Consider an economy with N = 100 consumers, in which borrowing and lending take place through a bank. One-half of the consumers are savers who deposit L = 500 consumption goods to the bank and receive the deposit rate r, = 0.1 on each unit of deposit. The other half of the consumers are borrowers. "Good" borrowers always repay their loans, while "bad" borrowers always default. The bank does not observe the type of the borrower, but each consumer knows their own type. (a) (5 points) Suppose that all good borrowers are identical and that each wants to borrow 500 consumption goods. Explain why a bad borrower will always request 500 goods as a loan. (b) (5 points) If 10% of all borrowers are a bad type (i.e., they default on their loans), what the real interest rate r2 will a profit-maximizing bank charge on loans? How will this rate compare with the deposit rate r, ? Explain. (c) (5 points) If the proportion of the bad borrowers increases from 10% to 15%, how will 12 change? Explain your response. (d) (5 points) What is an economic interpretation of the difference r2 - r,? What causes this difference to increase and decrease in the model? What changes in r2 - r, should we expect to see in booms and recessions? Explain