Consider the economy where the following set of stocks is traded: x1=(10,0,30) x2=(0,20,40) x3=(20,20,0)

for the prices (p1, p2, p3)=(12, 14, 8).

Suppose a start-up company wants to go public. The firm has total costs of $90,000 at date t=1 and sales of $100,000 in state 1, $120,000 in state 2, and $200,000 in state 3. The firm wants to issue 1,000 IPO shares. (A share is endowed with a cash flow right of 0.1% of the total profits of the firm.) The underwriter suggests an IPO price of $40 per share. Will this IPO be successful, i.e. will there be a positive demand for the shares?