1 Introduction
The theory of the credit market on which this work is founded highlights the particular features of
credit contracts due in particular to the relevance of uncertainty, limited information and transac-
tion costs. According to this conception, because of their particular institutional features, banks
can reduce the influence of market imperfections. Banking institutions can be considered to be
market solutions to the problems caused by the limited availability of information, and the high
cost that is necessary to undertake in order to obtain, select, and process the relevant information.
The peculiar institutional framework of contemporary banks, based on the joint provision of de-
pository and lending services, can be explained viewing the bank as an institution specialized in
the provision of liquidity, to both households and firms. Banks have been increasingly studied as
firms specialized in the analysis of a set of information, internal information, that is not available
to the market. The specific expertise that the intermediary develops in the analysis of information
provides the rationale for the actual existence of banking intermediaries.
The bank described in the model is a profit maximizing firm, that faces an infinite horizon
problem. The banking firm is assumed to be risk-neutral, so that the conclusions do not depend
on the assumption of risk-aversion on part of the bank. The need for an intertemporal framework
comes from the assumption of the existence of long term relationships between the bank and its
customers, either depositors or borrowers. The bank has to consider the effect that decisions made
in every point in time have on future period balance sheets. Short-run policy choices taken in
different periods are not independent, as it is normally assumed describing other markets. In a
credit transaction the object itself of the exchange contract is a promise, and time is explicitly
taken into account in every contract.
The model adopted is a dynamic model. Different market imperfections might determine the
need for a dynamic model. Most dynamic models of banking1 have simply assumed the presence
of quadratic adjustment cost for deposits, loans or both. Here the dynamic is driven by the
consideration that loans and deposits are not independent; loans feedback in deposits of future
periods.2 The feedback mechanism is quite complex and works through the interactions of the
entire banking system. Anyway it can be reasonable to formulate some drastically simplifying
assumptions, in order to take in consideration its effect. As it will be shown, considering the effect
of the feedback, the maximisation problem becomes dynamic even without explicitly formulating
quadratic adjustment costs for deposits or loans. If the bank takes into account the feedback,
a standard quadratic cost function on loans produces implicitly a quadratic adjustment cost on
deposits. The intuition behind this result is that the decision to extend any loan facility of the
bank implies a variation in the stock of deposits.
Three important limitations of the model must be spelled out.
We assume price and cost flexibility and neutrality, so that inflation has no effect. The only
market imperfections we want to consider are in fact linked to the limited and costly availability of
information. The limited availability of information produces both market power and the peculiar
structure of the cost functions that we introduce in the model.
In second order, we choose not to deal with liquidity problems, assuming that they are ad-
equately managed by means of the compulsory reserve requirement and the deposit insurance.
Liquidity costs could easily be introduced in the model, but they would complicate the results
without increasing the understanding of the problems that we want to study.
Finally, we disregard the influence of net worth that we introduce in the model in a peculiar way.
We discuss to some extent how the result would change partially relaxing our assumption, but a
general limitation remains: we do not introduce equity markets in the analysis. This simplification
is almost standard in the microeconomic theory of banking, but nevertheless this assumption is
a relevant omission. Our model in fact, in line with most of the recent literature, focus on an
explanation of the role of banking intermediaries based on the limited availability of information.
But when information is not perfect the Modigliani-Miller theorem does not hold, so that the
composition of the liabilities of the firm matters. In this work though we limit our analysis of the
liability of the bank to debt, deposits in particular. The explicit introduction of equity markets
woud be a fundamental extension of this line of research.
1 Such as Elyasiani, Kopecky and Van Hoose [8] and Cosimano [3] and [4].
2 This mechanism provides the dynamic constraint.