There are two types of projects in the market: A (safer) and B (riskier). At time 1, the payoff of A will be either $500 (probability 0.75) or $300 (probability 0.25). The appropriate discount rate for project A is 12%. The minimum price A can accept is $350. The payoff of B will be either $800 (probability 0.2) or $100 (probability 0.8). The appropriate discount rate for project B is 20%. In this simple economy, there is a 90% chance that the project will be A.

Evaluate the funding situation, i.e., which type of project will be funded and the price, based on the following scenarios:

(1) When there is no information asymmetry and everyone knows everything.

(2) When there is information asymmetry and investors cannot tell if the project is A or B.

(3) If an honest information service firm exists in the market that can separate A from B and provide credible certification. What is the maximum price that the agent can charge for the service? 

(4) If a bank exists and can provide partial financing and tell the difference between A & B but cannot verify the outcomes, what will be the maximum face values of loans to each project? 

(5) Following previous question (4), if A has an asset worth $400 at time 1 and A can use it as collateral, what will be the maximum face values of loan to A? Assuming risk-free rate in this economy is 5%.

(6) If a bank can tell whether the entrepreneur is endowed with project A or B, but cannot stop A from switching to B after A has receive the fund. What is the maximum face value of loan that the bank can lend to A without incur any monitoring costs, i.e., A will not have incentive to switch to B given this incentive compatible amount of loan and limited liability.