Consider a market where there are N rational traders. All of these traders have CARA preferences with risk aversion parameter = .5. They are

Consider a market where there are N rational traders. All of these traders have CARA preferences with risk aversion parameter γ = .5. They are considering a stock that will pay a terminal dividend in the next period. The expected payoff of the dividend is $100 per share with a standard deviation of $10. Assume that the discount rate is zero. That is, don’t worry about discounting future payoffs.

a) If there are 10 shares of the stock available, what is the price of the stock as a function of N?

b) Does the price increase or decrease as N increases? Explain the intuition of this result.

c) If N = 10, what is the price of the stock? How does the price change if γ increases to .6? Explain the intuition for why the price moves this direction when γ increases.