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 pb=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.

i. What's the repayment R(1) that the bank will charge in the first period? Compute the bank's first period profit (1).