This is a problem on moral hazard in credit markets. An entrepreneur has to decide between two projects, a safe project and a risky project. The safe project gives a return of 160 with probability 100%. The risky project gives a return of 300 with probability 50% and a return of zero with probability 50%. The investment required for both projects is 100. Assume risk neutrality (decisions based only on expected returns) and limited liability for the borrower.

a. Without borrowing. Suppose the entrepreneur saved a lot in the past years and he already has the capital required for the project (100). Which project will he choose without borrowing?

b. With borrowing. Suppose the entrepreneur did not save and he has to borrow the whole 100 from the bank. The interest rate is 10%. Which project will he choose with borrowing?

c. Effect of collateral. Suppose the entrepreneur did not save and he has to borrow the whole 100 from the bank. The interest rate is 10%. However, the bank now requires a collateral of 60. Which project will the entrepreneur choose with borrowing and collateral?

d. Effect of collateral. Suppose the entrepreneur did not save and he has to borrow the whole 100 from the bank. The interest rate is 10%. However, the bank now requires a collateral of 80. Which project will the entrepreneur choose with borrowing and collateral?

e. Effect of collateral. Suppose the entrepreneur did not save and he has to borrow the whole 100 from the bank. The interest rate is 10%. Find the minimum level of collateral that will lead the borrower to choose the safe project.

f. Effect of monitoring. Suppose the entrepreneur did not save and he has to borrow the whole 100 from the bank. The bank can monitor the borrower to make sure that he chooses the safe project. Monitoring is very effective: with monitoring, the borrower always chooses the safe project. The cost of monitoring is 50. What is the minimum interest rate the bank should charge if the bank wants to break even?

g. Effect of monitoring. Suppose the entrepreneur did not save and he has to borrow the whole 100 from the bank. The bank can monitor the borrower to make sure that he chooses the safe project. Monitoring is very effective: with monitoring, the borrower always chooses the safe project. The cost of monitoring is 30. What is the minimum interest rate the bank should charge if the bank wants to break even?

h. Effect of monitoring. Suppose the entrepreneur is considering a bigger project that requires an investment of 200. He has to borrow the whole 200 from the bank. The bank can monitor the borrower to make sure that he chooses the safe project. Monitoring is very effective: with monitoring, the borrower always chooses the safe project. The cost of monitoring is 30. What is the minimum interest rate the bank should charge if the bank wants to break even?