uppose there are two dates (0 and 1), two assets, and two possible states of nature at date . One asset is a risk-free bond that pays one unit of the consumption good in each state f nature; its price at date 0 is p. The other is a risky asset that pays one unit of the consumption good in state 1 and nothing in state 2; its price at date 0 is pr, where p >P2. An investor is endowed with w units of the risk-free bond and un units of the risky asset. Her utility function is U(a, 02), where c, is consumption in state s, for s 1,2. (a) Define the concept of a complete asset market. (b) Is this asset market complete? Justify your answer. [3 marks] 4 marks] (c) Write down the Lagrangian for the investor's problem and the first order conditions. 14 marks] (You do not need to solve the investor's problem.,) (d) Use these first order conditions to derive expressions for the marginal utilities and the marginal rate of substitution when the investor holds an optimal portfolio. [5 marks] (e) Discuss the significance for risk allocaton of the expression for the marginal rate of [4 marks] substitution that you found in part (d). uppose there are two dates (0 and 1), two assets, and two possible states of nature at date . One asset is a risk-free bond that pays one unit of the consumption good in each state f nature; its price at date 0 is p. The other is a risky asset that pays one unit of the consumption good in state 1 and nothing in state 2; its price at date 0 is pr, where p >P2. An investor is endowed with w units of the risk-free bond and un units of the risky asset. Her utility function is U(a, 02), where c, is consumption in state s, for s 1,2. (a) Define the concept of a complete asset market. (b) Is this asset market complete? Justify your answer. [3 marks] 4 marks] (c) Write down the Lagrangian for the investor's problem and the first order conditions. 14 marks] (You do not need to solve the investor's problem.,) (d) Use these first order conditions to derive expressions for the marginal utilities and the marginal rate of substitution when the investor holds an optimal portfolio. [5 marks] (e) Discuss the significance for risk allocaton of the expression for the marginal rate of [4 marks] substitution that you found in part (d)