## Credit Market Equilibrium under Multiple Activity/Investment Choice

Credit Market Equilibrium under Multiple Activity/Investment ChoiceSunghun is an entrepreneur who is considering between two investment projects. Both projectsare risky and both require an investment of $100. Project 1 is opening an Economics ConsultingFirm. Since Sunghun is an excellent economist, this project is pretty safe: with 80% probabilitySunghun will be a successful consultant and earn $250 of revenues, and with 20% probabilitySunghun will fail and earn only $100 of revenues. Project 2 is opening a âKlassic KoreanKimcheeâ Food Truck. Although Sunghun is a master chef, this project is much riskier. With20% probability the Food Truck is successful and generates $600 of revenues. With 80%probability the Food Truck fails and generates only $60 of revenues.Cristina is a banker who may offer Sunghun a loan. Cristinaâs opportunity cost of money is 30%.In other words, she would earn a 30% interest rate if she invested the money in a bank instead oflending it to Sunghun.1 In questions 1 – 4, we will explore the equilibrium contract that Cristinawill offer under different assumptions about liability, competition and asymmetric information.1. Standard Debt Contract and Symmetric Information. In this problem Cristina offersStandard Debt Contracts, also known as unlimited liability credit contracts. Under this typeof contract, Sunghun always has to repay the loan (full principal plus interest) whether hisproject succeeds or fails. We also assume symmetric information. This means that in thecredit contract, Cristina can specify and enforce the project that Sunghun must do. A creditcontract thus specifies two terms: the Project and the interest rate. Let denote the contract. For example, the contract means that Sunghunmust do Project 1 and the interest rate is 10%.a. Let ?! and ?! denote Sunghunâs income from Projects 1 and 2 respectively under astandard debt contract. Derive expressions for ?(?!) and ?(?!), the expected value ofSunghunâs income under the two projects, as functions of the interest rate, i. Yourexpressions should take the form: ?(?!) = ? + ?? where you have to find theâinterceptâ, A, and âslopeâ, B.b. Let ?! and ?! denote Cristinaâs profit from an UNLIMITED liability loan whichfinances Sunghunâs Project 1 and 2 respectively. Derive expressions for ?(?!) and?(?!), the expected value of Cristinaâs profits from loans that finance Projects 1 and 2respectively. Similar to part (1a), you should express these two expected profit functionsas functions of the interest ratec. In Excel, graph ?(?!), ?(?!), ?(?!) and ?(?!) as functions of the interest rate, i (i.e.,put i on the horizontal axis and graph over the range i = 0 to i = 2). Title this graphâFigure 1: Credit Market under Standard Debt Contractâ.d. What will the equilibrium contract be if Cristina is a monopolist? (A monopolist willmaximize her own expected profit while allowing the borrower to earn at least zeroexpected income.)e. What is Cristinaâs expected profit from this equilibrium contract? What is Sunghunâsexpected income?f. What will the equilibrium contract be if the credit market is instead characterized byperfect competition? (Under perfect competition, the equilibrium contract will make theborrower as well off as possible while allowing the lender to earn at least zero expectedprofit). 1 Equivalently, Cristina borrows in order to lend to Sunghun and has to pay 10% interest on her loan (evenif Sunghun defaults).g. What is Cristinaâs expected profit from this equilibrium contract? What is Sunghunâsexpected income?2. Standard Debt Contract and Asymmetric Information. Now assume that Cristina cannotobserve and/or enforce Sunghunâs project choice. Now a credit contract can only specify theinterest rate.a. What type of asymmetric information problem does Cristina face?b. Now what will the equilibrium interest rate be if Cristina is a monopolist? Whatproject will Sunghun choose?c. How much expected profit will Cristina earn under asymmetric information? Howmuch expected income does Sunghun earn? (continue to assume Cristina is amonopolist).d. Compare your answers for part 2b and 2c to your answers to 1d and 1e above(monopolist under symmetric information). If they are different, why are theydifferent? If they are the same, why?3. Limited Liability Contract and Symmetric Information. Now we return to our assumptionof symmetric information (Cristina can enforce Sunghunâs project choice) as in problem 1,but change our assumption about the contract structure. Specifically, we now assume thatCristina must offer a Limited Liability Contract. This means that the borrower does not haveto fully repay the loan when their project fails. In general, limited liability contracts can takemany forms. We will assume the following: If Sunghunâs project succeeds he must fullyrepay the loan (principal plus interest). If his project fails, he only has to repay 50% of thetotal debt obligation (For example, if the interest rate is 50%, he would have to repay0.5*(1+.5)*100 if his project fails).a. Derive expressions for ?(?!) and ?(?!), the expected value of Sunghunâs income underthe two projects, as functions of the interest rate, i, under the limited liability contractdescribed above. Again, your expressions should take the form: ?(?!) = ? + ?? whereyou have to find the âinterceptâ, A, and âslopeâ, B.b. Derive expressions for ?(?!) and ?(?!), the expected value of Cristinaâs profits fromlimited liability loans that finance Projects 1 and 2 respectively.c. In Excel, graph ?(?!), ?(?!), ?(?!) and ?(?!) as functions of the interest rate, i. Titlethis graph âFigure 2: Credit Market under Limited Liabilityâ.d. What will the equilibrium contract (remember to specify both Project & interest rate) beif Cristina is a monopolist? Which project does Sunghun choose?e. What is Cristinaâs expected profit from this equilibrium contract? What is Sunghunâsexpected income?f. What will the equilibrium contract if the credit market is instead characterized by perfectcompetition?g. What is Cristinaâs expected profit from this equilibrium contract? What is Sunghunâsexpected income?4. Limited Liability Contract and Asymmetric Information. Finally, we look at the implicationof asymmetric information when we have Limited Liability Contracts. Assume that contractsare limited liability as in question 3. But now Cristina cannot observe/enforce Sunghunâschoice of project.a. To generate intuition about the impact of asymmetric information, in a separate figure,graph Cristinaâs expected profit as a function of the interest rate. Title this graph âFigure3: Lenderâs Profit under Asymmetric Information and Limited Liabilityâ. Discuss theshape of your graph. (Make sure that you â like Cristina â consider how the interest rateaffects Sunghunâs choice of project!).b. Find the equilibrium interest rate be if Cristina is a monopolist? Which project doesSunghun choose?c. What is Cristinaâs expected profit from this equilibrium contract? What is Sunghunâsexpected income?d. What will the equilibrium interest rate be if the credit market is instead characterized byperfect competition?e. What is Cristinaâs expected profit from this equilibrium contract? What is Sunghunâsexpected income?f. Compare the total surplus generated under symmetric versus asymmetric information(question 3 versus question 4). Discuss your findings.