Consider a market where there are N rational traders. All of these traders have CARA preferences with risk aversion parameter = .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, dont worry about discounting future payoffs. Also, there are M irrational traders. They each will own one share of the stock no matter what the price.

a) If there are 10 shares of the stock available, what is the price of the stock as a function of N and M? (8 points)

b) If M increases, does the price of the stock rise or fall? Explain the intuition of this result. (10 points)

c) If M = 10, then how does the stock price respond to changes in N? Explain the intuition of this result. (10 points)