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tively, according to their own ideas for each IPO shares at t = 2 in the trading price for estimated as follows :

Rational investors :
Emotional investors :
Because emotional investors believe the bull market will certainly continue to t = 2, at t = 2 they demand is forecast to be two time periods t = 1,2 inductive total demand , so they are expected at t = 2 price and consistent , that is . Emotional investors and rational investors at t = 2 also shows the expected price they were willing to pay at time t = 1 the price .

Market reaches equilibrium, equal to the amount demanded and distribution , namely , there are:
 
 
Also , there is , namely , so . Rational investors at t = 2 the expected price is higher than its intrinsic value , which is due to rational market participants ( such as the issuer , underwriter ) expects at t = 2 to the probability of the remaining stock to sell perceptual investors.

Assuming the issuer to determine the amount of IPO shares issued and prices are for their own profit maximization. Suppose the stock of total circulation has given , then the number of shares outstanding has also been identified . Denoted IPO shares on the secondary market when t = 1 quantity sold for IPO shares on the secondary market at t = 2 the quantity sold . On the assumption that the issuer is rational, he expected at t = 2 price . The issuer concerned, he proceeds to include all of the outstanding shares were sold and non-tradable shares of revenue , ie,

 T = 1 when the transaction price , for investors, they are willing to pay in t = 1 for their expected share price at t = 2 in the transaction price. , As defined by the optimal time t = 1 requirements. At that time , t = 1 the issue of insufficient time t = 1 Inductive investor demand , emotional investors are optimistic market sentiment , they are more than rational investors on each stock 's valuation is higher , so the issuer in t = 1 when the price of shares of stock to each investor to sell sensibility . At that time , t = 1 the distribution is greater than the time t = 1 investor demand for emotional , sensual market investors will think well enough , but the market does not hold too much optimism , it does not buy stocks when t = 1 , so the issuer the price of shares of stock to sell each rational investors , so that they appear at t = 2 bull sold sensual investors.
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