Mathematical Modeling of the Impact of Monetary Policy on the Volume of Bank Credit
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Abstract
The present paper aims to construct an analytical mathematical model to study the impact of monetary policy on the volume of bank credit in Iraq from 2004 to 2021, by formulating purely functional and equilibrium relationships within the framework of mathematical economics. The problem of the research under investigation arises from the following question: How can the impact of monetary policy instruments (r: interest rate, M: money supply, and Y: gross domestic product) on the volume of bank credit (C) be represented with mathematical precision? The scientific hypothesis assumes a specific mathematical effect for each instrument, with the possibility of deriving the impact coefficients solely from equilibrium conditions. The main objective is to derive an analytical reduced-form equation linking bank credit to monetary policy instruments through a market equilibrium equation, The mathematical system is formulated as follows: Credit demand function: DC=α0−α1r+α2Y, where α1,α2>0; credit supply function: SC=β0+β1M, where β2r: β1,β2>0; and the equilibrium condition:
C=DC=SC. By solving this system algebraically, the following reduced-form equation is obtained:
C = γ0 + γ1M − γ2r + γ3Y, where:
Applying the method of comparative statics, the following mathematical multipliers are derived:
Short-run adjustment dynamics are also modeled using a first-order differential equation: =λ(C∗−C), λ ∈ (0,1), where C∗=γ0+γ1M−γ2r+γ3Y represents long-run equilibrium credit, solving this equation yields: C(t)=C∗+(C(0)−C∗)e−λt,
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