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 when I > P_x is

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 when I > P_x is

Quizplus · Accepted Answer

Using the first MRS equation: MU_x = y MUx/MUy = -Px/Py -x/(y+1) = -Px/Py Px = Py(x/(y+1)) Using the second MRS equation: MU_y = x+1 MUy/MUx = Px/Py (y+1)/x = Px/Py Px = Py((y+1)/x) Equating the two expressions for Px, we get: Py(x/(y+1)) = Py((y+1)/x) x^2 = y^2 + y Substituting y with (x/x-1): x^2 = (x/(x-1))^2 + (x/(x-1)) x^3 - 2x^2 + x = 0 x(x^2-2x+1) = 0 x = 1 or x = (sqrt(2) + 1) Since the demand curve is defined for prices greater than or equal to P_x, we can discard the solution x = 1. Therefore, the demand curve is given by: x^d = (sqrt(2) + 1) - 1 = sqrt(2) Thus, the answer is (C).

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