8. Hidden Characteristics and Costs of a Rating (10 points) Assume an economy with risk neutral investors and entrepreneurs. Funds are assumed to be abundant while investment projects are scarce. Projects are risky. If they fail, no return is generated. If projects succeeds they generate a return of 11 Mio . All projects have an initially required investment volume of 8 Mio . There are two types of entrepreneurs in the economy: Good entrepreneurs projects succeed with probability 90%, while bad entrepreneurs projects succeed only with probability 70%. Investors cannot distinguish good and bad entrepreneurs. They only know that a fraction of entrepreneurs are of the good type and a fraction (1- ) are of the bad type. Entrepreneurs do not have any own funds available. Consequently to pursue their project they need to borrow the entire investment volume. 1. Assume that is only 10 %. a) What is the weighted average success probability of a random borrower? (1point) b) Will a good borrower be able to obtain funding? (1points) c) How much would a good borrower be willing to pay for a rating that undoubtedly identifies him as a good borrower? (3points) 2. Assume that is only 50 %. a) What is the weighted average success probability of a random borrower? (1point) b) What minimum repayment do borrowers have to promise to lenders in order to obtain funding? (1 points) c) How much would a good borrower be willing to pay for a rating that undoubtedly identifies him as a good borrower? (3 points)