Equilibrium loan pricing under the bank-client relationship

We determine the loan interest rate policy of a lender who is better informed about a client than other potential lenders. The informational advantage possessed by the informed lender derives from the durability of information acquired as a result of an extant relationship. Given heterogeneous potential loan rate offers to the client by competitive lenders and client search costs, the incumbent lender's policy of loan interest rate offers is examined. We show that the optimal loan rate will exceed the incumbent lender's cost of funds and will exceed the average offer of competing lenders. The potential lenders will offer loan rates that are exceeded by their cost of funds, implying immediate losses in order to attract the client and to thereby earn expected profits in the future. Finally, we show that the expected remaining duration of a lender-client relationship is decreasing in the existing length of the relationship. Thus, clients that have been with a particular lender longer will be more likely to leave and establish a relationship with another lender.