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

Consider a market where there are N rational traders. All of these traders have CAR A preferences with risk aversion parameterγ=.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 ifγincreases to.6? Explain the intuition for why the price moves this direction whenγincreases.

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