The entrepreneur Assume that there are 2 types of potential borrowers: high-risk and low-risk. High-risk types get output R =4.5 with probability p=0.30, 0 otherwise. Low-risk types get output R =1.5 with probability p=0.90, 0 otherwise. For each 100 borrowers, 50 are high risk and 50 are low risk. All borrowers are risk neutral: u(c) = c, where c is consumption and c= y (y is income). Financing the investment costs L=1. The borrower does not have assets of her own, so she must borrow this money from the bank. The borrower is also protected from the lender through limited liability: she repays zero in case the project fails. The Bank The bank charges an interest rate of i on the loan. The bank could also lend its money at the risk-free rate r=0.10. We will assume that the lending market is characterized by perfect competition among banks. 2. The bank. Suppose that the bank knows a borrower is a safe type. (HINT: Slides 37-38). a. What is the expected profits E(II) if the bank lends to the borrower? (hint: this will be a function of i). b. What is the expected profits E(II) if the bank purchases the risk-free bonds? c. Write down the zero profit condition. d. What is the interest rate that the bank will charge to the safe type? Call this interest rate i. e. Suppose that the bank knows that another borrower is risky. Follow steps a-d to derive the interest rate the bank will charge her. Call this interest rate i,.