Y5

A bank faces a pool of high and low risk borrowers with measure one in two successive periods. In each period, each borrower wishes to borrow 1 from the bank. A low-risk borrower's project returns G=2 with probability pg=0.8 and high-risk borrower's project yields B=3 with probability p_b=0.2 in each period. If a project is unsuccessful, it yields zero. The bank knows that the proportion of low-risk borrowers is =0.5. However, the bank is unable to distinguish between low and high-risk borrowers, i.e. it doesn't have an appropriate screening technology.

Consider a bank which operates as a monopoly and wants to attract both types of borrowers in the first period.

How much will the bank charge to successful and failed borrowers in the second period (R⁽²⁾_S,R⁽²⁾_F)? Calculate the bank's second period profit (2). What's the total profit across the two periods (⁽¹⁾+⁽²⁾)?