Writing \(n_{H}\) as a function of \(\pi, n_{H}(\pi)\), show that \(c_{s}\) in Proposition 6.1.3 is given by

\[c_{s}=(1-\phi)(1-y)\left[\frac{1}{\bar{n}_{H}}-\frac{\gamma_{B}-1}{m}\right] K\]

with \(\bar{n}_{H}=n_{H}(\phi)\).

Data From Proposition 6.1.3:-

Transcribed Image Text:

Proposition 6.1.3 (Chemmanur and Fulghieri). There is an equilibrium in the case where the firm chooses to go public involving the following: If 0 = 0, the firm issues n shares, each at the price pH, raising a total amount K for the investment; if 0 = 0, with a probability = (0, 1], it pools with the good projects by issuing n shares, each at the price p, of which only a number xny are bought by investors in equilibrium (0 < x < 1), thus raising only the amount xK; with probability (1B), it separates from the good projects by issuing n, shares, each at the price p, with n > n and p < PH, thus raising the entire amount H