Financial Economics
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 pg = 0.9 and 0 otherwise, while a high risk borrower’s project yields B = 3.5 with probability p h = 0.5 and zero otherwise. The bank knows that the proportion of low risk borrowers is 7 = 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.
1. Consider a bank which operates as a monopoly and wants to attract both types of borrowers in the first period.
a. What is the repayment R(1) that the bank will charge in the first period? Compute the bank’s first period profit R-(1) .
Now, suppose there is perfect competition among banks in both periods. What would the repayment rate R(1)c be that the bank would charge in the first period? What would the repayment rates Rs(2)c, RE(2 be in the second period paid by successful and unsuccessful borrowers? How does competition affect overall risk taking in this model and why? Explain your finding carefully.
b. Calculate the posterior probabilities of a borrower being low risk given that the project was successful and also when the project failed after the first period (i.e. Pr(GIS) ,Pr(GIF), respectively).
c. What repayments R(s2), RFC will the bank charge to successful and failed borrowers, respectively, in the second period? Calculate the bank’s second period profit R-(2) . What is the total profit across the two periods
