Q2. Elaine is a typical student and she spends her $200 allowance on beer (X) and books (Y). Her utility function is given by U = 20 XY and P_X = $2 and P_Y = $5.

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

(b) By how much would Elaine’s utility change if her allowance were reduced by $0.50?

(c) In an attempt to discourage drinking on campus, a hefty tax is imposed on beer and the price increases to $5.00. Solve for Elaine’s new optimal purchases of X and Y.

(d) Calculate Elaine’s elasticity of demand for beer and her cross-price elasticity of demand for books with respect to the price of beer.

(e) Sketch Elaine’s demand curve for beer using at least four price-quantity demanded combinations.