. Calculate the bank expected profit as a function of the interest rate: Exp (IT) = [P(borrower has safe project) * B] + [P(borrower has risky project) * B * p(risky project gives high return)] - 100 Exp(n) = [0.5 * B] + [0.5 * B * 0.5] - 100 = 0.5B + 0.25B - 100 = 0.75B - 100 . Find r that gives Exp (n) = zero 0.75B = 100 = B=133.3 B = 100(1 +r) = 100(1 + r) = 133.3 r = 33.3%Question: which borrowers find this interest rate profitable? . if r = 33.3%, which borrowers are going to borrow? . Safe projects pays 150 with probability 100% . Safe borrowers, if r = 33.3%, have to pay back 133.3. . 150 - 133.3 > 0 . Therefore, it is still profitable. . Risky project pays 280 with probability 50% and zero with probability of 50%. [0.5 * (280 - 133.3)] + [0.5 * 0] > 0. It is also profitable. . But, in reality, we have excess demand for credit.Question: What is the minimum interest rate the bank should charge if the bank wants to break even? - Assume the size of loan is 100. - Notation: r = interest rate 71' = profit Expr) = expected profit 3 = principal + interest = 1000 + r)