if Charlie's utility function were X ⁶_AX_B, if apples cost 90 cents each, and if bananas cost 10 cents each, Charlie's budget line would be tangent to one of his indifference curves whenever A)X_A = 6X_B. B)X_B = 6X_A. C)X_B = X_A. D)6X_B = 9X_A. E)90X_A + 10X_B = M.

Question

Quizplus · Accepted Answer

To find the budget line tangent to one of Charlie's indifference curves, we need to use the marginal rate of substitution (MRS) between apples and bananas. MRS is the rate at which Charlie is willing to give up apples for bananas while still remaining indifferent (i.e. keeping his utility constant). Using the given utility function, we can find the MRS between apples and bananas as follows: MRS = MU(Apples) / MU(Bananas) = (⁶) / (_AX + _B) = 16 / (X + 1) Now, let's assume Charlie has a total budget of B dollars to spend on both apples and bananas. Then his budget line can be represented as: P(apples)A + P(bananas)B = B where P(apples) = 0.9 and P(bananas) = 0.1. Substituting B = 10Y and rearranging the budget equation, we get: A = (B/0.9) - (B/9)B = 10Y/0.9 - YB/9 The slope of the budget line (i.e. the rate at which the price of apples is traded off for the price of bananas) is given by: - P(apples) / P(bananas) = -9 Setting the MRS equal to the slope of the budget line, we get: 16 / (X+1) = -9 Solving for X, we get: X = 6 Therefore, the budget line will be tangent to one of Charlie's indifference curves at a quantity of 6 bananas and (10/0.9) * 6 = 67 apples. Thus, the correct answer is D.

If Charlie's Utility Function Were X 6A XB, If Apples

If Charlie's Utility Function Were X ⁶_AX_B, If Apples