Question $2$

Consider a market where there are $N$ rational traders. All of these traders have CARA

preferences with risk aversion parameter $=\mathrm{.}5.$ 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 $$ increases to

$\mathrm{.}6?$ Explain the intuition for why the price moves this direction when $$ increases.