Question

Donna and Jim are two consumers purchasing strawberries and chocolate. Jim’s utility function is U(x,y) = xy and Donna’s utility function is U(x,y) = x²y where x is strawberries and y is chocolate. Jim’s marginal utility functions are MU_X=y and MU_y=x while Donna’s are MU_X=2xy and MUy=x². Jim’s income is $100, and Donna’s income is $150.

• What is the optimal bundle for Donna if the price of strawberries is $2 and the price of chocolate is $4?

Answer 1

For Donna absolute MRS = MUX/MUY = 2XY/X^2 or 2Y/X. Optimal bundle has MUX/MUY = PX/PY which gives 2Y/X = 2/4. This gives Y = 0.25X

Budget equation is M = XPX + YPY

150 = XPX + 0.25X*4

150 = 2X + X

X = 150/3 = 50 units and Y = 0.25*50 = 12.5

Optimal bundle for Donna is 50 units of strawberries and 12.5 units of chocolate.