1. Suppose first that the bank offers an unsecured contract. A. The bank assumes that the only entrepreneur who applies for the loan is the safer one. What's in appropriate interest rate? Is this a Nash equilibrium? B. What is the optimal contract? What's the correct rate then? (The bank doesn't want to make a loss on an individual entrepreneur. Hint: the bank will make a profit in this case). 2. Suppose now the bank ask for a collateral. Find the optimal contracts offered by the bank to the borrowers. Hint: with adverse selection, the bank will offer two different contracts to induce borrowers to reveal their type (a secured contract to the safer guy and an unsecured contract to the riskier one). Assume a competitive market for banks