A farmer wants to buy a plot of land and requires a loan of 600 to complete the purchase. The loan she
is considering allows her to purchase the land now and requires one payment ps if the farm is successful
and the payment pf if it fails. When the farm is successful, the farmer has more assets available to make
the payment than when it is a failure. Specifically, she will have 1200 in assets if it is a success and 600 if
it is a failure. She can influence the probability of success by exerting more effort (High effort vs. Low
effort). The relationship between the key variables in the farmer’s problem are described below.
Effort Probability of Success Cost of Effort
High 4/5 200
Low 2/5 0
Both the farmer and the bank, who makes the loan, are risk neutral. The farmer is also protected by
limited liability and cannot be made to pay more than the value of her assets.
1. Assuming the bank sets pF = 600, how should it pick pS if the bank wants the farmer to exert high
effort? Justify your answer.

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