(31] points} Consider an expected prot maximizing monopolist who faces an uncertain demand. He supplies q units of goods at zem cost and sells it at price 3 q, where H is nnlmown. [The price and the supply level can be negative] (11] Asemmhg that 3 ~ N {3:152}, compute the monopolist's uptilnal Suppl}...r q and his expected prot under the optimal supply. [h] Suppose that, through market research, the monopolist can learn about H. In particularT by investing :12, he can learn the value of a random variable 1' before charming his Suppl]? 1;, such that. H = X+Y, X ~ N [[1,]. c] and lr' ~ N[,c]. How much should the monopolist invest? [Note that the utility function of the monopolist is [H q] q 22.] There are three periods, t = 0, 1,2. In t = 1 Mary maximizes her utility over leisure and consumption given the following function: UI(M, CI) = NICE subject to the following budget constraint: Ci + wiN = 24w1 where wi = 10. Note the price of the consumption good is assumed to be one in all periods. After she has made this decision, in t = 2 she maximizes this utility function: U2(N2, C2) = Nici subject to the following budget constraint: C2 + w2 N2 = 24w2 where w2 = 20. (a) (6 points) For t = 1, 2 calculate Mary's choice of leisure and consumption in each period. (b) (6 points ) For t = 1, provide economic intuition for the income and substitution effects of a wage increase on leisure. Can you say anything about the relative magnitudes of these income and substitution effects? (c) (7 points) Go back to your solution in part (a). If the interest rate is 10% per period, what is the present value of her consumption in t = 0? Please use 0.9 and 0.8 as approximations for 1/(1.1) and 1/(1.1) respectively. (d) (7 points) Mary now has the option of obtaining additional job training in t = 0 at an investment cost of $200. As a result, her wage rate increases in t = 1 to wj = 20 and in t = 2 to w2 = 30. Calculate the net present value of this investment on consumption. Consider only the value of consumption (and not the value of leisure). (e) (7 points ) For more general utility functions, when will the net present value of the investment on consumption from part (d) likely be negative? Use income and substi tution effects in your explanation. (f) (7 points) Does Mary have a Laffer curve for income taxes (as opposed to consumption taxes)?