1. Imagine that a bank will only lend if it can earn a rate of return of 6% on a loan. Further, imagine it incurs administrative costs of $40 per loan it makes, regardless of the size of the loan. Throughout the problem, assume for simplicity that the loans are all repaid with certainty, i.e. there is no risk.
a. If the bank makes five loans - of $100, $200, $500, $1000, and $10,000 - what are the respective interest rates it must charge to break even on each loan?
b. Imagine the bank makes the same five loans as in part a., but must charge all borrowers the same interest rate. What interest rate will it charge to break even overall? Which borrowers pay less, which pay more in this case than in part a.? This practice of making losses on some loans and profits on others is called "cross-subsidization". 2
c. How might competition between banks eliminate any one bank's ability to cross-subsidize smaller borrowers? Specifically, ci) could a rival lender lure away any of the customers of a bank carrying out the policy of part b., and cii) how would this affect the ability of a bank carrying out the policy of part b. to cross-subsidize smaller borrowers?
d. It may not be accurate to assume that every loan incurs the same administrative cost, irrespective of size. Larger loans may require more work. Redo part a. under the assumption that the administrative cost of servicing a loan is $40 per loan plus 1% of the size of the loan. (Thus a loan of $5000 would cost the bank $40 + 1%*$5000 = $90, while a loan of $500 would cost the bank $40 + 1%*$500 = $45.)