Let U(x,y) = $\sqrt { x y }$ with MU_x = $\frac { \sqrt { y } } { 2 \sqrt { x } }$ and MU_y = $\frac { \sqrt { x } } { 2 \sqrt { y } }$ . Let I = $100, P_x = $10 and P_y = $10 be the initial set of prices and income. Now, let P_x rise to $25. What are the (approximate) substitution and income effects of this change in prices? A) Income effect = -3.3; Substitution Effect = -2.1 B) Income effect = -2.3; Substitution Effect = -1.7 C) Income effect = -1.3; Substitution Effect = -1.7 D) Income effect = -1.7; Substitution Effect = -1.3

Question

Quizplus · Accepted Answer

The substitution effect is calculated using the change in relative prices while keeping utility constant, and the income effect is calculated by adjusting for the change in purchasing power. Given the utility function and price changes, the substitution effect is approximately -1.7 and the income effect is approximately -1.3.

Let U(x,y) = xy\sqrt { x y }xy​ With MUx = y2x\frac { \sqrt { y } } { 2 \sqrt { x } }2x​y​​

Let U(x,y) = $\sqrt { x y }$ With MU_x = $\frac { \sqrt { y } } { 2 \sqrt { x } }$