There is a mass 1 of identical entrepreneurs with the variable-investment technology described in Section 3.4. The representative entrepreneur has wealth A, is risk neutral, and is protected by limited liability. Denote the average investment by I and the indi- vidual investment i (in equilibrium i = I by symme- try but we need to distinguish the two in a first step in order to compute the competitive equilibrium). A project produces Ri units of goods when successful and 0 when it fails. The probability of success is pH in the case of good behavior (the entrepreneur receives no private benefit) and pL = pH − ∆p in the case of misbehavior (the entrepreneur then receives private benefit Bi). Assume that it is optimal to induce the entrepreneur to behave. The market price of output is P = P(Q), with P' 0, where Q is aggregate production (with P(Q) tend- R ≡ RS − RF denote the increase in income from the low to the high level. Show that the debt contract is optimal, but unlike in the variable-investment case it may not be uniquely optimal.
Exercise 3.17 (competitive product market interac- tions). There is a mass 1 of identical entrepreneurs with the variable-investment technology described in Section 3.4. The representative entrepreneur has wealth A, is risk neutral, and is protected by limited liability.
Denote the average investment by I and the indi- vidual investment i (in equilibrium i = I by symme-
try but we need to distinguish the two in a first step in order to compute the competitive equilibrium). A project produces Ri units of goods when successful and 0 when it fails. The probability of success is pH in
the case of good behavior (the entrepreneur receives no private benefit) and pL = pH − ∆p in the case of
misbehavior (the entrepreneur then receives private benefit Bi). Assume that it is optimal to induce the entrepreneur to behave.
The market price of output is P = P(Q), with P'
0, where Q is aggregate production (with P(Q) tend-
R ≡ RS − RF
denote the increase in income from the low to the high level. Show that the debt contract is optimal, but unlike in the variable-investment case it may not be uniquely optimal.
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