.Suppose that John spends $200 on good X and good Y. Moreover, suppose that his utility function is given by:

U(X, Y) = 30 XY

and that the price of X is $20 per unit while the price of Y is $10 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)Solve for John's optimal purchases of X and Y if the price of X is reduced, through a price subsidy, to $10.

(d)What would be the cost of this subsidy to the government?

(e) How much of a cash subsidy John would have to be offeredinstead of a pricesubsidyto be as happy as in part(d). Can you explain the difference in the cost of the two subsidies?