Suppose that Bob’s preferences can be represented by the utility function 𝑢(𝑥, 𝑦) = 2𝑥 + 3𝑦. The price of y is $20.

(a) Sketch a couple of indifference curves, with utility u= 64 and u=320. (5 points)
(b) Determine Bob’s demand function for x. Sketch it. (5 points)
(c) If the price of x is $10, and Bob’s income is $1000, how many x would Bob consume?
How much income would be devoted to spending on y? (5 points)
(d) Suppose that the price of x doubles to $20. Calculate the income and substitution effects. (10 points)
(e) Is x a normal or inferior good in the range you calculated in part (d)? (5 points)

1. Suppose the price of x₁ is $20 and the price of x₂ is $4. If good x₁ is on the horizontal axis, what is the slope of the consumer's budget constraint?

a. -0.20

b. -0.25

c. -5.0

d. -0.2

e. -4.0

f. -20.0

2. Suppose the price of x1 is $5 and the price of x2 is $1 and Toni's income is $20. Suppose Toni gets a $5 gift card that can only be used for the purchase of x1 and there is no resale value of the gift card. With the gift card, the commodity bundle (1,20) is on Toni's budget constraint.

True

False

3. Tiffany's utility function is given by the formula U(x1, x2) = min{20x1, 10x2}. If x1 = x2, which commodity will have a greater marginal utility?

A. Both x1 and x2 have the same marginal utility

B. It is not possible to determine which commodity has higher marginal utility

C. x2

D. x1

4. For U(x₁,x₂) = 6x₁^1/3 + x₂, preferences are

a. consistent with diminishing marginal rate of substitution.

b. consistent with constant marginal rate of substitution.

c. consistent with increasing marginal rate of substitution.

d. not consistent with a utility function.

5. For a utility function of the form U(x₁,x₂)=min{5x₁,10x_2}, the individual will have excess x₂ for commodity bundles where

a. x2>2x1 b. x2>5x₁

c. x₂>0.5x₁ d. x2>10x₁

6. Matt enjoys Fuji and Gala apples and finds 1 Fuji apple to be just as good as 4 Gala apples.

a. Matt's preferences over Fuji (F) and Gala (G) apples can be represented by the utility function U(F,G)=0.25F+G

b. Matt's preferences over Fuji (F) and Gala (G) apples can be represented by the utility function U(F,G)=F+4G

c. Matt's preferences over Fuji (F) and Gala (G) apples can be represented by the utility function U(F,G)=4F+.25G

d. Matt's preferences over Fuji (F) and Gala (G) apples can be represented by the utility function U(F,G)=4F+G

e. Both A and B

f. Both C and D

Kayo is going to dinner in a Spanish restaurant in New York and would love to have some sangrias (s) and tapas (t). Her preferences can be represented by the utility function:

U(s,t) = 2 ln (s) + 3 ln (t).

a. Compute the marginal rate of substitution of sangrias for tapas. Is the MRS increasing or decreasing in s? How do we interpret this?

b. Suppose that the price of sangrias is P_s = 2, the price of tapas is P_t = 5, and Kayo's dinner budget is $25. What exactly should Kayo order for dinner, so that her utility is maximized?

c. Suppose the price of sangria increases to P_s = 4. What should Kayo's new dinner order be?

d. Given the price increase, how much income does Kayo need, to remain as happy (have the same utility) as she was before the price change?

e. What exactly would Kayo order for dinner if she had that additional income, given the new prices?

22. [Consumer Theory] Ada, who has income M = $4,800 and utility U = XY pays Px = $20 and Py = $40. a) Provide a fully labelled indifference curve diagram (Good X on the horizontal axis) and supplemental calculations to illustrate the income and substitution ef- fects associated with the introduction of a $30 per unit subsidy on Good Y. Cal- culate bundle "b". Making reference to your diagram, explain how you can infer that Ada thinks that Good Y is a normal good. b) Make