Charlie consumes apples and bananas. His utility function is $\mathbf{U}\left(X_{A}, X_{B}\right) =x_{A} x^{2} B$
-refer to scenario above, Charlie's utility function is x_Ax_B.The price of apples used to be $1, the price of bananas used to be $2, and his income used to be $40.If the price of apples increased to $5 and the price of bananas stayed constant, the substitution effect on Charlie's apple consumption would reduce his consumption by

Question

Charlie consumes apples and bananas. His utility function is

\mathbf{U}\left(X_{A}, X_{B}\right) =x_{A} x^{2} B

-refer to scenario above, Charlie's utility function is x_Ax_B.The price of apples used to be $1, the price of bananas used to be $2, and his income used to be $40.If the price of apples increased to $5 and the price of bananas stayed constant, the substitution effect on Charlie's apple consumption would reduce his consumption by

Quizplus · Accepted Answer

The substitution effect can be calculated by finding the change in consumption when the price changes, holding utility constant. Initially, Charlie's budget constraint is $1x_A + 2x_B = 40$. After the price change, the constraint is $5x_A + 2x_B = 40$. Solving these equations while keeping utility constant shows a reduction of 8 apples due to the substitution effect.

Charlie Consumes Apples and Bananas U(XA,XB)=xAx2B \mathbf{U}\left(X_{A}, X_{B}\right)=x_{A} x^{2} B U(XA​,XB​)=xA​x2B

Charlie Consumes Apples and Bananas $\mathbf{U}\left(X_{A}, X_{B}\right)=x_{A} x^{2} B$