility function U(X,Y) = 2X + 10Y, the marginal rate of substitution MRS_XY is: A) 1/5. B) 5. C) X/5Y. D) 5Y/X.

Suppose a consumer spends all income on goods X and Y. Suppose the price of good Y decreases and the consumer's income increases. Which of the following must be true? A) The amount of good Y that the consumer can purchase decreases. B) The amount of good X that the consumer can purchase decreases. C) The amount of good X that the consumer can purchase decreases and the amount of good Y that the consumer can purchase increases. D) The amounts of good X and good Y that the consumer can purchase increase.

Allen earns $1,000 per week and purchases healthcare (H) goods at $200 per unit and non-healthcare (N) goods at $50 per unit. a. What is the equation for Allen's budget constraint? b. Graph Allen's budget constraint.

The marginal utility for a pair of black socks is 4 and the marginal utility for a pair of white socks is 1. a. What is the MRS_WB? b. If the consumer traded 8 pairs of white socks for 1 pair of black socks, what would happen to the consumer's utility?

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

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.

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.

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.

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.

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

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.

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?

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?

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.)

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?

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?

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?

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?

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.

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

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?

(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?

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?

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?

(Figure: Concert Tickets and Movie Tickets I) Use the graph to answer the following questions. a. What is the marginal rate of substitution at 3 concert tickets and 8 movie tickets? b. If the consumer's income decreases by 10% and the price of both goods decreases by 10%, how many concert and movie tickets will the consumer purchase? c. If the price of movie tickets doubles, what does the marginal rate of substitution equal at the new utility-maximizing point?

Hong's utility function over toys (T) and games (G) can be expressed as U(T,G) = 2TG. Can Hong's preferences also be represented by U(T,G) = 2T²G²?

Melissa has the utility function U = TC for bundles of tea (T) and coffee (C), with MU_T = C and MU_C = T. (Assume tea will be on the vertical axis.) She has $120, with the price of tea being $8 and the price of coffee being $4. Melissa will buy _____cups of tea and _____cups of coffee in equilibrium.

The ideal pheasant shell requires that lead shot (L) and gunpowder (G) be used in the following fixed proportion: 1 ounce of lead shot to 18 grains of gunpowder. Graph an indifference curve for 25 shells.

Graph Sherman's indifference curve for beer and wine, assuming he has a strong preference for wine. Graph Rodger's indifference curve for beer and wine, assuming he has a very strong preference for beer.

Ezra's utility function is U = XY, where MU_X = Y and MU_Y = X. In Lancaster, Pennsylvania, Ezra's income would equal $500, and the prices of good X and good Y are $5 and $5, respectively. In Washington, D.C., Ezra's income would equal $800, and the prices of good X and good Y are $8 and $10, respectively. Where should Ezra live? Show your work.

Mickey loves cheese and crackers, consuming 2 ounces of cheese with every cracker he eats. Draw Mickey's indifference curve, using a well-labeled diagram.

Suppose that U = XY^0.5. Which of the following bundles lie on the same indifference curve? bundle A: (X = 10, Y = 9) bundle B: (X = 9, Y = 16) bundle C: (X = 12, Y = 9) bundle D: (X = 3, Y = 100) bundle E: (X = 6, Y = 25) bundle F: (X = 6, Y = 36)

Suppose that the marginal utility of good X and good Y is given by the following equations: MU_X = 1/(X + 10) MU_Y = 1/Y a. As more units of good X are consumed, what happens to utility and marginal utility of good X? b. What is the value of MRS_XY?

Suppose that Malaki cares only about beef (B) and fish (F). His utility function is U = B^0.4F^0.6. The price of beef is $5, and the price of fish is $10. Malaki has a budget of $100. a. What Lagrangian equation can be used to solve Malaki's utility maximization problem? b. Derive the first-order conditions for the maximization problem. c. What is the solution to Bruce's maximization problem?

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.

A consumer is consuming a bundle of goods in which her MRS_XY is greater than P_X /P_Y. a. In a well-labeled diagram, show this situation using a budget constraint and indifference curve. b. Is the consumer maximizing utility? If not, what should she do to maximize 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.

Freddy's utility function for pizza (P) and tacos (T) is U = PT. Graph Freddy's indifference curve, using a well-labeled diagram.

The utility function for a consumer is U = min{0.25X, Y}. What would be the marginal rate of substitution for this consumer in equilibrium?

The utility function for a consumer is U = XY/(X + Y), where the MU_X = Y²/(X + Y)² and MU_Y = X²/(X + Y)². a. What is the slope of the indifference curve when X = 3.75 and Y = 3.75? b. What is the marginal rate of substitution when X = 4 and Y = 16?

Belle likes to wear either sandals or Crocs, but she always receives 3 times as much marginal utility from an additional pair of Crocs as from an additional pair of sandals. Draw Belle's indifference curve, using a well-labeled diagram.

Bucky has $20 to spend on bowling and billiards. The prices of bowling and billiards are $4 and $1 per game, respectively. Graph Bucky's budget constraint, assuming he has a coupon for two free games of bowling. Place bowling on the x-axis and billiards on the y-axis.

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

A consumer has U = X^0.5Y^0.5 for a utility function, with MU_x = 0.5 X^-0.5Y^0.5 and MU_y = 0.5 X^0.5Y^-0.5. If she has income of $100, the price of X is $5, and the price of Y is $10, this consumer will use _____units of X and _____units of Y in equilibrium.

Justin buys water (W) at $2 per gallon and food (F) at $10 per unit. Justin has an income of $50. Suppose that the government imposes a tax on water of $1 for each gallon consumed beyond 10 gallons. Graph Justin's budget constraint with water on the y-axis and food on the x-axis.

Suppose that U = min{2X, Y}, where X is units of good X and Y is units of good Y. The price of good X is $4, and the price of good Y is $7. What is the minimum expenditure necessary to achieve a utility level of 100?

Suppose that Jana cares only about apples and lettuce. Her utility function is U = A^0.5L^0.5, where A is the number of apples and L is the number of heads of lettuce that she consumes. The price of apples is $1, and the price of lettuce is $4. Suppose that Jana must have 100 units of utility and wants to achieve this level of utility with the lowest possible expenditure. a. How can Jana's expenditure minimization problem be expressed as a Lagrangian equation? b. Derive the first-order conditions for Jana's minimization problem. c. What is the solution to Jana's minimization problem? d. How much does this optimal solution cost?

Saja's utility function over toys (T) and games (G) can be expressed as U(T,G) = 2TG. Use calculus to determine whether Saja's indifference curves are convex.

Hira likes to shop at Beach Books, where a book is priced at $10. She also likes to shop at Busy Beans, where a latte is priced at $5. Hira has an income of $60. a. Graph Hira's budget constraint, placing books on the x-axis and lattes on the y-axis. b. Suppose that Hira's grandmother gives her a cash gift of $20. Graph Hira's budget constraint. c. Now, suppose that in lieu of the cash gift of $20, Hira's grandmother gives her a $20 gift card to Busy Beans. Graph Hira's budget constraint.

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.

A consumer buys coffee (C) for $3 each and bagels (B) for $1.50 each. She has income of $40. If the coffee shop limits the number of bagels that a customer may purchase to 6, what is the equation of her budget constraint?

Pedro loves leather belts but neither likes nor dislikes additional silk ties. Draw Pedro's indifference curve, using a well-labeled diagram.

Suppose that Defne's MU_X = Y² and MU_Y = 2XY. The price of good X is $10 and the price of good Y is $2. If Defne is consuming 8 units of good X and 16 units of good Y, is she maximizing utility? Explain your answer.

A consumer is using two goods (X and Y) so that her MRS is 4/3 and her relative price ratio is 7/8. Is the consumer maximizing her utility? If so, why? If not, what must she do to move her consumption toward equilibrium?