Typed solution.....

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.

a) 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?

b) 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?

c) When the bank changes the interest rate determined in part 3) will the

borrowers still try to get a loan and start the project?