let consider the economy above again where the

Question

Let 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).
 
Assume 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 needs 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?