the symmetry in banks’ balance sheets. Whereas in the status quo all banks have the same
deposits Dsq , the merged banks have now in general different deposit sizes than competitors,
i.e., Dmm = 2. This is what we assume here, although the opposite could also happen: starting
from a situation of an asymmetric banking system, the merger could reduce the asymmetry
among banks and make the system more homogenous.
4.3 Individual Banks’ Liquidity Risk and Expected Needs
The effects of the merger on both banks’ reserve holdings and loan competition affect also
banks’ liquidity risks and expected liquidity needs. The results for competitor banks are
quite straightforward. As they follow the same optimal reserve rule as in the status quo,
they face the same liquidity risk φc = φsq = rDD^r (see Corollary 1). Their expected
liquidity needs, however, change with their balance sheet, as ωc = rDIDc. The merged
banks experience more far reaching changes in probability of facing a liquidity shortage and
in the size of the expected needs.
Corollary 3 The merged banks have lower liquidity risk than a single bank in the status
quo.
This result derives directly from the readjustment of the merged banks’ reserve holdings.
As stated in Proposition 2, when the relative cost of refinancing is below the threshold ρ,
the merged banks increase their reserve-deposit ratio and their liquidity risk goes down. In
the other case, although they choose a lower reserve-deposit ratio than in the status quo,
they still keep it sufficiently high to decrease the liquidity risk. This effect is so strong that
the liquidity risk of the merged banks is not only lower than the risks of two banks in the
status quo, but it is even lower than that of a single bank.
Corollary 4 The merged banks have lower expected liquidity needs than in the status quo
if Dm < h, where 2 < h ≤ 4, and higher ones otherwise.
The merger changes the merged banks’ expected needs for three reasons. First, it creates
the internal money market, which reduces ceteris paribus expected liquidity needs. Second,
the merger modifies the merged banks’ optimal reserve-deposit ratio, which reduces ceteris
paribus expected liquidity needs when the relative cost of refinancing is low. Third, the
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