Exam 4: Consumer Behavior

For the utility function U(X,Y) = X^0.5Y^0.5, the marginal rate of substitution MRS_XY is:

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.

(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?

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?

For the utility function U(X,Y) = 10X + 4Y, the marginal utility of X is:

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?

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

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?

(Figure: Coats and Sweaters II) What is the marginal rate of substitution between points A and B?

(Figure: Good Y and Good X V) Suppose the budget constraint shifted from constraint 2 to constraint 1. What could have caused this change?

(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?

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

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?

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)

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

(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.

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 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.

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.

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?