1: Corprate Financing with Collateral. Consider entrepreneur i endowed with a business where investment I generates stochastic revenue equal R with probability pi and 0 with probability 1 pi. The business has positive expected net value: piR > I The entrepreneur has no wealth at the beginning and needs to finance such investment with a loan from a competitive lender. Both the entrepreneur and the lender are risk-neutral. The lender makes zero expected profit on any loan. a. What is the repayment promised to the lender if project is succesful? Now, assume there are two types of entrepreneurs: good, for whom probability of success is p such that pR > I and bad for whom probability of success is q such that qR < I. The share of good types among entrepreneurs is , the share of bad ones is 1 . Assume the lender cannot observe borrower's type. b. What would be the equilibrium repayment rate in a loan contract that is accepted by borrowers of both types? Assume that the lender makes zero profit. c. Explain how equilibrium of this model involves an inefficient amount of investment. Now assume that projects of bad borrowers have lower net present value than projects of good borrowers but are nonetheless efficient: pR I > qR I > 0 Consider situation where borrowers are endowed with collateral that may be turned over to lender upon termination of their project. Any amount of collateral can be pledged. Collateral loses value when taken by lender: if a borrower hands over colleteral of value c, lender collects value c, where 0 < < 1. In presence of collateral, loan contracts are now characterized as pairs of numbers (RI,C) where R is repayment in case of success, C is collateral returned in case of failure. d. Under symmetric information, would any collateral be pledged in an equilibrium contract? Explain as sharply as you can. 1 e. UUnder asymmetric information, there may be a separating equilibrium where two contracts (RG,CG), (RB,CB) are available to all borrowers, good types self-select to (RG,CG) and bad types self-select to (RB,CB). Characterize this equilibrium as sharply as you can: f. Write down what conditions need to be satisfied by RG,CG,RB,CB? Which contract involves more collateral? Which contract involves greater repayment? What is the amount of collateral pledged in equilibrium by the bad type, CB? Explain. g. Consider the same model as above with one change: "bad" type's business is assumed to be inefficient (negative NPV): qR I < 0 Does that change the equilibrium? How