Exam 4: Consumer Behavior

Marsha 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.

The marginal utility for a pair of black socks is 4 and the marginal utility for a pair of white socks is 1.

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 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?

Billy is maximizing utility subject to his limited income. As a result, which of the following statements is TRUE?

Susie likes to shop at the Flower Mart, where a vase of flowers is priced at $10. She also likes to shop at Yummy Freeze, where a cup of frozen yogurt is priced at $5. Susie has an income of $60.

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.

Carl's budget constraint is 75 = 10X + 4Y. a. How many units of good X can Carl afford? b. What is the vertical intercept of the budget constraint? c. What is the slope of the budget constraint? d. Can Carl afford to buy 4 units of good X and 10 units of good Y? e. If Carl's income increases by 10%, what happens to the slope of the budget constraint? f. What is Carl's MRS_XY at the utility-maximizing point?

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

Frank's utility function is U = 10X + 6Y. Frank 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 Frank purchase?

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?

David's utility is U = 10S + T, where S is rounds of sporting clays and T is rounds of trap.

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

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

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?

Fisher's utility function for trout (T) and salmon (S) is given by U = ST, where the MU_T = S and MU_S = T. Which set of consumption bundles lies on the same indifference curve?

Randy likes baseball more than football, football more than basketball, and basketball more than baseball. Which assumption about consumer preferences does this violate?

Use the following to answer question: Figure 4.11 -(Figure 4.11) 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.

If a consumer's budget constraint has a slope that is less than -1:

Jewel'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?