is the total expected cost of refinancing, and the last one is the total expected repayment
to depositors. The operation of the internal money market can be seen in the third term of
(11), where the total demand for liquidity, xm = δ1D1 + δ2D2, and reserves, Rm = R1 + R2,
are pooled together.
A preliminary step before deriving the optimal reserve-deposit ratio of the merged banks
is to understand their ‘deposit market policy’. Whether they raise equal or different amounts
in both regions affects the distribution of the demand for liquidity xm , and thus the size of
the expected cost of refinancing. We have the following lemma.
Lemma 1 The merged banks raise an equal amount of deposits in each region, i.e., D1 =
D2 = Dm.
Lemma 1 shows that the merged banks not only raise deposits in both regions, but they
even do it symmetrically. Choosing equal amounts of deposits in both regions minimizes
the variance of xm and maximizes the benefits of diversification, thus reducing the expected
refinancing cost. (We will come back to this point in Section 5 when studying the effect of
the merger on aggregate liquidity demand.)
Given D1 = D2 , the merged banks choose reserves Rm so as to maximize their combined
profits in (11). Let km = Dm be the reserve-deposit ratio for the merged banks and recall
that ksq is the one for banks in the status quo defined in (10). The following proposition
compares these two ratios.
Proposition 2 The merged banks choose a lower reserve-deposit ratio than in the status
quo (km < ksq) if the relative cost of refinancing is higher than a threshold ρ (rrI > ρ), and
a higher one otherwise.
Proposition 2 contains the first main result of the paper indicating that the merged
banks may have a higher or a lower optimal reserve-deposit ratio than individual banks.
The result depends on the relative strength of two effects:
• A diversification effect that reduces the probability of extreme shocks for the merged
banks;
• An internalization effect consisting in the possibility to use any unit of reserves to
cover a deposit outflow at either of the banks that make up the merged bank. This
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