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

rent, the investor must take into account his future opportunistic behavior
when solving for the optimal contract. This boils down to making the in-
vestor’s claim more sensitive to the effect of competition on firm 1’s profit.

More formally, the optimal contract offered to F1 is the solution to the
following progra_hm:                                    _i

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)

(ICI) e(R^H-Rb^H)+(1-e)(R^L-Rb^L) ≥

(e - ∆)(R^H -Rb^H)+(1-e+∆)(R^L-Rb^L)+V2

(LL) R_b^H ≥ 0, R_b^L ≥ 0

This program may be referred to as the third best optimum: when a po-
tential entrant exists, the optimal contract must also satisfy the investor’s
incentive compatibility constraint (ICI). The third best solution is described
in the following:

Lemma 2 Assume that at t=2 firm 2 will ask for funding to compete with
firm 1. Assume also that condition (1) holds. Then the optimal financial
contract induces a level of effort e^CP <e^M . Also, there exists a threshold level
W = e^CPΨ⁰(e^CP) - Ψ(e^CP) for firm 1’s reservation wage such that:

(i) for W ≤ W the optimal contract is: RL = 0, RH = Ψ⁰(eCP)

(ii) for W > W the optimal contract is: RL = b = W — IW, RH =
b+Ψ⁰(e^CP)

Proof. If condition (1) holds for e = e^M, then any contract specified in
Lemma 1 fails to satisfy (IC)I, and thus cannot be a solution to the above
program. In order to solve his Coase problem the investor must make his claim
riskier, i.e. reduce Ψ⁰(e) = R_b^H — R_b^L. This requires inducing an effort level
e^CP lower than e^M . Clearly, effort is reduced only until the incentive constraint
holds strictly. Therefore e^CP is uniquely determined by:

∆(R^H — R^L — Ψ⁰(e^CP)) =V2

From the firm’s (IC) constraint it then follows that R_b^H = R_b^L + Ψ⁰(e^CP).
Therefore, we are left with choosing the optimal level of R_b^L .

If W≤ W effort e^CP is induced by paying the entrepreneur R_b^L =0
and R_b^H = Ψ⁰ (e^CP), which satisfy as an inequality the entrepreneur’s (IR)
constraint. This contract is uniquely optimal for the investor, in that raising
R_b^L would only raise agency costs.

If W>W then the previous contract fails to satisfy the entrepreneur’s
(IR). Therefore R_b^L must be increased up to b > 0 to satisfy: e^CPΨ⁰(e^CP)+b —
Ψ(eCP) = W. Accordingly, RH = b + Ψ⁰(eCP). ■

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