3. You are a banker and are eonfronted with a pool of loan applicants, each of whom can be either low risk or high risk. There are 000 low risk applicants and 400 high risk applicants and each applicant is applying for a $100 loan. A. low risk borrower will invest the $100 loan in a project that will yield $150 with probability 0.0 and nothing with probability 0.2 one period hence. A. high risk borrower will invest the $100 loan in a project that will yield $155 with probability 0.? and nothing with probability 0.3 one period hence. You know that 00% of the applicant pool is low risk and 40% is high risk, but you cannot tell whether a specic borrower is low risk or high risk. You are a monopolist. banker and have $50,000 available to lend. Everyone is risk neutral. The current riskless rate is 3%. Each borrower must be allowed to retain a prot of at least $5 in the successful state in order to be induced to apply for a bank loan. You have just learned that 1,000 loan applicants have been received after you announced a 451% loan interest rate. You can satisfy only 500. 1inllr'hat should be your optimal [protmaximising} loan interest rate? Should it he 45% (at which you must ration half the loan applicants} or a higher interest rate at which there is no rationing