Sep 19, 2017

# (LENDER MARKET POWER). (I) FIXED INVESTMENT. AN ENTREPRENEUR HAS CASH AMOUNT A AND WANTS TO…

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(lender market power). (i) Fixed investment. An entrepreneur has cash amount A and wants to invest I>A into a (fixed-size) project. The project yields R > 0 with probability p and 0 with probability 1 − p. The probability of success is pH if the entrepreneur works and pL = pH − ∆p (∆p > 0) if she shirks. The entrepreneur obtains private benefit B if she shirks and 0 otherwise. The borrower is protected by limited liability and everyone is risk neutral. The project is worthwhile only if the entrepreneur behaves. There is a single lender. This lender has access to funds that command an expected rate of return equal to 0 (so the lender would content himself with a 0 rate of return, but he will use his market power to obtain a superior rate of return). Assume

and let A and Aˆ be defined by

Assume that A > 0 and that the lender makes a take-it-or-leave-it offer to the borrower (i.e., the lender chooses Rb, the borrower’s compensation in the case of success). • What contract is optimal for the lender? • Is the financing decision affected by lender market power (i.e., compared with the case of competitive lenders solved in Section 3.2)? • Draw the borrower’s net utility (i.e., net of A) as a function of A and note that it is nonmonotonic (distinguish four regions: (−∞, A), [A, ˆA)ˆ , [A, I) ˆ , [I, ∞)). Explain.

(ii) Variable investment. Answer the first two bullets in question (i) (lender’s optimal contract and impact of lender market power on the investment decision) in the variable-investment version. In particular, show that lender market power reduces the scale of investment. (Reminder: I is chosen in [0, ∞). The project yields RI if successful and 0 if it fails. Shirking, which reduces the probability of success from pH to pL, yields private benefit BI. Assume that pHR > 1 > pH(R − B/∆p). Hint: show that the two constraints in the lender’s program are binding.)

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