Sep 19, 2017

(LOAN SIZE AND COLLATERAL REQUIREMENTS). AN ENTREPRENEUR WITH LIMITED WEALTH A FI- NANCES A…

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(loan size and collateral requirements). An entrepreneur with limited wealth A fi- nances a variable-investment project. A project of size I ∈ R if successful yields R(I), where R(0) = 0, R > 0, R L = pH − ∆p if she misbehaves (she then receives private benefit BI). The entrepreneur can pledge an arbitrary amount of collateral with cost0 to the entrepreneur and value φ(C) for the investors withφ(0) = 0, φ > 0, φ

The entrepreneur is risk neutral and protected by limited liability and the investors are competitive, risk neutral, and demand a rate of return equal to 0. Assume that the first-best policy does not yield enough pledgeable income. (This first-best policy is

Assume that the entrepreneur pledges collateral only in the case of failure (on this, see Section 4.3.5), and that the investors’ breakeven constraint is binding. Show that as A decreases or the agency cost (as measured by B or, keeping pH constant, pH/∆p) increases, the optimal investment size decreases and the optimal collateral increases.


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