Questions on microeconomics, try and provide solutions for these.

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)?\f3. Bergson becomes a benevolent dictator. He has a subjects i = 1,... .n with CARA utilities w1...., un, respectively. (Write o, for the absolute risk aversion of i.) The total wealth in the society, Y, is a function of an unknown state w and is normally distributed with mean / and variance of. Bergson can choose any allocation r = (21, ... .2,) such that an (@) + ... +2, (w) I from her savings so that her wealth at t + 1 is my+1 = " (wt - 2,) if her wealth at t is wy and she consumes r, at t. (b) Find a sophisticated-optimal consumption strategy for her in which the self at any given date s consumes yes. Compute the constant y and briefly verify that this is indeed a subgame-perfect equilibrium of the multi-agent game. (c) For 8