A farmer requires 30 Rupees to invest in fertilizers and farming equipment. She has 10 Rupees of her own savings to invest and borrows the remaining 20 from a local moneylender using a standard debt contract. The rate of interest on the debt is a 10%. The farmer can choose whether to cultivate wheat or corn, both of which involve some risk due to environmental conditions. Wheat cultivation yields a crop value of 60 Rupees with probability 2/3 , and 30 Rupees with probability 1/3 . Corn cultivation yields a crop value of 75 Rupees with probability 2/3 and 0 with probability 1/3 .
(a) What are the total expected return net of total investment from wheat and corn cultivation? Which crop is more risky?
(b) Calculate the expected returns to the farmer and the moneylender, respectively, net of their investments, from each crop.
(c) Why would the farmer and the moneylender disagree about which crop should be planted ? Explain carefully, with the aid of a diagram.
(d) What kinds of economic institutions in the credit market would you expect to arise in response to this kind of fundamental problem ? How would you expect such institutions to vary across the formal and informal sectors and why?