Question: A firm is planning to go public by selling 2,000 shares. The true value of each share is either $8 or $12 with equal probabilities. Therefore, the expected value of the each share is $8 x (1/2) + $12 x (1/2) = $10. There are two groups of investors, 1,000 informed investors and 2,000 uninformed investors, planning to subscribe for the new shares. Each investor can at most subscribe for one share. Informed investors learn the true value of the shares before the IPO. Uninformed investors do not know the true value but they know the expected value of each share. New shares will be allocated among all subscribers on a pro rata basis if total number of shares subscribed exceeds 2,000.
Required:
1. What is uninformed investors' expected payoff for subscribing for new shares at $10 per share?
2. What is the highest price at which all shares (2,000 shares) will be sold?
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