Problem
Two types of potential borrowers: type 1 and type 2. Starting a project costs $100. Type 1 borrower generates a gross return of y 1 = $200 with 90 percent chance and zero otherwise. Type 2 borrower can achieve a return of y 2 =$400 with 60 percent probability and zero otherwise. Assume that all borrowers in this economy are protected by limited liability. If the potential borrowers cannot access loans, they can work as laborer and earn $40.
1. Find the expected value of type 1 and type 2 project, respectively. If you have to choose one project, which one would you prefer? Can you explain why?
2. If the bank cannot tell type 1 from type 2 but knows that about 60 percent of the potential borrowers are type 1 borrowers, how much does the bank need to charge to break even?
3. When the bank changes the interest rate determined will the borrowers still try to get a loan and start the project?