You work for an investment bank that underwrites technology IPOs. Firms in this sector can be either good or bad. Good firms are worth $30 per share and bad firms are worth $20 per share. There is an equal proportion of good firms and bad firms in the economy. That is, with 50% probability, an IPO is a good IPO and its opening price is $30 at the start of trading, and with 50% probability, an IPO is a bad IPO and its opening price is $20 at the start of trading. Each type of firm issues 1,000 shares in its IPO. A proportion of IPO investors are informed and can distinguish between good and bad IPOs. These informed investors only bid on the good IPOs. The remaining investors are uninformed and bid on every IPO. For every uninformed investor, there are three informed investors. Assume that conditional on bidding, each investor bids for all of the shares offered, and bids are filled on a pro-rata basis.
a) What is the expected value of an IPO of unknown type?
b) What are the aggregate expected profits to informed investors in an IPO if the offer price is set at the expected value of an IPO of unknown type?
c) What are the aggregate expected profits to uninformed investors in an IPO if the offer price is set at the expected value of an IPO of unknown type?