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 $120, how many units of bananas would he consume if he chose the bundle that maximized his utility subject to his budget constraint?A) 30B) 15C) 60D) 6E) 90

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Jolly Karungi · 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 = $120.The Lagrangian for this problem is:L = x A x B  + \lambda(m - p A x A  - p B x B )Taking the partial derivatives of L with respect to x A , x B , and \lambda, we get:\frac{\partial L}{\partial x A } = x B  - \lambda p A  = 0\frac{\partial L}{\partial x B } = x A  - \lambda p B  = 0\frac{\partial L}{\partial \lambda} = m - p A x A  - p B x B  = 0Solving these equations, we get:x A  = \frac{m}{p A  + p B } = \frac{120}{1 + 2} = 40x B  = \frac{m}{p B  + p A } = \frac{120}{2 + 1} = 60Therefore, Charlie would consume 60 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 $120, how many units of bananas would he consume if he chose the bundle that maximized his utility subject to his budget constraint?

A) 30
B) 15
C) 60
D) 6
E) 90

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Learning Objectives

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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 $120, how many units of bananas would he consume if he chose the bundle that maximized his utility subject to his budget constraint?A) 30B) 15C) 60D) 6E) 90

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Learning Objectives

Learning Objectives

Related questions

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 $120, how many units of bananas would he consume if he chose the bundle that maximized his utility subject to his budget constraint?

A) 30
B) 15
C) 60
D) 6
E) 90