Aunt Joyce purchases two goods, perfume and lipstick. Her preferences are represented by the utility function U(P, L) = PL , where P denotes the ounces of perfume used and L denotes the quantity of lipsticks used. Let PP denote the price of perfume, PL denote the price of lipstick, and I denote Aunt Joyce's income.

a) Write out the consumer's utility maximization problem.

b) Derive her demand for perfume. Your answer should be an equation that gives P as a function of PP , PL , and I. Determine this by using calculus and maximizing the objective function, do not use the tangency condition.

c) Derive her demand for lipstick. Your answer should be an equation that gives L as a function of PP , PL , and I. (Hint: look for symmetry between L and P).

d) What can be said about her cross-price elasticity of demand of perfume with respect to the price of lipstick?