The money market is a market in which a special commodity – money – is sold and bought. Its main elements are the demand for money, the supply of money, the price of money (interest rate). The role of money is performed not only by cash, but also by demand deposits, term deposits, etc. Therefore, to calculate the amount of money, economists introduced the concept of monetary aggregates: M1, M2, M3, M4 (in descending order of the degree of liquidity). The composition and number of monetary aggregates used vary by country. According to the classification used in the United States, monetary aggregates are represented as follows:
Ml – cash outside the banking system, demand deposits, traveller’s cheques, other cheque deposits;
M2 — Aggregate Ml plus non-cheka savings deposits, term deposits (up to $100,000), one-day buyback agreements, etc.;
MZ – aggregate M2 plus term deposits over 100 thousand dollars, fixed-term repurchase agreements, certificates of deposit, etc .;
M4 is an aggregate of M3 plus Treasury savings bonds, short-term government liabilities, commercial paper, etc.
In macroeconomic analysis, aggregates Ml and M2 are used more often than others. Sometimes the indicator of cash (MO or C from the English “currency”) is distinguished as part of M1, as well as the indicator “quasi-money” (QM) as the difference between M2 and Ml, i.e., mainly savings and term deposits, then M2 = M1 + QM.
The dynamics of monetary aggregates depends on many reasons, including the movement of the interest rate. So, with an increase in the interest rate, the aggregates M2, MZ can outpace Ml, since their components bring income in the form of interest. Recently, the emergence of new types of interest-bearing deposits in Ml smoothes out the differences in the dynamics of aggregates due to the movement of the interest rate.
The quantity theory of money determines the demand for money using the equation of exchange:
MV=PY,
where M is the amount of money in circulation;
V — velocity of money circulation;
P — price level (price index);
Y is the volume of output (in real terms).
It is assumed that the velocity of circulation is a constant value, because it is associated with a fairly stable structure of transactions in the economy. However, over time, it may change, for example, in connection with the introduction of new technical means in banking institutions that accelerate the settlement system. With constancy V, the equation of exchange is of the form:
Subject to the constancy of V, the change in the amount of money in circulation (M) should cause a proportional change in the nominal GNP (PY). But, according to classical theory, the real GNP (Y) changes slowly and only with a change in the magnitude of the factors of production and technology. It can be assumed that Y changes at a constant rate, and for short periods of time it is constant. Therefore, fluctuations in nominal GNP will reflect mainly changes in the price level. Thus, the change in the amount of money in circulation will not affect the real values, but will affect the fluctuations of nominal variables. This phenomenon is called “neutrality of money”. Modern monetarists, supporting the concept of “neutrality of money” to describe the long-term relationships between the dynamics of the money supply and the price level, recognize the impact of money supply on real values in the short term (within the business cycle).
The equation of exchange can be represented in tempo notation (for small changes in its quantities):
According to the rule of monetarists, the state should maintain the growth rate of the money supply at the level of the average growth rate of real GNP, then the price level in the economy will be stable.
The above equation of exchange MV = PY is associated with the name of the American economist I. Fisher. Another form of this equation is also used, the so-called Cambridge equation: M = kPY, where 
is the value inverse of the velocity of money circulation. The coefficient k also carries its own semantic load, showing the share of nominal cash balances (M) in income (PY). Strictly speaking, the values V and k are related to the movement of the interest rate, but in this case for simplicity are taken constantly. The Cambridge equation assumes the presence of different types of financial assets with different yields (and not only cash or Ml) and the possibility of choosing between them when deciding in what form to keep income.
To eliminate the impact of inflation, they usually consider the real demand for money, that is,
,
where the 
value is called “real cash reserves”, or “real cash balances”.
The Keynesian theory of the demand for money , the theory of liquidity preference – identifies three motives that encourage people to keep part of the money in the form of cash:
transaction motive (cash requirement for current transactions); precautionary reason (keeping a certain amount of cash in case of unforeseen circumstances in the future); speculative motive (the intention to save some reserve in order to benefit from a better knowledge of what the future will bring compared to the market).
Speculative demand for money is based on the inverse relationship between the interest rate and the bond rate. Let you purchase a bond at the rate of 100,000 rubles, bringing a fixed income of 5,000 rubles. per year, which corresponds to the existing interest rate at this time, equal to 5%. You then decided to sell that bond. But the interest rate in the market has changed and is already equal to 8%. For what amount can you now sell your bond, provided that it brings the same 5000 rubles. income? At a rate of 100 thousand, it will no longer be bought, because this money can bring 8,000 rubles. income at the existing market rate. Assuming that 5000 rubles. corresponds to 8% of income, we get a new bond rate equal to 62500 rubles The general formula for determining the current rate of the bond is as follows: 
, where B is the rate of the bond at the moment; a is the fixed amount of income that the bond brings; i is the current market interest rate. In our example 
, Keynes for simplicity suggested that there are only two forms of financial assets: cash and bonds.
If the interest rate rises, the price of the bond falls, the demand for bonds rises, which leads to a reduction in the stock of cash (the ratio between cash and bonds in the portfolio of assets changes), i.e. the demand for cash decreases. Thus, the inverse relationship between the demand for money and the interest rate is obvious.
Summarizing these two approaches – classical and Keynesian – we can distinguish the following factors of demand for money:
income level; the speed of money circulation; interest rate.
The classical theory relates the demand for money mainly to real income. The Keynesian theory of the demand for money considers the interest rate to be the main factor. Keeping money in the form of cash involves certain costs. They are equal to the interest that could be obtained by putting money in the bank or using it to buy other financial assets that generate income. The higher the interest rate, the more we lose potential income, the higher the opportunity cost of keeping money in cash, and therefore the lower the demand for cash.
Leaving aside the most complex and contradictory factor – the velocity of money circulation, about which there is no unanimity of views among economists, we can imagine the function of demand for real money balances as follows:
,
where R is the interest rate; Y is real income.
From the formula it can be seen that the factor of quantitative demand for money (MD) is the price level. If we assume that the relationship between MD and demand factors has a linear relationship, we get:
,
where the coefficients k and h reflect the sensitivity of the demand for money to the income and interest rate. The money demand function shows that at any given level of income, the amount of demand will fall with an increase in the interest rate and vice versa. The increase in the level of income will be reflected by a shift in the demand curve for LD money to the right by the value of kΔY (Fig. 6.1.).
Empirical evidence supports the theoretical model of demand for money, however, revealing that there is a certain time lag between the change in factors and the reaction of demand for money.
There are nominal and real interest rates. The nominal rate is the rate set by banks on credit operations. The real interest rate reflects the real purchasing power of the income earned as a percentage. The relationship between the nominal and real interest rates is described by fisher’s equation:
i = r + π,
where π is the rate of inflation; i – nominal interest rate.
The equation shows that the nominal interest rate can change for two reasons: due to changes in the real rate and the rate of inflation.
The quantity theory and Fisher’s equation together give a relationship between the volume of money supply and the nominal rate of interest: an increase in the money supply causes inflation to rise, and the latter leads to an increase in the nominal interest rate. This relationship between inflation and the nominal interest rate is called the Fisher effect.
Note that in the long term, the “neutrality of money” noted by the classics is preserved, that is, a change in the nominal variable (in this case, the π) can affect only another nominal variable (i), without affecting the real values (r). In the short term, a change in the nominal value may affect the real variable for some time. Thus, when inflation rates change, banks may not immediately change the interest rate (i) assigned to them, then, for example, rising inflation (π) will reduce the real interest rate for some time, which will create favorable conditions for investors and other recipients of loans. In this case, r = i – π at high rates of inflation, a more precise formula is used to determine the real interest rate:
Taking into account the increased influence on the processes in the economy of inflation expectations of economic agents, as well as the fact that, setting a certain interest rate, banks have in mind the expected inflation rate (πe) in the future, since its actual value is not known at the moment, Fisher’s formula is somewhat modified:
i = r + πe
On the basis of two main approaches to the analysis of the demand for money, many modern monetary theories are developing, focusing on different aspects of the demand for money. Thus, the basis of the Baumol-Tobnn model is the transactional demand for money. With this model, it is possible to determine, for example, how much on average for a period an eco-comical agent can keep in cash depending on the level of his income, the opportunity cost of keeping money in cash (usually interest rates, i), the cost of transferring his assets from one form to another. At the same time, the question of how often assets should be transferred from one form to another is also being addressed (see N.G. Mankiew Macroeconomics, Ch. 18).
The portfolio approach to the demand for money proceeds from the fact that cash is only one of the components of the portfolio of financial assets of economic agents. In deciding the optimal amount of funds that can be held in cash, the portfolio owner proceeds from what income other types of assets can provide him, and at the same time how risky it is to keep funds in one form or another of financial assets. Rising stock and bond yields, for example, will reduce demand for cash. On the other hand, the growing risk of losing income from non-monetary forms of assets increases the desire to keep money in the form of cash. The demand for money is also made dependent on the total wealth of the individual, since the size of this wealth determines the volume of the portfolio of assets as a whole, and hence all its components. The impact of inflation is also taken into account. The general formula is as follows:
,
where: rs is the estimated real income per share,
rb — estimated real income on bonds,
πe is expected inflation, W is real wealth.
And only the last factor is positively related to the demand for money. For example, in the case of high inflation, the demand for money decreases, economic agents tend to transfer their funds to real assets that are not so affected by inflation.
Obviously, this approach to the demand for money makes sense primarily for the units of M2, M3 and wider money. The components of the Ml aggregate bring practically no income, but the degree of risk is almost similar to many assets on the right side of the above formula (for example, government bonds). In this case, the point of comparing the right and left parts of the formula is lost: it is obviously unprofitable for owners of a portfolio of assets to keep funds in the form of cash or Ml, if they can be placed in more profitable, but at the same degree of risk, financial assets.
An empirical assessment of the demand for money can be based on the available data on the ratios between the demand for money and GNP, the interest rate, and inflation that existed in previous periods. However, in the context of a transition economy, such assessments have limited application in the implementation of structural adjustment, financial reform, etc..
Another approach may be to determine the demand for money based on an estimate of the likely change in the velocity of money, the expected inflation, and the planned change in the amount of real GNP (that is, based on the equation MV= PY).