Exam 4: Consumer Behavior

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?

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.

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?

For the utility function U(X,Y) = 6X + Y^0.5, the marginal utility of Y is:

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 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?

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

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?

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?

Which of the following statements is FALSE?

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:

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.

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)?

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.

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?

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?

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.

For the utility function U(X,Y) = 2X + 10Y, the marginal rate of substitution MRS_XY is:

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?

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