microeconomics

e. Compute the equivelenit variation, Problem 4 (25 points): Rachel spends her income, Y, on Rock Shows (R) and Sunglasses (S) with prices pp and ps. Rachel's preferences are given by the Cobb-Douglas utility function 0.8 0.2 U(X, Y) = R S a. Write out the Lagrangian for Rachel's utility-maximization problem. b. Use the Lagrangian to derive Rachel's optimal choice, (R*,S*). c. For a given utility level, U, derive Rachel's Expenditure function E(PRPs, U.). d. Use the Expenditure function to derive Rachel's compensated demand for Rock Shows