8. Information and Credit Markets [36 pts]. In the village of Green Pastures, 25% of the farmers are EXPERIENCED farmers and 75% are NEW farmers. Both types of farmers have zero wealth and need a loan of $100 in order to buy the inputs needed to farm. Both types of farmers have no way, other than farming, to earn income; so if they don't farm, their income is zero. The only difference between EXPERIENCED and NEW farmers is as follows: EXPERIENCED farmers have lots of experience and thus know how to protect their harvest against bad weather. An EXPERIENCED farmer always has a good harvest and earns revenue equal to $200. NEW farmers have little experience and thus they don't know how to protect their harvest against bad weather. With 60% probability a NEW farmer will have a good harvest and earn revenue equal to $200. With 40% probability, a NEW farmer will have harvest failure and earn revenue equal to $0. Bilal is a moneylender who lives in Green Pastures. His opportunity cost of money is 0.2 (i.e., he would earn 20% interest if he put the money in a savings account instead of making a loan). Bilal offers limited liability loans, so a farmer does not have to repay the loan if he has harvest failure (zero revenues). Since Bilal lives in Green Pastures, he has perfect information about the farming experience of everybody in the village. This implies that he knows who is an EXPERIENCED farmer and who is a NEW farmer. Partial credit may be awarded for all parts of this question, so you should write the initial equation used to setup your response in each part. a. What is the highest interest rate an EXPERIENCED farmer would be willing to pay for a loan from Bilal?b. What is the lowest interest rate Bilal would be willing to charge on a loan to an EXPERIENCED farmer? c. What is the highest interest rate a NEW farmer would be willing to pay for a loan from Bilal? d. What is the lowest interest rate Bilal would be willing to charge on a loan to a NEW farmer?For parts E - H, assume that Bilal is a monopolist. e. What is the equilibrium interest rate Bilal would charge to an EXPERIENCED farmer? f. How much expected profit does Bilal earn on a loan to an EXPERIENCED farmer? g. What is the equilibrium interest rate Bilal would charge to a NEW farmer?h. How much expected profit does Bilal earn on a loan to a NEW farmer? Now assume Bilal retires and no longer offers loans in the village. Nina is a loan officer from a bank in a nearby city. She is considering offering limited liability loans to farmers in Green Pastures. Just like Bilal, Nina's opportunity cost of money is 0.2. Nina, however, does not know the farmers in Green Pastures so she cannot tell who is an EXPERIENCED farmer and who is a NEW farmer. All she knows is that 25% are EXPERIENCED and 75% are NEW farmers. As a result, she has to charge a single interest rate to everybody. For the rest of this problem, assume that the market for formal loans is described by perfect competition. i. What type of asymmetric information problem does Nina face? Explain your answer in one or two sentences.j. Write down an expression for E(x), Nina's expected profit from a loan, assuming that both EXPERIENCED and NEW types apply for a loan. Express this function as A + Bi, where i is the interest rate. k. Will Nina be willing to offer loans to farmers in Green Pastures? 1. If yes, what interest rate will she charge and which type of farmer(s) will take the loans? If no, why can she not make loans in the village
