Consider a monopolist lender who lends to borrowers on an infinitely repeated basis. The loans are informal and not backed up by written contracts. The lender has no way to recover a loan if the borrower chooses to default. The lender, however, threatens to cut off credit in the future to any defaulting borrower. Borrowers discount next periods earnings by a discount factor of 0.5 (that means, say, $10 next year is worth $5 to me today).

Borrowers use this loan in cultivation. Cultivation can be done using one of two techniques. The first requires initial working capital of $100 and produces net output worth $300. The second requires $500 of working capital and yields net output of $1,000. Find the amount of loan the lender will advance to each borrower every period in order to maximize his own profits. How much is the scheduled repayment and the implicit interest rate? How much are these profits and how much does each borrower earn every period from the deal?