Page 100 - Azerbaijan State University of Economics
P. 100
THE JOURNAL OF ECONOMIC SCIENCES: THEORY AND PRACTICE, V.82, # 2, 2025, pp. 96-116
2
∑ ∞ [ ( ) − ],
0
=0
{ , , , , } 2
(1)
subject to the period budget constraint:
+ + + = + (1 + ) −1 + (1 + ) −1 + + (1 +
) −1 − . (2)
Where:
● : consumption.
● : investment, its price.
● : nominal bank deposits held at the end of period t.
● : nominal SDC holdings (central bank liability) held at end of period t.
● : foreign bonds (open-economy asset).
● : deposit interest rate (banks pay).
● : SDC remuneration rate (central bank sets).
● : return on foreign bonds (exogenous world rate plus premium).
● Another standard notation applies.
Households use both deposits and SDC for payments and as stores of value. The
payment services and convenience yield from each instrument are imperfect
substitutes. Following standard practice, we model transactions-technology based
money-in-utility or cash-in-advance friction; here we use a generalized transactions
cost that implies demand for liquid assets (deposits and SDC).
The household first-order conditions yield stochastic Euler equations and liquidity
demand relations. In particular, the (log) relative demand for SDC vs deposits depends
on the relative remuneration ( − ), the convenience yields, and parameters
governing substitutability.
Banks
Banks accept deposits , pay interest , hold reserves and lend them to firms .
Banks are monopolistically competitive in deposit markets (markup over marginal
cost), capturing deposit market power. The bank profit maximization problem:
= (1 + ) − (1 + ) − ( , ), (3)
where is the lending rate. Deposit demand elasticity is finite, so SDC competition
(if attractive) will force banks to raise deposit rates, affecting net interest margins and
loan supply.
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