Erika purchases two goods, perfume and lipstick. Her preferences are represented by the utility function U(P,L)= P2L MUP : 2PL MUL : P2 where P denotes the ounces of perfume used and L denotes the quantity of lipsticks used. Let R: denote the price of perfume, PL denote the price of lipstick, and I denote Erika's income. a. Derive her demand for perfume. Your answer should be an equation that gives P as a function of Pp, PL, and I. b. Derive her demand for lipstick. Your answer should be an equation that gives L as a function of Pp, PL, and I. c. Is lipstick a normal good? Draw her demand curve for lipstick when I = 200. Label the demand curve D1. Draw her demand curve for lipstick when I : 300 and label this demand curve D2. Suppose Erika has $240 to spend on perfume and lipstick and that the prices of perfume and lipstick are P132343 and PLZ'Z, respectively. d. What is Erika's optimal bundle given these prices and her income? e. Suppose the price of perfume decreases to $6 while Erika's income and price of lipstick remains unchanged. What is Erika's optimal bundle? f. What is Erika's decomposition basket? g. What is the income and substitution effect from decrease in the price of perfume from $8 to $6