Question

Question 5

Complete parts 1 and 2 below:

Part 1:

Suppose in Janet’s utility function 2 hot dogs are perfect substitutes for 1 cheeseburger. If the price of one hot dog is $1 and the price of one cheeseburger is $3, how should Janet allocate her $15 budget between hot dogs and cheeseburgers to maximize her satisfaction?

A. she should spend all money on cheeseburgers

B. she should purchase 6 hot dogs and 3 cheeseburgers

C. she should purchase 9 hot dogs and 2 cheeseburgers

D. none of the others

E. she should spend all money on hot dogs

Suppose in Janet’s utility function 2 hot dogs and 1 bottle of coke are perfect complements. If the price of one hot dog is $1 and the price of one coke is $1.5, how should Janet allocate her $7 budget between hot dogs and cheeseburgers to maximize her satisfaction?

A. she should spend all money on hot dogs

B. she should purchase 4 hot dogs and 1 bottle of coke

C. she should purchase 1 hot dog and 4 cheeseburgers

D. none of the others

E. she should spend all money on cheeseburgers

Part 2:

We observe that Shelton purchased 20 apples and 10 orange in period 1, when the price of apple is $1 and the price of orange is $2. Suppose Shelton has regular preference (strictly monotone, transitive, complete, convex). Which statement cannot be inferred from the given information?

A. Shelton prefers (20,10) to (30,3)

B. Shelton prefers (30,22) to (20,10)

C. Shelton prefers (20,10) to (10,10)

D. Shelton prefers (20,10) to (10,20)

We observe that Shelton purchased 20 apples and 10 oranges in period 1, when the price of apple is $1 and the price of orange is $2. We also observe that Shelton purchased 10 apples and 20 oranges in period 2, when the price of apple is $1.5 and the price of orange is $1.

A. Shelton prefers (20,10) to (10,20)

B. We can say for sure Shelton is not maximizing utility

C. Shelton‘s income is not changing

D. Shelton prefers (10,20) to (15,10)

Answer 1

Solution:

1. Given the description, we can write Janet's utility function as: U(H, C) = H + 2C, so 2 hot dogs give same utility as 1 cheese burger (H denotes hot dogs quantity and C denotes cheeseburger quantity). Then, Marginal rate of substitution, MRS = marginal utility of H/marginal utility of C

MRS = (dU/dH)/(dU/dC)

MRS = 1/2 = 0.5

Price ratio = price of hotdog/price of cheeseburger = 1/3 = 0.33

As MRS > price ratio (0.5 > 0.33), so only hotdogs should be consumed. The correct option is (E).

2. With 2 hotdogs and 1 bottle of coke as perfect complements, utility function can be written as: U(H, C) = min{H, 2C} where H is quantity of hotdogs and C is quantity of coke bottles. Optimal in this case occurs where H = 2C

Given the prices and income, we can write budget line as: 1*H + 1.5*C = 7

With above condition, we have: 2C + 1.5C = 7

C = 7/(2 + 1.5) = 2, so H = 2*2 = 4

Thus, correct option is (D).

3. Among given options, B and C show that the preferred bundle is the one which has more of at least one of the goods, so these are accurate inferences (assuming both goods to be 'good'). Fo option A, bundle (30, 3) costs 1*30 + 2*3 = 36 < 40 (= 1*20 + 2*10), so it's rational to assumes (20, 10) preference over (30, 3).

Thus, the correct option is (D).

4. We have already seen that period 1 bundle costs $40. Period two bundle costs = 1.5*10 + 1*20 = $35. Also, note that the old bundle at new prices is still affordable: 1.5*20 + 1*10 = 40. So, preference doesn't seem rational and so cannot be commented on anymore. However, he still has $5 saved by current choice assuming period 1 to have expense match the exact income (40 - 35 = 5). So, we can say that Shelton could still purchase more of at least one good, and so still have room for a higher utility.

Thus, the correct option is (B).