Diane spends her weekly allowance of $200 on good X and good Y; her utility function is given by:U = 15 XY
When the price of X is $5 and the price of Y is $10, Diane consumes 20X and 10Y.
(a) Show that at Diane's equilibrium the ratio of the marginal utility of the two goods equals their price ratio.
(b) By how much would Diane's utility change if her allowance were reduced by $1.50?
(c) Solve for Diane's optimal purchases of X and Y if the price of Y is reduced, through a price subsidy, to $5.
(d) What would be the cost of this price subsidy to the government?
(e) How much of a cash subsidy Diane would have to be offered instead of a price subsidy to be as happy as she was initially