Q9. Suppose that John spends $320 on good X and good Y; his utility function      is given by U(X, Y) = 20 XY and that the price of X is $4 per unit while the price of Y is $8 per unit.

(a) Solve for John’s optimal purchases of X and Y.

(b) By how much would John’s utility change if his allowance were reduced by $1.50?

(c) Redo part (a) if the price of Y is reduced, through a price subsidy, to $4.

(d) Use your answers from (a) and (c) to calculate the price elasticity of demand for Y and the cross-price elasticity of demand for X with respect to the price of Y.

(e) What is the cost of this subsidy to the government?

(f) How much of a cash subsidy John would have to be offered instead of the price subsidy to be as happy as in part (c). Can you explain the difference in the cost of the two subsidies?