Charlie consumes apples and bananas; his utility function is U(a, b)= ab.Charlie's fruit farm yielded 5 apples and 10 bananas.In addition, Charlie has $10 that he was given by a secret admirer.Charlie can buy or sell apples at $2 each and he can buy or sell bananas at $1 each.Charlie will consume
A)more apples and more bananas than he grows
B)more apples and fewer bananas than he grows
C)fewer apples and more bananas than he grows
D)fewer apples and more bananas than he grows.
E)exactly as many apples as he grows and more bananas than he grows.

Question

Quizplus · Accepted Answer

Charlie's marginal rate of substitution (MRS) is Ua/Ub = b/a. At the initial endowment, MRS = 10/5 = 2. The price ratio is Pa/Pb = 2/1 = 2. Since MRS = Pa/Pb, Charlie is initially on his optimal consumption bundle. With $10, Charlie can buy 5 more apples or 10 more bananas. If he buys 5 more apples, his MRS will become 15/5 = 3, which is greater than the price ratio. This means that Charlie will substitute apples for bananas until his MRS equals the price ratio again. Therefore, Charlie will consume more apples and more bananas than he grows.

Charlie Consumes Apples and Bananas; His Utility Function Is U(a