Charlie has a utility function U(x_A, x_B)=x_Ax_B, the price of apples is $1, and the price of bananas is $2.If Charlie's income were $320, how many units of bananas would he consume if he chose the bundle that maximized his utility subject to his budget constraint? A)80 B)40 C)160 D)16 E)240

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Quizplus · Accepted Answer

The optimal bundle is found by solving the following problem:max U(x_A, x_B) = x_Ax_Bsubject to p_Ax_A + p_Bx_B = mwhere p_A = $1, p_B = $2, and m = $320.The Lagrangian for this problem is:L = x_Ax_B + λ(m - p_Ax_A - p_Bx_B)Taking the partial derivatives of L with respect to x_A, x_B, and λ, we get:∂L/∂x_A = x_B - λp_A = 0∂L/∂x_B = x_A - λp_B = 0∂L/∂λ = m - p_Ax_A - p_Bx_B = 0Solving these equations, we get:x_A = m/(p_A + p_B) = $320/($1 + $2) = 80x_B = m/(p_A + p_B) = $320/($1 + $2) = 80Therefore, Charlie would consume 80 units of bananas if he chose the bundle that maximized his utility subject to his budget constraint.

Charlie Has a Utility Function U(xA, XB)=xAxB, the Price of Apples

Charlie Has a Utility Function U(x_A, X_B)=x_Ax_B, the Price of Apples