ANTI-COMPETITIVE FINANCIAL CONTRACTING: THE DESIGN OF FINANCIAL CLAIMS.

3 The optimal contract without potential en-
trants

3.1 The commitment case

Before dealing with the investor’s Coase problem, we solve the benchmark
(monopoly) case where Firm 1 faces no threat of entry by potential competi-
tors. This is equivalent to assuming that the investor can credibly commit
not to fund any other firm in the industry. In this case the optimal financial
contract for the investor solves:

hi

Max_RbH _,RbL _,e e(R^H - R_b^H)+(1 - e)(R^L - R_b^L) - I1)

(IR)    eR_b^H +(1 - e)R_b^L - Ψ(e) ≥ W

(IC)    Rb^H - Rb^L = Ψ⁰(e)

(LL)    R_b^L ≥ 0, R_b^H ≥ 0

We will refer to the solution to this program as the second best optimum,
and denote the associated effort level by e^M (M for monopoly).¹³ R_b^L and R_b^H
are the borrowing firm’s payoffs in case of failure and success. (IR) is the firm’s
participation constraint and (IC) is the firm’s incentive constraint. (LL) is the
limited liability constraint. The solution to this program depends on the level
of W. We state this result in the following:

Lemma 1 In the absence of potential competitors, the investor’s optimal claim
is debt: R_b^L =0 and R_b^H = Ψ⁰(e^M),wheree^M is the second best effort. Also,
there exists a threshold level W1 = e^MΨ⁰(e^M) -Ψ(e^M) for the firm’s reservation
wage such that:

(i) for W≤ W₁ optimal effort e^M solves R^H - R^L = Ψ⁰(e) + eΨ⁰⁰(e).

(ii) for W₁ < W ≤ W optimal effort e^M solves eΨ⁰(e) — Ψ(e) = W and
therefore increases with W.

Effort levels satisfy: e^M < e* (the first best effort) for any W.

Proof. See Appendix ■

The interpretation of this result is straightforward: as the security design
literature has pointed out, the optimal financial contract minimizes agency
costs by paying the entrepreneur only in case of success, which boils down to

¹³If effort was? observable then the optimal financial ,contract would solve:

Max_RbL _,RbH _,e e(R^H — R_b^H )+(1— e)(R^L — R_b^L ) — I1

eR_b^H +(1— e)R_b^L — Ψ(e) ≥ W              (IR)

R_b^L ≥ 0, R_b^H ≥ 0

The first best level of effort e* is thus defined by the first order condition:

RH — RL = Ψ⁰(e*).

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