4 Multiple Assets Suppose an agent is trying to maximize utility U=logc1+(logcb+(1)logcr) log is the natural log. Exogenous output is given by: y1=2000,yb=2240,yr=1400,=.8 The other parameters are given by: =.8 and 1+r=1.25. There are two assets. One is a riskless bond, and one is a stock that pays more in the boom. If you buy one unit of the riskless bond, you get 1+r in the second period no matter what. If you buy one unit of the stock, you get pb in the boom, or pr in the recession. The budget constraints are that: 2 yb=cb+x2,yr=cr+x2,y1=c1+x1 But now, you can choose to allocate your capital account between stocks and bonds: x1=b+s where b is your bonds and s is your stocks. In period 2, the captial account/current account is given by: xb=b(1+r)+spb,xr=b(1+r)+spr Assume that the stock pays 1.5 in the boom and 0.25 in the recession, so pb=1.5,pr=0.25 1. Rewrite the problem as an unconstrained maximization problem in terms of b and s. 2. What is the first-order condition with respect to b ? What about with respect to s ? 3. Solve for b and s. What sign does s have? Can you give an economic intuition as to why it has that sign? 4. What is x1 ? How does it compare to your answers to the last two questions