An agent with wealth levelY0= $100 lives for two periods. In period 1, he invests $20 in a risk free bond, consumes some of his wealth and invests the rest of his wealth in the stock market portfolio. The market portfolio provides an uncertain payoff. Stock market's return in a good, average and bad year is 8%, 4% and -5% respectively. The probability of a good, average and bad year for stock market is 30%, 45% and 25% respectively. The risk-free security provides a certain payoff of 3%. The discount rate for the second period's consumption is 0.7. The utility function of the investor isU(C) =ln(C) over consumption.

a) Use Excel to graph the expected utility of the investor as a function of his invested amount in the stock market.

b) How much of the agent's wealth should be invested in the stock market for the next period?

c) Determine the optimal level of investment in the stock market if an investor has $200 in initial wealth.