Exam 4: Consumer Behavior

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.

Which assumption(s) allow(s) us to draw indifference curves?

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?

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.

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.

(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:

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?

(Figure: Tomatoes and Carrots IV) Which of these indifference curves is convex to the origin?

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?

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?

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?

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?

(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.

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

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?

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?

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?

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.

The utility function U = Y/X violates the assumption(s) of:

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.