Monopolistic Pricing in the Banking Industry: a Dynamic Model



to be dependent on the initial level of the rates. When the rates are low the direct effect of the
interest rate is likely to be predominant, because the opposite effect due to the correlation should
not be very large. For higher initial levels of the rate the direct effect of the interest rate is likely
to be largely offset by the correlation. When initial interest rates are high, the higher correlation
could even imply the dominance of the effect of the covariance. In this final case we would observe
the paradoxical result of an increase of the direct lending activity after a positive interest rate
shock, notwithstanding the market power of the bank. This could possibly happen in the case of
high inflation, when nominal rates are very high and the demand for loans remains strong.

Finally, following the same line of reasoning, in the case of heavy shocks we might expect that
the effects are not symmetric in the case of a positive or negative shock. The reduction in the
issuance of loans following a large positive shock should be smaller than the increase following a
proportional reduction.

3.2 Credit quality shocks

Different types of shocks of real origin affect borrowers, producing variations of current and expected
default costs. To keep the analysis simple, we have assumed that the coefficient of the expected
default costs are the same as the coefficient of the cost of the current period, and are revised when
the current cost changes. As a consequence the only shocks that we consider are those that are
regarded as permanent ones by the banker. Shocks that are supposed to affect negatively and
permanently the borrowers reduce the average quality of the portfolio of loans, increasing default
costs.

Higher default costs reduce the size of the whole portfolio. The higher volatility of the portfolio
of bonds implies that the impact on the purchase of bonds is proportionally much stronger than
on the issuance of loans. The bank reacts to higher default cost shrinking the whole portfolio,
reducing notably the amount of bonds in order to reduce less the issuance of loans. So when an
industry is affected by a negative shock and the placement of bonds becomes difficult because
spreads get wider, the banking industry does not increase the issuance of loans. The bank cannot
lend more because default costs affect the size of the portfolio, and only indirectly the composition.
The portfolio shrinks, and the composition changes favouring the issuance of loans just because
the reduction of the size affects bonds more. On the contrary when default cost gets smaller the
share of bonds in the portfolio grows more than proportionally.

This result shows the usefulness of a dynamic framework, where the size of the portfolio is
endogenous. Variations of the size of the whole portfolio are not captured by static portfolio
models, and may induce in error. In the case of a negative shock affecting the credit quality a
borrower or of an industry, our model predicts that banks reduce the issuance of loans, providing
insurance against the shock to a limited extent only. As long as their information allows the
formulation of expectations regarding future default cost, banks provide direct lending facilities,
but proportionally reducing the amounts involved. On the contrary, after the shock it may become
very difficult for the less informed lenders of the market to properly price the risk, so the bond
market may easily dry out because of the insurgence of a lemon problem. In the last case borrowers
are pushed to rely on banks, the demand for loans surges and bonds are not a substitute for loans
any more as a source of finance for risky projects.

A strong enough increase of the demand could in principle push the bank to lend more, since
demand grows more than proportionally as default costs rise. But this may be the case only when
the initial demand is low, for example when the shock hits an industrial sector whose main source
of finance is the bond market. This can easily be realised from Equation (26), which shows that
the increase of the demand
21 change just one of the components of the equilibrium level of loans,
while the default costs affects other terms of the sum too. Besides the absence of competition
from bonds
22 has both a positive and a negative impact in the issuance of loans. The positive
effect comes from the higher coefficient of the covariance term, the negative because the coefficient
measuring the direct effect of the interest rate on bonds becomes larger. When the level of the
rates on bonds affects the demand for loans, if the coefficient is large enough, the higher demand

21 A variation of the intercept a of the demand for loans schedule, increased by the lower elasticity of the demand,
measured by a lower coefficient
b.

22Shown by a value of zero for the coefficient d.

16



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