Pecking order with variable investment:-
Consider the privately-known-prospects model with risk neutrality and variable investment. For investment I, the realized income is either RSI (in the case of success) or RFI (in the case of failure), where RS > RF 0. A good borrower has probability pH of success when working and pL when shirking; similarly, a bad borrower has probability qH of success when working and qL when shirking, where pH - pL = ?p = qH - qL, for simplicity.
The entrepreneur's private benefit is 0 when working and BI when shirking. The entrepreneur is risk neutral and protected by limited liability; the investors are risk neutral and demand a rate of return equal to 0.
(i) Let U˜SI b denote the bad borrower's gross utility under symmetric information.80 Consider the problem of maximizing the good borrower's utility subject to the investors' breaking even on that borrower, to the mimicking constraint that the good borrower's terms not be preferred by the bad borrower to her symmetric-information terms, and to the no-shirking constraint. Let {RS b, RF b} denote the (nonnegative) rewards of the good borrower in the cases of success and failure. Write the separating program.
(ii) Show that
(iii) (Only if you have read the supplementary section.) Show that the separating outcome is the only perfect Bayesian equilibrium of the issuance game if and only if α α∗ for some threshold α∗.