Reputational capital:
Consider the fixed-investment model. All parameters are common knowledge between the borrower and the investors, except the private benefit which is known only to the borrower. The private benefit is equal to B with probability 1 - α and to b with probability α, where B > b > 0.
(i) Consider first the one-period adverse-selection problem. Suppose that the borrower has assets A > 0 such that
(ii) Suppose now that there are two periods (t = 1, 2). The second period is described as in question (i), except that the belief α˜ at date 2 is the posterior belief updated from the prior belief α, and that the borrower has cash A only if she has been successful at date 1 (and has 0 and is not funded if she has been unsuccessful). So, suppose that the first-period project is funded and that the borrower receives at the end of date 1 a reward A when successful and 0 when unsuccessful. The first-period funding is project finance and does not specify any funding for the second project. Suppose for notational simplicity that the private benefit is the same (B or b) in period 1 and in period 2. Let ?p1 denote the increase in the probability of success when diligent in period 1. Assume that
A "pooling equilibrium" is an equilibrium in which the borrower's first-period effort is independent of her private benefit. A "separating equilibrium" is (here) an equilibrium in which the b-type works and the B-type shirks in period 1. A "semiseparating" equilibrium is (here) an equilibrium in which in period 1 the b-type works and the B-type randomizes between working and shirking.
- Show that there exists no pooling and no separating equilibrium.
- Compute the semiseparating equilibrium. Does this model formalize the notion of reputational capital?