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Suppose a farmer can invest in one of two projects to improve the productivity of his farm. Both projects call for an initial start-up capital of 100,000 pesos. The first is risk-free (i.e. p=1) and will gross the farmer 150,000 pesos by the end of the year. The second project is riskier but generates a gross return of 300,000 pesos with probability of success of 40% (p=.4). To finance either project, the farmer has to borrow the start-up capital of 100,000 pesos from the village bank at an annual interest of 20%.
A) Calculate the expected return from each project. Show that the farmer will choose to undertake the risky project as long as he does not have to put up any collateral.
B) Explain how this problem illustrates the moral hazard problem in rural credit markets.
C) Solve for the value of the collateral that is necessary for the farmer to choose the safe
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