Questions in the picture..

If need be, write several matlab codes entitled he2a.m, hv2b .m , and so on (and hv2aF .m, hw2bF.m, and so on, if a function les are needed). Have all results saved to a diary les with poetxes * .mout. Always attach scans of any code used to produce your results. 1. [60 points] Consider the basic asset pricing model of Chapter 8. In this basic (BASIC) model, the household maximizes lifetime discounted utility: Zane\"). s=0 subject to each period's real budget constraint of: C! + 3:01! - 011) = dim1 + is, where y is real labor income, c denotes consumption, a denotes share purchases, .9 denotes the real share price, and d are real dividends. The agent takes income, share 1- prices, and dividends as given. Assume the utility function is u(q) = 51:: where 7 = 2. (a) Write out the problem in dynamic programming style by nding the Bellman's equation. Be sure note all the elements of the DP problem. (b) Find the optimality equations (Euler and budget). In your derivation of the Euler, show that it relates the lost utility from purchasing one more amet share to the discounted future benet of the purchase and explain the economic reasoning behind this equation. (c) nd a numerical value for the steadystate real stock price E by writing a matlab code and function le. Assume the steadystate values if = 1, g = 0, and param- eter value 5 = .95. Also assume that the supply of shares is inelasticly chosen by the rm to be a = 1. (d) Suppose now that dividends future dividends are uncertain but follow a Markov chain: (in) = .50 or d\") = 1.50 with probability transition matrix: .50 .50 H' [.50 .50]' Based on the Markov chain, construct two expressions for the real stock price in each state, 3\") and 3'\