shifts probability mass from high revenue to low revenue outcomes.
Preferences:
All agents are risk-neutral. Firms 1 and 2 are identical. Entrepreneur i’s
von Neumann-Morgernstern utility function is
U(Rbi,ei)=Rbi - Ψ(ei)
where Rbi is the expected monetary payment borrowing firm i receives af-
ter revenues are realized. Effort ei costs Ψ(ei) to the entrepreneur. Thus,
were he to receive a flat payment, he would exert the lowest possible effort.
The function Ψ ( ∙ ) is strictly increasing, twice continuously differentiable and
convex. Entrepreneurs have reservation wage Wi . The simplest way to think
of this parameter is in terms of the entrepreneur’s outside wage: how much
he could earn if he did not borrow from the investor to start his own firm.
A related idea is that the entrepreneur has some bargaining power in dealing
with the investor, and so is able to extract rents of value Wi . However, one
could also think of Wi as the best offer that the entrepreneur i has received
from competing investors. In this case a higher Wi would correspond to more
competition between investors. A third interpretation for Wi is in terms of
assets provided by the entrepreneur. This third interpretation would result in
the investor solving somewhat different optimization programs, but the basic
insights would be similar. For concreteness we will proceed in terms of the
first interpretation because it yields the most straightforward analysis.
For notational simplicity, we will omit the subscript 1 when referring to
Firm 1: therefore Firm 1’s return, effort and reservation wage will be Rb , e
and W throughout.
Timing:
t=1 The investor offers a contract to firm 1. Firm 1 accepts or rejects. If
Firm 1 accepts, then it picks a level of effort e ∈ [∆, 1]. The effort decision is
pure moral hazard, not observed by the investor.
t=2 The investor decides whether to fund Firm 2 or not; if it decides to
do so, it offers a contract to Firm 2, which then accepts or rejects. Firm 2
observes whether firm 1 has been funded when considering the investor’s offer.
If Firm 2 accepts the contract, then it picks an effort level e2 ∈ [∆, 1].
t=3 Payoffs are realized according to the manager’s level of effort and to
whether the investor has funded one or both firms
The timing of the model is summarized in the following figure:
standard arguments, we work with the simpler case where efforts are neither complements
nor substitutes in order to focus attention on the new form of entry deterrence.