Model Answer
0 min readIntroduction
The money multiplier is a key concept in monetary economics, representing the magnified effect of a change in the monetary base on the overall money supply. Traditionally, it’s calculated as 1/Reserve Ratio. However, this simplistic model assumes that banks lend out all excess reserves and that the public doesn’t hold any cash. In reality, a portion of the money supply is determined exogenously by the central bank (e.g., through open market operations), while another portion is created endogenously by the banking system through lending. Understanding how these two components interact is crucial for accurately assessing the impact of monetary policy. This answer will derive the money multiplier when both exogenous and endogenous components of the money supply are considered.
Understanding Exogenous and Endogenous Money
Exogenous money refers to the portion of the money supply directly controlled by the central bank. This includes currency in circulation and commercial banks’ reserves held with the central bank. The central bank influences this through tools like open market operations, the reserve requirement ratio, and the discount rate. Endogenous money, on the other hand, is created within the banking system as a result of lending activities. This happens when banks make loans, creating new deposits, which then expand the money supply.
Derivation of the Money Multiplier
Let's define the following variables:
- M = Total Money Supply
- MB = Monetary Base (Exogenous component)
- Me = Endogenous component of money supply
- r = Reserve Requirement Ratio
- c = Currency Ratio (ratio of currency held by the public to deposits)
- k = Loan demand function (describes the public’s demand for loans as a function of the interest rate)
The total money supply can be expressed as:
M = MB + Me
The monetary base (MB) is composed of currency in circulation (C) and commercial banks’ reserves (R):
MB = C + R
The money supply can also be expressed as:
M = C + D (where D represents deposits)
We know that C = cD, therefore:
M = cD + D = (c+1)D
Also, R = rD (assuming banks hold reserves equal to the reserve requirement ratio on deposits).
Substituting R and C into the monetary base equation:
MB = cD + rD = (c+r)D
Therefore, D = MB / (c+r)
Substituting this value of D back into the money supply equation:
M = (c+1) * [MB / (c+r)] = [(c+1)/(c+r)] * MB
However, this assumes that all excess reserves are lent out. In reality, banks may choose to hold excess reserves. Let’s introduce the concept of excess reserves. The total reserves are R = rD + ER, where ER represents excess reserves. The money multiplier is affected by the public’s desire to hold currency (c) and the banks’ desire to hold excess reserves. The endogenous component of money supply (Me) is determined by the loan demand function (k). The total money supply is then:
M = MB + k(i) (where i is the interest rate)
To derive a combined multiplier, we need to consider the impact of the monetary base on both the endogenous and exogenous components. The overall money multiplier (μ) can be expressed as:
μ = ΔM / ΔMB
Considering both exogenous and endogenous components, the money multiplier becomes more complex. It’s not a single fixed number but rather a function of various factors, including the reserve requirement ratio, the currency ratio, the loan demand function, and the banks’ willingness to hold excess reserves. A simplified representation, incorporating the currency ratio and reserve requirement, is:
μ = 1 / (r + c)
This multiplier applies to the exogenous portion of the money supply. The endogenous portion is influenced by the loan demand function and the banks’ lending behavior. Therefore, the total change in the money supply (ΔM) is a combination of the change in the monetary base (ΔMB) multiplied by the multiplier, plus the change in the endogenous component due to lending.
Factors Affecting the Money Multiplier
- Reserve Requirement Ratio (r): A higher reserve requirement reduces the money multiplier.
- Currency Ratio (c): A higher currency ratio reduces the money multiplier, as more money is held outside the banking system.
- Excess Reserves: Banks holding excess reserves reduces the amount of money available for lending, lowering the multiplier.
- Loan Demand: If loan demand is low, banks will not lend out all available funds, reducing the multiplier effect.
Conclusion
In conclusion, the money multiplier is not a static value but is influenced by a complex interplay of factors, including the reserve requirement ratio, currency ratio, and the behavior of both banks and the public. The derivation presented demonstrates that when considering both exogenous and endogenous money supply components, the traditional 1/r formula is insufficient. A more nuanced understanding of these factors is crucial for effective monetary policy implementation. Central banks must account for these complexities when attempting to control the money supply and influence economic activity.
Answer Length
This is a comprehensive model answer for learning purposes and may exceed the word limit. In the exam, always adhere to the prescribed word count.