Money supply and Money multiplier with derivation

Concept of Money Supply

Money supply refers to the total amount of money circulating within an economy at a given point in time. It includes currency, coins, and various types of deposits held by individuals and non-money-creating institutions (such as hospitals, schools, universities, insurance companies, provident funds, etc.). But currency held by money-creating institutions, such as Central Bank and Bank and Financial Institutions, is not considered as money supply. 

Basically, there are four definitions of money supply.

M0 or Base money: This is the total amount of physical currency and coins in circulation, as well as deposits held by commercial banks in their accounts with the central bank.

M1 or Narrow money: This includes all of the currency and coins in circulation, as well as demand deposits, which are funds held in checking accounts and other accounts that can be accessed quickly and easily.

M1+ or Intermediate money: M1+ is an intermediate money supply, which includes M1 plus funds held in saving and call accounts. M1+ is used in Nepal.

M2 or Broad money: This includes everything in M1, as well as savings deposits, time deposits, and other less liquid types of deposits held by individuals and institutions. M2 is also known as the Chicago approach.

M3 or Broad money liquidity: This includes everything in M2, large-time deposits, foreign deposits (or deposits in terms of foreign currency), deposits in postal saving services, and deposits with non-banking financial institutions. M3 is also known as Gurley and Shaw Approach.

M4: This is the broadest measure of money supply, and includes all of the money in circulation, as well as money market mutual funds, commercial paper, and other types of short-term debt instruments. M4 is also known as the Redcliffe committee approach.

Table 1: Disaggregation of Money Supply

In million Rs.
Year 2021 Jan 2022 Jan 2023 Jan
Broad Money (M2) [TD+(M1+)] 4637223.9 5298673.7 5705068.2
Money Supply (M1+) [M1+SCD] 2569060.3 2664576.2 2507290.6
Money Supply (M1) [C+DD] 867812.9 935962.5 897725.2
Currency (C) 523526.2 532505.5 495238.6
Demand Deposits (DD) 344286.7 403457.1 402486.6
Saving and Call Deposits (SCD) 1701247.4 1728613.7 1609565.4
Time Deposits (TD) 2068163.6 2634097.4 3197777.6
Foreign Deposits (FD) 88076.7 87539.3 99191.5
Broad Money Liquidity (M3) [M2+FD] 4725300.5 5386213.0 5804259.6

Source: Nepal Rastra Bank

Table 2: Disaggregation of High-Powered Money

In million Rs.
Year 2021 Jan 2022 Jan 2023 Jan
Currency Outside ODCs 571971.8 532505.5 495238.6
Currency Held by ODCs 99629.2 100233.9 106927.5
Currency (C) 671600.9 632739.4 602166.1
Deposits of Commercial Banks 229681.9 136705.7 210678.1
Deposits of Development Banks 14003.0 15739.9 20440.3
Deposits of Finance Companies 4358.9 3104.6 4653.6
Reserve (R = RR+ER) 248043.8 155550.2 235772.0
Other Deposits (OD) 11946.7 11912.3 11116.7
Reserve Money (C+R+OD) 931591.4 800201.9 849054.8

Source: Nepal Rastra Bank

Money Multiplier

The money multiplier (m) is the ratio of the aggregate stock of money (M) to the High-powered money (H).
\[M=m\times H\]
\[\Delta M=\Delta m\times H\]
\[\Delta M=m\times \Delta H\]

It shows that the change in aggregate stock of money supply is the product of the change in the value of the money multiplier and the size of base money.

There are many money multiplier models developed by different economists at different time periods like the general model (or IMF model), the Cagon model, the Luckett model, the Friedman model, Pesek and Saving model, Jerry and Jordon model, etc.

Here, we follow Jerry and Jordon's model of money multiplier.

We use the following monetary variables to derive the money multiplier.

M1 = Narrow Money

M2 = Broad Money

C = Currency held by public

DD = Demand deposit

TD = Time deposit

D = Total Deposit (DD+TD)

R = Reserve held by BFIs at the central bank

RR = Required reserve

ER = Excess reserve

OD = Other deposits

Using these variables, we derive the money multiplier.




Since OD's share in base money is very small (about 1.3 percent in the case of Nepal (see Table 2)), we can reformulate equation (3.1) as


Further, Reserve (R) has two components (i) Required Reserve (RR) and (ii) Excess Reserve (ER).

So, equation (3.2) can be written as


Now, we make a bold assumption. We assume that C, TD, and ER are constant multiples of DD. So,




Further, BFIs must maintain the required reserve as a percentage of the total deposit. Such a percentage is mandated by the central bank. so,


The ratios in equation 4.1 to equation 4.4 are also called Behavioral ratios.


We begin with equation (1) and gradually substitute the values.


We consider Broad Money, so M = M2 in our case


We divide the numerator and denominator of RHS of equation (5.1) by DD


Here, $RR = r\times D = r(DD+TD)$



Equation (5.2) is the final equation depicting the broad money multiplier.

The narrow money multiplier is


After the derivation of the money multiplier, we can scrutinize the determinants or factors affecting the money multiplier or money supply as a whole.

Broadly, we can classify it as the proximate and ultimate determinant of Money Supply.

Proximate determinants of money supply

The behavioral ratios we discussed earlier in equation 4.1 to equation 4.4 are the proximate determinants of the money supply.

1. Currency holding ratio (c)

The relative amount of cash and demand deposits that the community wishes to hold has great significance. If people are in habit of keeping less in cash and more in the form of deposits with commercial banks, the money supply will be more. This is because banks can create more credit with larger deposits. Thus, higher $c$ can be seen as a leakage from the chain of deposit creation, which implies a lower money supply ($M^S$).


$c \uparrow \rightarrow M^S \downarrow $

2. Reserve requirement ratio (r)

The central bank requires all commercial banks to hold reserves equal to a fixed percentage of both time and deposit-deposit. This, it is a policy-determined variable. An increase in $r$ reduces $M^S$ and a decrease in $r$ increases $M^S$ with the commercial banks. It can be explained by credit creation.

\[\text{Credit creation} = \frac{\text{Initial Deposit}}{\text{Required reserve ratio}} \]


$r \uparrow \rightarrow M^S \downarrow $

3. Time deposit ratio (t)

If $t$ goes up, the narrow money multiplier goes down.


$t \uparrow \rightarrow \text{Narrow money} \downarrow $

If $t$ goes up, the broad money multiplier goes up.


$t \uparrow \rightarrow \text{Broad money} \uparrow $

4. Excess reserve ratio (e)

The effect of the excess reserve is similar to that of the required reserve. As BFIs hold reserves more than the required reserve set by the central bank, the money supply gets contracted. This is because banks are unable to amplify the funds that they park at the central bank as reserves.


$e \uparrow \rightarrow M^S \downarrow $

Ultimate determinants of money supply

The ultimate determinants of money supply are those factors that affect behavioral ratios. Now, let's discuss on factors affecting each behavioral ratio.

1. Currency holding ratio (c)

Income: Higher the income, the lower will be the value of $c$, and the greater will be the money supply. This suggests that individuals will a high level of income hold a small fraction of income in cash with them.

Banking habits: If people have more sophisticated banking habits, they will hold less cash, that is, $c$ will be lower resulting in a higher money supply. This suggests that people with easy access to BFIs save their income on BFIs which increases the money supply.

Relative changes in prices: If food prices or prices of necessaries rise more than the price of consumer durables, people would want to hold more cash, that is, $c$ goes up. Hence, the money supply goes down. 

2. Reserve requirement ratio (r)

The reserve requirement ratio is mandated by the central bank. So, it depends upon the behavior of the central bank. The behavior of the central bank is determined by the following variables.

Inflation: The ultimate objective of the central bank is to maintain price stability. So, as inflation rises beyond the desirable threshold, central banks urge to contain it by manipulating interest rates. Such manipulation is done through changes in reserve requirement or CRR. When inflation is high, the central bank may increase the reserve requirements to reduce the amount of money in circulation. This can help to reduce demand and stabilize prices.

Balance of Payments: Another objective of the central bank is to maintain external sector stability. Central banks increase interest rates to discourage excessive growth in aggregate demand that eventually lessens imports.

Economic growth: Central banks may lower the reserve requirements to encourage banks to lend more money. This can increase the amount of money in circulation and stimulate economic growth.

Liquidity: Central banks may adjust the reserve requirements to manage liquidity in the banking system. By increasing the reserve requirement, the central bank can reduce the amount of liquidity in the system and prevent banks from becoming too dependent on short-term borrowing.

3. Time deposit ratio (t)

Interest rates: Interest rates are one of the primary factors that influence the time deposit ratio. Higher interest rates can encourage individuals and businesses to invest their money in time deposits, which can increase the time deposit ratio.

Economic conditions: Economic conditions, such as inflation, unemployment, and economic growth, can influence the time deposit ratio. When economic conditions are uncertain, individuals and businesses may be more likely to invest their money in time deposits to protect their savings.

Government policies: Government policies, such as tax policies, can influence the time deposit ratio. For example, if the government provides tax incentives for individuals and businesses to invest in time deposits, this could increase the time deposit ratio.

Bank policies: Banks may also influence the time deposit ratio through their own policies, such as offering higher interest rates on time deposits compared to other types of deposits.

Consumer preferences: Consumer preferences can also influence the time deposit ratio. For example, if consumers prefer to keep their money in easily accessible accounts, such as checking accounts or savings accounts, this could reduce the time deposit ratio.

4. Excess reserve ratio (e)

Discount rate: Lower discount rate means easy credit facility to the commercial banks provided by the central bank. At a lower discount rate, commercial banks can easily borrow from the central bank at a lower cost. This induces them to have a less excess reserve, that is, low $'e'$.

Market interest rate: An increase in the market rate of interest means more bank lending. Excess reserves, as result, will decline and the money multiplier will be higher.

Economic conditions: Economic conditions, such as inflation and economic growth, can affect the excess reserve ratio. If inflation is high, banks may be more cautious and choose to hold more reserves, which would increase the excess reserve ratio.

Technological advancements: Technological advancements in the banking industry can also influence the excess reserve ratio. For example, if online banking becomes more prevalent, banks may require fewer physical reserves, which would decrease the excess reserve ratio.

Summary of Ultimate Determinants

$\rightarrow$ Proximate determinants
$\downarrow$ Currency Ratio (c) Reserve requirement ratio (r) Time deposit ratio (t) Excess reserve ratio (e)
Ultimate Determinants Income Inflation Interest rate Discount rate
Banking habits Balance of payments Economic conditions Market interest rate
Relative changes in price Economic growth Government policies Economic conditions
Liquidity Bank policies Technological advancement
Consumer preferences

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