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

We provide the following interpretation for the above result. When the
Coase problem arises, the financial contract must solve a double-sided moral
hazard problem. The investor is faced with the following trade-off. To induce
high levels of effort he would like to have the entrepreneur bear most of the
risk. But on the other hand, the investor has to bear sufficient risk to prevent
himself from funding the second firm. In other words, he must internalize the
uncertainty induced by increased competition, which pushes towards a less
high-powered incentive scheme for the entrepreneur. The Coase problem can
be solved only at the expense of less entrepreneurial effort.

The optimal contract for which we have just solved is simply a profit-
sharing rule. We now ask ourselves how this rule can be implemented through
existing financial instruments. It turns out that the third best contract is
more equity-like than the second best contract defined in the previous section.
The features of the “anti-competitive” financial contract are described in the
following:

Proposition 3 An investor wanting to supply only the monopoly amount of
capital to the industry designs his financial claim in order to solve his “Coase
problem”:

(i) if W ≤ W then he holds risky debt. The entrepreneur owes him Dr =
R^H - Ψ⁰ (e^CP); in the case of failure the entrepreneur defaults and the investor
seizes the firm’s cash R^L. This claim is riskier than debt D^M.

(ii) if W>W then the investor holds a combination of safe debt and equity.
He is entitled to the debt reimbursement D_s = RL — b^(R0(_ec^R) ), and also owns
an equity share s = 1 — ^ψH(e_-j^_l) in Firm 1.

Proof. (i) From Lemma 2 (i), the investor’s shares of returns are R^L and
R^H — Ψ⁰ (e^CP). It is straightforward to interpret this as holding debt D_r. From
e^CP <e^M and Ψ⁰⁰ > 0 it follows that Dr >D^M : reimbursement is larger
and default more likely. (ii) Suppose the investor holds debt D_s and an equity
share s. Then his payoff in case of failures is:          ´ ₃                        ´

D-Le RL D — RL ^b(RH ^-RL) I 1    ^ψ0(e^cP )   RL   RL I b^(RH ^-rL)

Ds + ^{s r -} Ds ≡ ^r     _ψ0(_eCP ) ^{+ 1 -} RH _-RL   ^{r - r +} _ψ0(_eCP )

≡ RL — b. Analogously, his payoff in case of success is:                   ´

D I Rh^r D ∖ — RL b^(RH ^-rL) I i    ^ψ0(e^cp )    rh   RL , b^(RH ^-rL)

Ds ⁺ s(^{R -} Ds) ≡ ^r     _ψ0(_eCP ) ^{+ 1 -} RH _-rL   ^{r - r +} _ψ0(_eCP )

≡ R^H — b — Ψ⁰(e^CP).

Therefore, the optimal return-splitting rule is being implemented ■

This result is quite intuitive: an investor holding fairly safe debt in firm
1 will always want to fund Firm 2, as his claim is insensitive to the effects
of competition. Also, the temptation to expropriate Firm 1 by funding Firm
2 will be stronger the higher is W, the entrepreneur’s stake in the project.
To solve this commitment problem the investor will make his claim riskier.

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