Consider the economy (above) again where the following set of stocks is traded:
x1=(2,2,0) x2=(1,0,3) x3=(0,2,4)
for the prices (p1, p2, p3)=(1, 1, 1).
Suppose a start-up company wants to go public. The firm has total costs of $10,000 at date t=1 and sales of $20,000 in state 1, $30,000 in state 2, and $100.000 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 $26 per share. Will this IPO be successful, i.e. will there be a positive demand for the shares?