Charlie has the utility function U(x_A, x_B)=x_Ax_B.His indifference curve passing through 12 apples and 64 bananas will also pass through the point where he consumes 2 apples and A)386 bananas. B)48 bananas. C)96 bananas. D)394 bananas. E)384 bananas.

Question

Quizplus · Accepted Answer

Given Charlie's utility function appears to be a Cobb-Douglas form, which typically looks like U(x, y) = x^ay^b, where x and y are quantities of two goods (in this case, apples and bananas), and a and b are constants that represent the preferences of the consumer. The utility level remains constant along an indifference curve, meaning the consumer is equally satisfied with any combination of goods on the same curve.To find the combination of apples and bananas that would lie on the same indifference curve as 12 apples and 64 bananas, we use the property of Cobb-Douglas utility functions that the ratio of the quantities of the two goods raised to their respective powers (a and b) remains constant along an indifference curve.Given the initial point (12 apples, 64 bananas), and the second point (2 apples, y bananas), we can set up the equation based on the constant utility:(12^a * 64^b) = (2^a * y^b)Without the specific values of a and b, we can't solve this directly, but we know that the quantities of goods are directly substitutable based on their ratio in the utility function. Since the question does not provide specific values for a and b, we look for an answer that reflects a logical outcome based on the properties of Cobb-Douglas preferences.Given the drastic reduction in apples from 12 to 2, to remain on the same indifference curve, the quantity of bananas must increase significantly to compensate for the loss in utility from consuming fewer apples. Among the provided options, 384 bananas (E) is a significant increase that would likely compensate for the decrease in apples, maintaining the same level of utility, assuming the utility function's properties and the absence of specific parameters.

Charlie Has the Utility Function U(xA, XB)=xAxB

Charlie Has the Utility Function U(x_A, X_B)=x_Ax_B