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.

Are strawberries a normal good or an inferior good for Jim? Explain your answer.

Answer 1

Jim has a marginal rate of substitution = MUX/MUY = Y/X. The price ratio is taken as PX/PY. At the optimum bundle selected, MUX/MUY = PX/PY or Y/X = PX/PY. This gives Y = X*(PX/PY)

Now with an income of M the budget equation is M = XPX + YPY. Use X*(PX/PY) in this equation to get

M = XPX + X*(PX/PY)PY

M = XPX + XPX

M = 2XPX

X* = M/(2PX)

Find derivative of X with respect to X: dX/dM = (1/2PX) > 0. This implies that if income increases, demand for X also rises. This shows that X or strawberries is a normal good.