Charlie has a utility function U(x A , x B ) =x A x 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) 80B) 40C) 160D) 16E) 240

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Homsukon Warintornn · Accepted Answer

Final Answer : A, Explanation :  The optimal bundle is found by solving the following problem:max U(x A , x B ) = x A x B subject to p A x A  + p B x B  = mwhere p A  = $1, p B  = $2, and m = $320.The Lagrangian for this problem is:L = x A x B  + λ(m - p A x A  - p B x 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 A x A  - p B x 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(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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Charlie has a utility function U(xA, xB) =xAxB, 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) 80B) 40C) 160D) 16E) 240

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