Consider the following lending contract between a farmer and a bank, both of whom are riskñneutral....

Consider the following lending contract between a farmer and a bank, both of whom are riskñneutral. The farmer needs to borrow $120 in order to buy seeds for a new crop that she has not grown before. If she puts in the e§ort needed to learn how to cultivate the crop properly, her investment will pay o§ for sure and generate a crop yielding a value of $300. However, if she does not put in this e§ort the crop yield is uncertain. SpeciÖcally, her yield will be $300 with probability 0:5, but may end up being 0 with probability 0:5. The value of the time needed to learn about the correct cultivation methods is assumed to be 80 and the net cost per dollar lent for the bank is 30%. The bank must decide what repayment R it will require as part of the contract. Assume that the borrower has limited liability and no collateral. (a) For a given repayment R, what is the expected income of the borrower if she learns about the crop? What is her expected income if she does not learn? (b) Use your answer to part (a) to derive the maximum repayment R that the bank can charge while still inducing the borrower to learn. Will the bank make the loan ? Suppose now that two such borrowers form a group and borrow from the bank under a joint liability clause. Assume also that the borrowers act in unison so as to maximize their joint expected payo§. (c) For a given repayment R, what is the expected joint income of the borrowers if they both learn about the correct method? What is their expected joint income if they do not learn? (d) Derive the maximum repayment, R, that the bank can charge while still inducing borrowers to learn. Will the bank make the loan now?

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Rahul Sunny answered 1 year ago

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