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Problem 1 Limited Liabilig and Smmetric Information. Ram is a moneylender who lives in the village of Ralampm in India. Half of the farmers in Balampm are SAFE farmers and the other halves are RISKY farmers. Both types of farmers need a loan of $200 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 $400 with 100% probability. They never have a bad harvest. RISKY farmers have a good harvest in which they earn revenues of $600 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 20%. Ram o'ers 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 ys and yr denote the incomes of SAFE and RISKY farmers, respectively. Derive expressions for E(ys) and E(yr), the expected incomes of SAFE and RISKY farmers respectively. Report your expressions in intercept-slope format as in the questions above. (b) Let in and 2:, denote Ram's prots 'om a loan to SAFE and RISKY farmers, respectively. Derive expressions for E(:rs) and E013), the expected values of Ram's prots from loans to SAFE and RISKY farmers respectively, as functions of the interest rate, i. Report your expressions in intercept- slope format as in the questions above (c) Graph Eats), Eon) , E05) and 1902;) 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 as intervals). Label this \"Figurel. Credit Market under Symmetric Information\" and copy the gure in the box provided below. ((1) Using your equations and graph, answer the following questions: i. What is the highest interest rate a SAFE farmer would be willing to pay for a loan? ii. What is the highest interest rate a RISKY farmer would be willing to pay for a loan? iii. What is the lowest interest rate Ram would be willing to charge on a loan to a SAFE farmer? iv. What is the lowest interest rate Ram would be willing to charge on a loan to a RISKY farmer? (e) Assume that Ram is a monopolist. i. What is the equilibrium interest rate Ram would charge to a SAFE farmer? ii. What is the expected prot that Ram, cams on this loan to SAFE farmers? iii. What is the equilibrium interest rate Ram would charge to a RISKY farmer? iv. What is the expected prot that Ram earns on this loan to RISKY farmers? ENTREPRENEURS/BORROWERS Two types: safe vs risky (50% of pop. each) 0 Both need $100 loan to start a business Both want to max E (y): risk neutral Both only take a loan if E01) 2 0 Revenue Safe type:$200 with probability 1 Risky type: $320 prob. 0.5, $0 prob. 0.5 Income as a function of interest rate 2': Y 2 Revenue (1 + i) * loan Expected income as a function of interest rate 1': E (Y) = P(success) * Ysuccess + P(f ail) * Yfau LENDERS Either perfect competition or monopolist Want to choose 1' that max E (11): risk neutral Opportunity cost of money: 0.25 Offer limited liability loans in which borrower does not [24126 to r4319! dig/thing If project fails Only offer loan if E (T!) 2 0 Prots for a g'ven contract: n = loan * (1 + i) loan * (1 + opp. cost) Expected profit for a given contract: E01) = P(success) * nsuccess + P(f ail) * arm-l