Please help to answer : The task is using consumption based model to derive the basic pricing equation and so on. Please see the attachment

There are two equally likely states of nature that can occur at date t+1, either there is in an expansion or there is a recession. An investor has preferences over consumption at dates :5 and t+ 1 that can be represented by the utility function U(Ctz6t+1) = 10803:) + {3513 (108(Ct+1)) where )3 E (0,1). The investor can trade a riskfree bond and shares of a firm in a competitive market. Let p? and p? denote the price of a bond and a share of a firm in period t, respectively. A risk-free bond issued at date t is a promise to pay 1 unit at date tl 1. The payoff of a share at date tl 1 is pi\" +dt+1, where dt+1 are the firm's dividends at t+ 1. The optimal consumption plan for this investor is such that the growth rate of consumption takes values p + 0' in an expansion and y a in a recession, and the investor does not face any binding borrowing constraint. (3) Use the consumption based model to derive the basic pricing equation for any payoff. Justify your answer. (10 marks) (b) Find )1)? as a function of y, or and [3. (10 marks) (c) How does the risk-free rate changes as y, (3 and cr changes? What is the economic intuition? Justify your answer. (10 marks) (d) Suppose the growth rate of dividends, '53ng is equal to the growth rate of the investor's consumption plan. Show that p? : %dt. (10 marks) (e) Which basic facts of asset returns the model in this exercise can explain and which ones it cannot? Explain your answer carefully. (10 marks)