A bank faces a pool of borrowers with measure one in twosuccessive periods. In each period, each borrower wishes toborrow 1 unit from the bank. In each period, a low riskborrower's project returns G = 2 with probability p, = 0.9 andO otherwise, while a high risk borrower's project yields B = 3.5with probability p, = 0.5 and zero otherwise. The bank knowsPgthat the proportion of low risk borrowers is y = 0.4. However,the bank is unable to distinguish between low and high riskborrowers, i.e. it doesn't have an appropriate screeningtechnology. 1. Consider a bank which operates as a monopoly andwants to attract both types of borrowers in the firstperiod.a. What is the repayment R1) that the bank will chargein the first period? Compute the bank's first periodprofit 7 (1).b. Calculate the posterior probabilities of a borrowerbeing low risk given that the project was successfuland also when the project failed after the first period(i.e. Pr(G|S) ,Pr(G|F), respectively).c. What repayments R, R will the bank charge tosuccessful and failed borrowers, respectively, in thesecond period? Calculate the bank's second periodprofit 7 (2) . What is the total profit across the twoperiods (T() + 7(2)) ?

A bank faces a pool of borrowers with measure one in two successive periods. In each period, each borrower wishes to borrow 1 unit from the bank. In each period, a low risk borrower's project returns G = 2 with probability p = 0.9 and 0 otherwise, while a high risk borrower's project yields B = 3.5 with probability p = 0.5 and zero otherwise. The bank knows that the proportion of low risk borrowers is y = 0.4. However, the bank is unable to distinguish between low and high risk borrowers, i.e. it doesn't have an appropriate screening technology.

A bank faces a pool of borrowers with measure one in two successive periods. In each period, each borrower wishes to borrow 1 unit from the bank. In each period, a low risk borrower's project returns G = 2 with probability p = 0.9 and 0 otherwise, while a high risk borrower's project yields B = 3.5 with probability p = 0.5 and zero otherwise. The bank knows that the proportion of low risk borrowers is y = 0.4. However, the bank is unable to distinguish between low and high risk borrowers, i.e. it doesn't have an appropriate screening technology.

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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