Consider the problem of an entrepreneur/borrower with no money and a project requiring L=200to be carried out. Assume that the borrower cannot use his illiquid assets to finance the project.The entrepreneurOnce the entrepreneur undertakes the project, she decides either to work hard or to shirk.• If she works hard, then she earns a high return R=$500 with probability p=0.75 and earnsnothing with probability (1-p)=0.25.• If she shirks, she earns a high return with probability q=0.25 and earns nothing withprobability (1-q)=0.75.The borrower has ex-post utility u(y)=y-D if she works hard and u(y)=y if she does not workhard, where y is her income (after loan payments) carned from the project. Assume D=125.The bank:A bank is willing to finance the project and lend $200 to the borrower. The bank charges theagent an interest rate of i on the loan.The borrower always repays the loan when she succeeds. If she fails, she is protected by limitedliability: she repays nothing to the bank.Finally, assume that the bank could also purchase $200 in risk-free bonds with a return ofr=0.10, and that the financial markets are perfectly competitive.Section A1: No collateral1. The borrowerSuppose the borrower takes a loan of $200 from the bank. Supposethat the interest rate charged on the loan is i (we'll find i later).a. What is her ex post income yail if she fails? NOTE: I'm asking for realizedincome, NOT utility!b. What is her ex post income ysuceed if she succeeds? (hint: this will be a function ofthe interest i). 2. The bank.Suppose that the bank believes the agent will work hard. (HINT: Slides 6-12).a. What is the expected profits E(II) if the bank lends to the borrower? (hint: thiswill be a function of i).b. What is the expected profits E(II) if the bank purchases the risk-free bonds.c. Write down the zero profit condition.d. What is the interest rate that the bank will charge?Will the borrower work hard at that interest rate? (hint: plug the3. Equilibriuminterest rate the bank will charge in the No-shirking condition and check whether thecondition holds).

Credit markets channelize the funds between savers and investors. It improves the allocative…

Section A1: No collateral 1. The borrower Suppose the borrower takes a loan of $200 from the bank. Suppose that the interest rate charged on the loan is i (we'll find i later). a. What is her ex post income yfail if she fails? NOTE: I'm asking for realized income, NOT utility! b. What is her ex post income ysucceed if she succeeds? (hint: this will be a function of the interest i).

Section A1: No collateral 1. The borrower Suppose the borrower takes a loan of $200 from the bank. Suppose that the interest rate charged on the loan is i (we'll find i later). a. What is her ex post income yfail if she fails? NOTE: I'm asking for realized income, NOT utility! b. What is her ex post income ysucceed if she succeeds? (hint: this will be a function of the interest i).

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter7: Uncertainty

Section: Chapter Questions

Problem 7.8P

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