2. Suppose that my tastes for roses (x) and chocolate (y) can be represented by the utility function U (x, y) = 9x + y, where MU 9x+y, where MU = and MU = 1. Assume price of roses is pr, price of the chocolate is py and my money income is $M. (a) State the optimization problem. What are the endogenous variables in this problem? Exogenous variables? (b) Derive my ordinary (Marshallian) demand for roses and chocolate. (c) Derive my compensated (Hicksian) demand for roses and chocolate. (d) Are roses normal or inferior good? Is chocolate normal or inferior good? Explain. (e) Are roses substitutes or complements for chocolate? Is chocolate sub- stitute or complement for roses? Explain. (f) What is the equation of the inverse demand curve for roses? Draw this on a graph. If income were to increase, what would happen to the inverse demand curve for roses? Illustrate on your graph. Assume that my income is $24, price of the chocolate is $3 and rose also costs 1 dollars each. (g) What is the utility-maximizing choice of the chocolate and roses? (h) What is the level of utility at the optimal basket? Show your result in the optimal choice diagram. Assume that my income and the price of the roses stay at $24 and $1 re- spectively. Price of the chocolate, however, decreased to $2. (i) What is the utility-maximizing choice of the chocolate and roses? (Hint: Is the tangency condition satisfied?) (j) What is the level of utility at the optimal basket? Show your result in the optimal choice diagram.