Page 113 - Azerbaijan State University of Economics

Nazim Hajiyev, Daniyar Aliyev: A DSGE Framework For Sovereign Digital Currency
Adoption in Small Open Economies: Macro-Financial Channels, Bank Intermediation, and
Policy Trade-Offs

1
: = . (A4)

( − − ): = [ +1 (1 + )] + . (A5)

+1

ℎ : = [ +1 (1 + +1 )] + . (A6)

: = [ +1 (1 + +1 )]. (A7)

Subtracting (A5) and (A6) and log-linearizing yields the relative demand relation:

− = + ( − ) + , (A8)
0

2
1

with > 0 (remuneration increases SDC share), and collecting

1
transactions/preference shocks.

A.2 Bank problem and deposit pricing
Banks earn:

= (1 + ) − (1 + ) − ( , ) − , (A9)

with balance-sheet constraint
= ( + ), 0 < ≤ 1, (A10)

where denotes other funding.

′
FOC for deposit-rate choice (using deposit demand derivative ):

′
−(1 + ) − + = 0. (A11)

Under standard assumptions this implies a markup condition (deposit-rate depends on
marginal cost and elasticity), which after log-linearization leads to a loan supply relation
of the form:
= ( + ) − ( − ). (A12)

A.3 Central bank recycling and multiplier
Define recycling share ∈ [0,1]. For small deposit outflow and substitution ≈
− :
= (1 − ) . (A13)
Thus = 1 fully offsets funding loss; = 0 implies full disintermediation effect.
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