Limited Liability and Symmetric Information

  Ram is a moneylender who lives in the village of Palampur in India. Half of the farmers in Palampur are SAFE farmers and the other halves are RISKY farmers. Both types of farmers need a loan of $300 in order to farm. Farmers will take a loan as long as they can earn at least zero expected income. SAFE farmers have a good harvest in which they earn revenues of $450 with 100% probability. They never have a bad harvest. RISKY farmers have a good harvest in which they earn revenues of $800 with 50% probability. They have a bad harvest in which they earn revenues of $0 with 50% probability. Ram has perfect information about the farmers, i.e. he knows who is a SAFE farmer and who is RISKY. As a result, he can offer different contract terms to SAFE and RISKY types. Ram’s opportunity cost in money is 25%. Ram offers limited liability credit contracts in which the farmers must repay the full loan plus interest if harvest is good, but nothing if harvest is bad. (a) Let 𝑦𝑦s and 𝑦𝑦r denote the incomes of SAFE and RISKY farmers, respectively. Derive expressions for 𝐸𝐸(𝑦𝑦s) and 𝐸𝐸(𝑦𝑦r), the expected incomes of SAFE and RISKY farmers respectively. Report your expressions in intercept-slope format for the given information. (b) Let 𝜋𝜋s and 𝜋𝜋r denote Ram’s profits from a loan to SAFE and RISKY farmers, respectively. Derive expressions for 𝐸𝐸(𝜋𝜋s) and 𝐸𝐸(𝜋𝜋r), the expected values of Ram’s profits from loans to SAFE and RISKY farmers respectively, as functions of the interest rate, i. Report your expressions in interceptslope format as in the questions above 3 (c) Graph 𝐸𝐸(πs), 𝐸𝐸(πr) , 𝐸𝐸(𝑦𝑦s) and 𝐸𝐸(𝑦𝑦r) as functions of the interest rate, i (i.e., put i on the horizontal axis and graph over the range i = 0 to i = 3 with 0.1 intervals). Label this “Figure1. Credit Market under Symmetric Information