Question

1. At Joe’s current consumption bundle of A= (4,4) his MRS is 2. He is on his budget constraint and hefaces price of 1 for x and 2 for y.

(a) How much income is he able to devote to consuming x and y?

(b) What proportion of his income is he currently devoting to x?

(c) If you were to counsel Joe as to how he should reallocate purchases of x and y, would you suggest he increase, decrease, or maintain his consumption of x(in the face of constant prices and income).

(d) Provide a graph that is consistent with your recommended reallocation. Graph the MU vector{M Ux, M Uy}and price vector {Px, Py} here and confirm your recommendation.

Answer 1

Joe’s current consumption bundle is A= (4,4) where x = 4 and y = 4. His MRS is 2 and currently at A, he is on his budget constraint. Prices are Px = 1 and Py = 2

(a) With the price levels Px = 1 and Py = 2 and consumption bundle x = 4 and y = 4, the income needed to buy A is 1*4 + 2*4 = $12. (sum of products of price and quantity of each good)

(b) Income is $12 and expenses on x is $4. Hence $4/$12 = 33.33% of income is currently devoting to x

(c) If you were to counsel Joe as to how he should reallocate purchases of x and y, would you suggest he increase, decrease, or maintain his consumption of x(in the face of constant prices and income).

Since MRS is 2 (absolute value) and price ratio Px/Py = 1/2 = 0.5, we see that MRS (absolute value) > Px/Py. Hence the marginal utility of x per dollar of x is more than marginal utility of y per dollar of y. So he should consume more x and less y.

(d) The graph is shown below