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 e
ffect of competition on firm 1’s profit.

More formally, the optimal contract offered to F1 is the solution to the
following progra
hm:                                    i

MaxRbH ,RbL ,e e(RH - RbH)+(1 - e)(RL - RbL) - I1

(IR)eRbH +(1 - e)RbL - Ψ(e) W

(IC)RbH-RbL0(e)

(ICI) e(RH-RbH)+(1-e)(RL-RbL)

(e - ∆)(RH -RbH)+(1-e+∆)(RL-RbL)+V2

(LL) RbH 0, RbL 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 e
ffort eCP <eM . Also, there exists a threshold level
W = eCPΨ0(eCP) - Ψ(eCP) 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 =
b0(eCP)

Proof. If condition (1) holds for e = eM, 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) = RbHRbL. This requires inducing an effort level
eCP lower than eM . Clearly, effort is reduced only until the incentive constraint
holds strictly. Therefore
eCP is uniquely determined by:

∆(RHRLΨ0(eCP)) =V2

From the firm’s (IC) constraint it then follows that RbH = RbL + Ψ0(eCP).
Therefore, we are left with choosing the optimal level of RbL .

If WW effort eCP is induced by paying the entrepreneur RbL =0
and RbH = Ψ0 (eCP), which satisfy as an inequality the entrepreneur’s (IR)
constraint. This contract is uniquely optimal for the investor, in that raising
RbL would only raise agency costs.

If W>W then the previous contract fails to satisfy the entrepreneur’s
(IR). Therefore
RbL must be increased up to b > 0 to satisfy: eCPΨ0(eCP)+b
Ψ(eCP) = W. Accordingly, RH = b + Ψ0(eCP). ■

13



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