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 Jim, and for Donna, when the price of strawberries rises to $3?

Answer 1

Question :

Answer : Jim Utility function : U = x*y

Donna Utility Function : U = x² * y

The prices are normalized to $1 for both goods

P_x = Price of Strawberries

P_y = Price of Chocolate

For Jim,

At Px = Py = $1

x = y = 50

At Px = $3 and Py = $1

x = 50/3 and y = 50

For Donna,

At Px = Py = $1

x = 100 and y = 50

At Px = $3 and Py = $1

x = 100/3 and y = 50