Suppose the consumer's utility function is given by U(x,y) = xy + y where MU_x = y MU_y = x+1 The equation for this consumer's demand curve for $x$ when I P_x is A) x^d = 0 B) x^d = $\frac { I } { 2 P _ { x } }$ C) x^d = $\frac { I } { 2 P _ { x } }$ -$\frac { 1 } { 2 }$ D) x^d = 1/2

Question

Suppose the consumer's utility function is given by U(x,y) = xy + y where MU_x = y MU_y = x+1 The equation for this consumer's demand curve for $x$ when I > P_x is A) x^d = 0 B) x^d = $\frac { I } { 2 P _ { x } }$ C) x^d = $\frac { I } { 2 P _ { x } }$ -$\frac { 1 } { 2 }$ D) x^d = 1/2

Quizplus · Accepted Answer

The consumer's demand curve for $x$ is derived by setting the marginal rate of substitution (MRS) equal to the price ratio and solving for $x$. The MRS is $\frac{MU_x}{MU_y} = \frac{y}{x+1}$. Setting this equal to $\frac{P_x}{P_y}$ and solving for $x$ gives the demand function. Given the budget constraint $I = P_x x + P_y y$, the solution leads to option C.

Suppose the Consumer's Utility Function Is Given by U(x,y) = xxx

Suppose the Consumer's Utility Function Is Given by U(x,y) = $x$