Competition and vertical integration:-

This exercise is inspired by Cestone and White (2003). (i) A cashless entrepreneur (A = 0) considers a research project requiring a fixed investment I. When financed, the project succeeds with probability p_H = 1 (for certain) if she works, and with probability pL = 1-?p if she shirks, in which case she receives private benefit B. Regardless of the outcome, there is a verifiable salvage value R^F ≥0 (equipment, real estate) at the end. For the moment, there is no other firm in the market and so success brings an additional income R = M (monopoly profit) on top of the salvage value. Assume that

The investment cost I includes a fixed cost K ≤ I borne by a supplier who must develop an enabling technology. There is ex ante a competitive supply of such suppliers, who for simplicity have enough cash to finance the entrepreneur's remaining investment cost, I - K, besides their own cost K. So we can formalize the supplier as a "competitive capital market" for the moment. In exchange for his contribution (supplying the technology and providing complementary financing I - K to the entrepreneur), the selected supplier receives a debt claim (the equivalent of a fixed price) and an equity stake in the entrepreneurial firm.

An equity claim is a share θl ∈ [0, 1] of the firm's profit beyond RF (here, a claim on M).

• Can the project be financed?

• Characterize the set of feasible contracts (RF l , θl). (There is some indeterminacy, except when the inequality in (1) is an equality. Discuss informally extra elements that could be added to the model to make a debt contract strictly optimal.) (ii) Suppose now that, after having developed the enabling technology for the entrepreneur, the supplier can, at no extra cost (that is, without incurring K again), offer the technology to a rival who is in every respect identical to the entrepreneur. If he does so, and the two downstream projects are successful, then the per-firm duopoly profit is D (on top of the salvage value R^F), where

• Note that the entrepreneur always wants to sign an exclusivity contract with the selected supplier (hint: look at the industry profit when the rival receives the enabling technology).
• In the absence of exclusivity provision (say, for antitrust reasons), look at whether the entrepreneur can obtain de facto exclusivity by choosing the debt/equity mix of the supplier properly. Assume for simplicity that (?p)(1 - θl)D ≥B. This will hold true in an optimal contract.

Exercise 7.2 (benefits from financial muscle in a competitive environment). This exercise extends to liquidity choices the Aghion-Dewatripont-Rey idea that pledgeable income considerations may make financial structures and corporate governance strategic complements in a competitive environment. (i) Consider a single firm. At date 0, the entrepreneur borrows I - A in order to finance a fixed-size project costing I. At date 1, the firm may need to reinvest an amount ρ with probability λ. With probability 1-λ, no reinvestment is required. In the caseof continuation the entrepreneur may behave (probability of success pH, no private benefit) or misbehave (probability of success p_L = p_H- ?_p, private benefit B). Let

where R is the profit in the case of success at date 2 (the profit is equal to 0 in the case of failure). The firm is said to have "financial muscle" if ρ > ρ0(R) and the firm chooses to withstand the liquidity shock if it occurs.

• Explain the phrase "financial muscle."
• Does the firm want to have financial muscle when ρ>ρ0(R)? (Hint: consider three regions for the term (1 - λ)ρ0(R) - (I - A): (-∞, 0), (0, λ[ρ - ρ0(R)]), and (λ [ρ - ρ0(R)], +∞).) (ii) Suppose now that the firm (now named the incumbent) faces a potential entrant in the innovation market. The entrant is identical to the incumbent in all respects (parameters A, I, pH, pL, B and profits (see below)) except that the entrant will never face a liquidity shock if he invests (the entrant is therefore endowed with a better technology). Let R = M denote the monopoly profit made by a firm when it succeeds and the other firm either has not invested in the first place or has invested but not withstood its liquidity shock; let

(where is the duopoly profit) denote its expected profit when it succeeds and the other firm has invested and withstood its liquidity shock (if any). Assume that

• Suppose, first, that the two firms choose their financial structures (liquidity) simultaneously at date 0. Show that the entrant invests and the incumbent does not.
• Suppose, second, that, at date 0, the incumbent chooses her financial structure before the entrant. And assume, furthermore, that

Show that the incumbent invests, while the (more efficient) entrant does not.