If Charlie's utility function is X ⁴_AX_B, the price of apples is p_A, the price of bananas is p_B, and his income is m, then Charlie's demand for apples will be A)m/(2p_A). B)0.25 p_Am. C)m/(p_A + p_B). D)0.08m/p_A. E)1.25p_B m/p_A.

Question

Quizplus · Accepted Answer

Using the utility maximization rule of equating marginal utility to price, we get:
MU of apples / p of apples = MU of bananas / p of bananas
Using the given utility function, we get:
(14S1 - S1) / pS1U1B1AS1U1B0 = B1 / pS1U1B1BS1U1B0
Simplifying and solving for S1, we get:
S1 = (B1 / 14) * pS1U1B1AS1U1B0 / pS1U1B1BS1U1B0
Substituting S1 in the budget constraint, we get:
(S1U1P1 + S1U1P0) * pS1U1B1AS1U1B0 + B1 * pS1U1B1BS1U1B0 = m
Solving for B1, we get:
B1 = (m - pS1U1B1AS1U1B0 F1F1F1S1F1F1F10) / pS1U1B1BS1U1B0
Substituting the value of B1 in the expression above, we get:
S1 = (m - pS1U1B1AS1U1B0 F1F1F1S1F1F1F10) / (14pS1U1B1AS1U1B0 + pS1U1B1BS1U1B0)
Substituting the value of S1 in the demand function for apples, we get:
X = S1U1P1 = (m - pS1U1B1AS1U1B0 F1F1F1S1F1F1F10) / (14pS1U1B1AS1U1B0 + pS1U1B1BS1U1B0) * 0.08
Simplifying, we get:
X = 0.08m / pS1U1B1AS1U1B0

If Charlie's Utility Function Is X 4A XB, the Price

If Charlie's Utility Function Is X ⁴_AX_B, the Price