Exam 4: Consumer Behavior

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.

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)?

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?

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.

Suppose that U = U(P, M), where P and M are peanuts and marshmallows. The marginal utility of marshmallows, MU_M, is given by:

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?

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 graph of the utility function U = 4Y + X would reveal that goods X and Y are:

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?

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?

For the utility function U(X,Y) = X^0.75Y^0.25, the marginal utility of Y is:

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.

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?

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.

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?

Mika's marginal rate of substitution of apples (A) for oranges (O) is 5 (MRS_AO = 5). This information implies that:

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.

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?

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.