Problem
A risk averse market maker's goal is to maximize their expected end-of-holding-period wealth (w) minus a risk adjustment of 0.0001 (i.e. 10-4) times its variance: Utility = E[w] - 0.0001 x variance(w) The market maker is again trading a very risky company's stock which is worth either $80 (vL) or $120 (vH) with probability 1/2 each, to be revealed at the end of their holding period. There are no traders who have superior information.
1. Compute the variance of one unit of the stock's end-of-period value, and the variance for y units.
2. Write down the market maker's utility if they start out with no stock in inventory and sell y units at price p.
3. Derive their competitive supply function y(p), that is, how many shares (y) they will supply for any given price (p). At what price would they supply 100 shares?
4. What average price would render the market maker indifferent between selling 100 shares of the security and not selling any shares at all? Your answer should be different from the price you obtained in part c. - can you explain why?