answer all the questions briefly, I will give u a thumb!

4. There are two types of borrowers: risky and safe. Both types of borrowers are seeking a loan of 100 dollars for investment. The structure of the investment opportunities differs between the two types of borrowers, and is described in the following table Probability of Success Retun on Investment if Successful C Risky Safe 75% 22% 90% 15% In the event of success, both types of borrowers will repay the loan with interest. Otherwise, both types of borrowers will default (a) Suppose the lender can distinguish these two types of borrowers, find the interest rate for each type of borrowers in a competitive market with free entry of lenders (i.e., zero profit in the long run) (b) Suppose the lender CANNOT distinguish these two types of borrowers, and hence charges a single interest rate to whoever is seeking a loan. Moreover, the lender expects that 40 percent of the potential borrowers are of the risky type. Now, find the interest rate such that lender's expected profit is zero. (c) Given the interest rate as determined in part 2, which type of borrowers will seek loan from the lender? Why? (d) Given your answer in part 3, determine the expected profit of the lender given the interest rate from part 2. (e) Suppose the lender asks for collateral from the borrower in order to screen risky borrowers from safe ones. The collateral will be deposited by the borrower and seized by the lender in the event of default by the borrower. Suppose the collateral is 40 dollars. Now show that at an interest rate of 10%, only safe borrowers will seek loan from the lender (f) Show that with the interest rate and collateral in part 5, the lender's expected profit is positive, and hence, transaction will emerge (g) Suppose the lender charges an interest rate of 10%. Find the minimum collateral such that only the safe type borrowers will seek loan. Also find the maximum amount of collateral such that there will be borrowing and lending in equilibrium