| Abstract: | This paper studies the bank's lending decision, based on three observed phenomena: banks earn substantial profits from off‐balance sheet activities and services, which they take into account in their lending decisions. Secondly, the critical point in the customer relation is the loan decision: the probability of the customer staying with the bank is a function of the loan extended each time one is applied for. Third, what is at stake in the loan decision is the expected value of the entire customer relation, which is the probability times the present value of expected future profits. The bank is a maximizer of this expected present value, while making decisions on individual loan applications. It is shown that the bank is in a corner solution with respect to its good customers, and other customers often have an incentive to get to a corner. Therefore, corner solutions may be the rule rather than the exception in the bank's customer relations, and there is no mechanism making the bank indifferent, at the margin, between lending to different customers. It can be optimal to extend loans to (present and expected future) good customers at an interest rate loss. A rationed customer with a concave enough probability function can receive a larger loan by asking for less. Loyalty increases the customer's value to the bank but improves its loan terms only if the customer makes it conditional on the loan extended. |
