Sep 19, 2017

(COMPETITIVE PRODUCT MARKET INTERACTIONS). THERE IS A MASS 1 OF IDENTICAL ENTREPRENEURS WITH THE…

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(competitive product market interactions). 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 individual investment i (in equilibrium i = I by symmetry 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

Show that the equilibrium is unique. Compute the equilibrium level of investment. (Hint: distinguish two cases, depending on whether A is large or small.)



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