Let r n be the inflation-adjusted interest rate (nominal interest rate), r be the real bank interest rate (real interest rate), i be the inflation rate.

Let S(0) be capital at the beginning of the year. Then, the capital at the end of the year on the one hand should be equal to:

S(1) = (1+rn) S(0).

On the other hand, it is equal to:

S(1) = (1+i) (1+r) S(0).

Equating the capitals at the end of the year, calculated according to different formulas, we obtain the Fisher formula, which relates the nominal r n and the real r interest rate to the inflation rate i:

r n = r + i + i r (2.25)

The value i r– is called the inflationary premium.

Example 18.

The Bank charges interest at a nominal rate of 16%. The inflation rate is 12%. Determine the real bank interest rate, taking into account the inflation premium.

From the Fisher formula we calculate the real interest rate r through the nominal interest rate r n and inflation rate i:

In our case, we get:

Thus, with high inflation, the real bank interest rate, equal to 3.57%, is less than the difference between the nominal rate and inflation 16% - 12% = 4%.

Example 19.

Initial capital in the amount of 200 thousand rubles. issued for three years, interest accrues at the end of each quarter at a nominal rate of 8%. The inflation rate is 12%.

Determine the accumulated amount with and without inflation premium.

The accumulated amount excluding inflation from (2.11) is equal to:

Thousand rub.

The accumulated amount, taking into account inflation, can be calculated using the compound interest formula (2.10):

Thousand rub.

Due to the fact that the inflation rate is greater than the nominal interest rate, the accumulated amount, taking into account inflation, is less than the initial capital.

Example 20.

There is a bill of the following form:

« 20000 rub. St. Petersburg. September 1, 2010 I undertake to pay 60 days after this date, by order of citizen A, 20,000 rubles. with an interest rate of 11% per annum.

/signature/ citizen B».

Solution.

The amount that citizen A should receive after 60 days is calculated according to the simple interest scheme and is equal to rub.

From this comes the equation: rub.,

where S(0) is the amount that the bank will pay for the bill.

Finally S(0)=20206.70 rub.

Task 10.

During the first month, the price of the good increased by 30%, and during the next month, the new price of the good decreased by 10%. By what percentage has the price of the product changed in 2 months?

Answer.

Effective rate

The compound interest formula (2.10) includes four unknowns S(0), S(t), r, t. Knowing the three unknowns from equation (2.10), we can determine the fourth unknown. The compound interest formula itself (2.10) defines the future capital S(t) through the present capital S(0), the interest rate r and the time t.

IN example 11 the time t of capital accumulation is found for known values ​​of the present S(0) and future capital S(t) and the interest rate r. In the previous section on discounting, in formula (2.23), the present value S(0) of capital is determined by its future value S(t), interest rate r, and time t. From the compound interest formula (2.10), only the interest rate r was not determined through the present S(0) and future S(t) capital and time t. The solution to this problem is connected with a very important economic concept. effective rate.

For comparison various options transactions convenient to use the effective rate.

efficient is called the annual compound interest rate that provides a given ratio of the amount received S(t) to the amount issued S(0), regardless of which payment scheme is used in this particular transaction.

From (2.10) we have an equation for determining :

,

where t is the duration of the transaction in years.

. (2.26)

Obviously, the effective rate does not depend on the volumes of specific amounts S(0) and S(t), but is determined only by the ratios of these amounts.

Example 21.

Find the effective rate of the transaction, as a result of which the initial capital tripled in 5 years.

According to (2.26) we have .

Example 22: Doubling GDP.

Find the annual GDP growth rate at which it will double in 10 years, in 7 years, in 3 years.

Solution:

Using the effective rate formula (2.26):

,

we obtain the annual GDP growth rate, respectively, for 10 years, 7 years and

Example 23.

The loan amount is 2 million rubles. with the condition of return in 2.5 years 3 million rubles. Then the effective rate in this transaction is equal to:

.

Example 24.

A loan of 2 million rubles was issued. for 3 months at 100% per annum. Find an effective rate.

Given that the loan is short-term, the amount paid after 3 months will be equal to:

then the effective rate will be:

, where S(0)=2 million rubles, S(t)=2.5 million rubles, years.

.

Example 25.

The bill was issued in the amount of 50 million rubles. and contains an obligation to pay the owner this amount in 4 months. The owner presented the bill to the bank ahead of schedule. The bank agreed to discount the bill, but with a discount of 24% per annum. Find an effective rate.

Solution:

The resulting amount will be:

Then the effective rate will be:

, where S(0)=46 million rubles, S(t)=50 million rubles, years.

.

Example 26.

Promissory note 3 million rubles. issued for 2 years with an annual discount rate of 10% discounted twice a year. Find an effective rate. Using formula (2.24), we find the initial amount paid on the bill:

Then . Therefore, for the effective rate we have:

.

Example 27.

Manhattan Island was sold in 1624 for $24. In 1976, its cost was $40×10 9 . What is the effective transaction rate?

Solution:

In this problem, intuition deceives a person: it seems that the effective interest rate will be very large. However, calculation by formula (2.26) gives next value:

.

The decisive factor leading to such a modest value of the effective interest rate is time. The duration of the transaction is long - 352 years.

In some cases, to compare different options for transactions, instead of the effective rate, the spot interest rate r s is used. It is defined similarly to the effective rate, but instead of compound interest, continuous interest is used.

1st cycle - textile factories, industrial use of coal. 2nd cycle - coal mining and ferrous metallurgy, railway construction, steam engine. 3rd cycle - heavy engineering, electric power industry, inorganic chemistry, steel production and electric motors. 4th cycle - production of automobiles and other machines, chemical industry, oil refining and internal combustion engines, mass production. 5th cycle - development of electronics, robotics, computing, laser and telecommunications technology. 6th cycle - perhaps NBIC convergence (convergence of nano-, bio-, information and cognitive technologies). After the 2030s (2050s according to other sources), a technological singularity is possible, which is not amenable to this moment analysis and forecast. Thus, the Kondratiev cycles are likely to end closer to 2030.

18. Equation of exchange by Irving Fisher. Nominal and real interest rates (formula).

Fisher's equation - the equation describing the relationship between the tempo inflation, nominal and real interest rates:

where is the nominal interest rate;

Real interest rate;

The rate of inflation.

The equation shows that the nominal interest rate can change for two reasons:

due to changes in the real interest rate;

due to the rate of inflation.

Distinguish between nominal and real interest rates.

Real interest rate is the interest rate minus inflation.

The relationship between the real, nominal rate and inflation is generally described by the following (approximate) formula:

Nominal interest rate

Real interest rate

Expected or projected rate of inflation.

Irving Fisher proposed a more precise formula for the relationship between real, nominal rates and inflation, expressed by the Fisher formula named after him:

For and both formulas give the same value. It is easy to see that for small values ​​of the inflation rate, the results differ little, but if inflation is high, then Fisher's formula should be applied.

According to Fisher, the real interest rate should be numerically equal to marginal productivity of capital.

11. The level of cyclical unemployment: the law a. Okun. Economic losses from the operation of the law a. Okun (on the graph of the as curve).

Studies of the relationship between the rate of increase in real GDP and the unemployment rate are expressed in the so-called Okun's law. Okun's law(the law of the natural rate of unemployment) - if the actual unemployment rate exceeds the natural rate by 1%, then the gap between the actual GDP and the potential one is 2.5% unemployment.

Economic costs - a consequence of the operation of Okun's law - the lag of the actual volume of GDP from its potential volume.

12. Cycle and trend. Characteristics of the phases of the economic cycle.

Business cycles - cyclical changes in the economic environment, regular fluctuations in the level of business activity from economic recovery (boom) to recession (economic depression). Four relatively clearly distinguishable phases are distinguished in business cycles: peak, decline, bottom(or "lowest point") and climb.

Climb occurs after reaching the lowest point of the cycle (bottom). It is characterized by a gradual increase in employment and production. Many economists believe that low inflation rates are inherent in this stage. There is an introduction of innovations in the economy with a short payback period. Demand deferred during the previous recession is realized.

Peak, or the top of the business cycle, is " highest point» economic recovery. In this phase, unemployment usually reaches its lowest level or disappears altogether, production capacities operate at maximum or close to it load, that is, almost all material and labor available in the country are involved in production. resources. Usually, though not always, inflation rises during peaks. The gradual saturation of markets increases competition, which reduces the rate of return and increases the average payback period. The need for long-term lending is growing with a gradual decrease in the ability to repay loans. Recession (recession) is characterized by a reduction in production volumes and a decrease in business and investment activity. As a result, unemployment increases. Officially, the phase of the economic downturn, or recession, is considered to be a fall in business activity that lasts more than three months in a row. Bottom(depression) of the economic cycle is the "trough" of production and employment. It is believed that this phase of the cycle is usually not long.

1The subject of macroeconomics and its place in the structure of the socio-economic formation.

Macroeconomics- studies the functioning of the national economy as a whole. The patterns of development of productive forces and production relations on the scale of the whole society. The objects of research are: gross national product; the national income of society; general price level; employment and unemployment across society; inflation, etc.

Economic theory-science, predstavl. a system of knowledge, a cat. describes, explains and predicts the functioning of certain economies. phenomena. John Keynes differentiated the economy into positive (characterized as a positive economy, describes what is in the national economy at the moment) and normative (characteristic of those economic processes and phenomena that should occur in the future)

ME began to develop in the 20-30s of the last century. The author of the term is Ragnar Frisch.

Subject of ME study:

Functioning of the national economy; -analysis of ext. links that unite the entire economy into a single whole; - the inclusion of the national economy in the world.

Subject of study-circulation of resources and funds in the economy-models---:

F. Quesnay's table, 2) K. Marx's reproduction schemes, 3) balance method, 4) system of national accounts.

Methodology for calculating the ME indicators: by total expenses, by total income, by the value added method

Economic growth, 2) price stability, 3) full employment, 4) equilibrium of foreign trade operations, in which exports are equal to imports (“magic quadrangle”)

Monetary Aggregates

The indicators of the structure of the money supply are monetary aggregates. Monetary aggregates are called types of money and funds that differ from each other in the degree of liquidity (the ability to quickly turn into cash). IN different countries ah, monetary aggregates of different composition are distinguished. The IMF calculates the M1 indicator common to all countries and the broader “quasi-money” indicator (term and savings bank accounts and the most liquid financial instruments circulating on the market). Monetary aggregates are a hierarchical system - each subsequent aggregate includes the previous one. The most commonly used units are:

• M0 = cash in circulation,
• M1 = M0 + checks, demand deposits (including bank debit cards).
• M2 = M1 + term deposits
• М3 = М2 + savings deposits
• L = M3 + securities

Fisher's equation

Prices and the amount of money are directly dependent. Depending on various conditions, prices may change due to changes in the money supply, but the money supply can also change depending on changes in prices. The equation of exchange is as follows:

Fisher formula

Undoubtedly, this formula is purely theoretical and unsuitable for practical calculations. Fisher's equation does not contain any single solution; within the framework of this model, multivariance is possible. However, under certain tolerances, one thing is certain: The price level depends on the amount of money in circulation. Usually two assumptions are made:

• the speed of money turnover is a constant value;
• All production capacities on the farm are fully utilized.

The meaning of these assumptions is to eliminate the influence of these quantities on the equality of the right and left sides of the Fisher equation. But even if these two assumptions are met, it cannot be unconditionally asserted that the growth of the money supply is primary, and the rise in prices is secondary. The dependence here is mutual. Under conditions of stable economic development the money supply acts as a regulator of the price level. But with structural imbalances in the economy, a primary change in prices is also possible, and only then a change in the money supply

15. The essence of the market and the conditions for its formation and development. Main types of markets. The Essence of the Market: The market is a system of relations in which the bonds of buyers and sellers are so free that the prices of the same commodity tend to quickly equalize. The essence of the market is manifested in its Functions.
1. Information. Through constantly changing prices, interest rates on credit, the market provides production participants with objective information about the socially necessary quantity, assortment and quality of those goods and services that are supplied to the market.
2. Intermediary. Economically isolated producers in conditions of a deep social division of labor must find each other and exchange the results of their activities. Without a market, it is practically impossible to determine how mutually beneficial this or that technological and economic relationship between specific participants in social production is. 3. Pricing. Products and services of the same purpose that usually enter the market contain an unequal amount of material and labor costs. But the market recognizes only publicly necessary costs, only the buyer agrees to pay them. Consequently, a reflection of social value is formed here, which no computer is capable of calculating. Thanks to this, a mobile relationship is established between cost and price, which is sensitive to changes in production, needs, and market conditions.
4. Regulatory - the most important. It is connected with the influence of the market on all spheres of the economy, and above all on production. The market is inconceivable without competition. Intra-industry competition stimulates the reduction of costs per unit of output, encourages the growth of labor productivity, technical progress, and the improvement of product quality. Intersectoral competition through the flow of capital from industry to industry forms the optimal structure of the economy, stimulates the expansion of the most promising industries. Preservation and maintenance of a competitive environment is one of the most important tasks of state regulation in countries with a developed market system.
5. Sanitizing. The market mechanism is not a charitable system. It is characterized by social stratification, ruthlessness towards the weak. With the help of competition, the market clears social production of economically unstable, unviable economic units and, on the contrary, gives the green light to more enterprising and efficient ones. As a result of this, the average level of sustainability of the entire economy as a whole is continuously increasing. Conditions for the formation of the market. In order for a market economy to be built, a real market to function, which would perform its inherent functions, the prerequisites tested by world practice must be reproduced. These include: the presence of subjects of market relations, which, being economically and legally independent, can enter into equal partnerships regarding the purchase and sale. This can be achieved by creating various owners - individual, private, joint-stock, state, cooperative, mixed; equivalent exchange of goods. The market, by its nature, does not recognize economic assistance; competition, which provides all business entities with the opportunity of free entrepreneurial activity: the freedom to choose buyers, suppliers, any counterparties, forces entrepreneurs to use the most advanced equipment and technology, thereby contributing to a reduction in production costs and an increase in the efficiency of the economy; free pricing, as an element of competition and the main mechanism of the control and regulatory function of the market, contributes to the unification of the interests of subjects of economic life, stimulating them to rationally use the elements of production; real information about the market and its subjects.
In the economic literature, more than a dozen criteria are distinguished for characterizing the structure and system of the market, its classification. Let's consider some of them.

• According to the economic purpose of objects of market relations: 1) Market of goods and services (consumer market); 2) Securities market; 3) Labor market (labor market); 4) Market and currencies; 5) Market information; 6) Market of scientific and technical developments (patents, know-how licenses), etc.
• By product groups: 1) Markets for industrial goods; 2) Markets for consumer goods (for example, food); 3) Markets for raw materials and materials, etc.
• By geographic location: 1) Local (local) markets; 2) Regional markets; 3) National market; 4) World market.
• By subjects or their groups: 1) Market of buyers; 2) Market of sellers; 3) Market of state institutions; 4) Market of intermediate sellers - intermediaries, etc.
• According to the degree of restriction of competition: 1) Monopoly market; 2) Oligopolistic market; 3) The market of monopolistic competition; 4) Market of perfect competition.
• Saturation level: 1) Equilibrium market; 2) Scarce market; 3) Excess market.
• By degree of maturity: 1)Undeveloped market; 2) Developed market; 3) Emerging market.
• According to the law: 1) Legal (official) market; 2) Illegal, or shadow, market ("black" and "gray").
• By nature of sales: 1) Wholesale market; 2) Retail market.
• By the nature of the product range: 1) A closed market, in which the goods of only the first manufacturer are presented; 2) A saturated market, which presents many similar products from many manufacturers; 3) A wide range market, in which there are a number of types of goods related to each other and aimed at satisfying one or more related needs; 4) A mixed market in which there are a variety of goods that are not related to each other.
• By industry: 1) Car market; 2) Oil market; 3) Computer equipment market, etc.

In the market structure, the following types of markets are also highlighted: 1) Markets for goods and services, which includes markets for consumer purposes, services, housing and non-industrial buildings. 2) Factor markets, which include markets for real estate, tools, raw materials, energy resources, minerals.3) Financial markets, those. capital markets (investment markets), credit, securities, currency and money markets. 4) Smart Product Markets, where innovations, inventions, information services, works of literature and art act as objects of sale. five) labor markets, representing an economic form of movement (migration) of labor resources (labor).

16. External (side) effects. Individual and public goods. External (side) effects (externalities)) are the costs or benefits of market transactions that are not reflected in prices. They are called "external", as they concern not only the economic agents participating in this operation, but also third parties. They arise as a result of both the production and consumption of goods and services. Side effects are the costs or benefits that fall to individuals or groups of some third party not involved in the market transaction. An example of a side cost would be environmental pollution, and an example of a side benefit would be vaccinations. Externalities are divided into positive and negative: Negative externality occurs when the activity of one economic agent causes costs to others. At the same time, the amount of output exceeds the effective volume of output, since external costs are not taken into account. positive externality arises if the activity of one economic agent brings benefits to others. In the presence of a positive external effect, an economic good is sold and bought in a smaller volume compared to the effective one, i.e., there is an underproduction of goods and services with positive external effects.

The essence of the problem of externalities lies in the inefficient allocation and use of resources and products in the economy due to the discrepancy between private and social costs or private and public benefits.

An important function of the state in a market economy is the elimination of external (external) effects of economic activity. This is a type of market fiasco when it functions with such shortcomings that the prices of goods do not reflect all production costs. environment. Given this circumstance, an externality can be defined as such a result of the production or consumption of a certain product that is transferred to another enterprise or person without the right to choose and without any payment.

Public and private goods. Most of the goods offered by producers and in demand by consumers are goods intended for personal consumption, or private goods. A good is private if, being consumed by one person, it cannot be simultaneously consumed by another. But there are goods that are socially necessary and, moreover, perform important social functions. A large-scale example of public goods would be goods intended to meet the needs of national defense, and an example of a “local” would be navigational signs (such as, say, beacons or lighthouses). These goods are called public goods because of two distinctive characteristics. First, the consumer of public goods, as a rule, does not pay for them himself, which means that the marginal cost of consumption is zero. Secondly, there is no practical possibility to limit the number of consumers or exclude someone from this number. Most public goods require very significant production and distribution costs. Thus, there is a certain special group of goods, the production and distribution of which, based on their very nature, is subject to state control. The problem of free use arises when the number of users is large and it is not possible to exclude even one of them.
The experience of post-industrial society shows that the market is able to identify and satisfy the demand only for private goods. The creation and implementation of public goods is the task of the state. However, public goods are not homogeneous. They act as purely and partially public goods. The production of purely public goods is entirely the responsibility of the state (public order, for example). At the same time, the creation of partially public goods (education, healthcare, social insurance) can be carried out both by the state and the private sector of the economy. At the same time, the state guarantees only such a level of reproduction of partially public goods, which at a given moment can be provided with the resources of the state budget, which in turn is determined by the development of production.

17. Demand. The law of demand. The amount of demand. Non-price factors of demand. Demand is the quantity of goods and services that buyers are willing and able to purchase at a given price and within a given period of time, other things being equal. The essence of the law of demand is an inverse relationship between the price of a commodity and the demand for it, other things being equal, i.e., the demand for a commodity increases when its price falls, and, conversely, the demand for a commodity decreases when its price rises. The reasons for the existence of an inverse relationship between price and demand are as follows: 1) the lower the price, the greater the propensity of people who have previously bought this product to buy it again; 2) more low price enables people who previously could not afford a purchase to purchase this product; 3) the low price of the product encourages buyers to reduce the consumption of more expensive substitute products. VALUE OF DEMAND The quantity of a good or service of a particular kind that a buyer is willing to buy at a given price within a given period of time. If the curve D 0 shifts to the right, demand increases. If the curve D 0 shifts to the left, then demand will decrease. Non-price factors of demand are otherwise called non-price determinants of demand.

1 | |

Mathematically, Fisher's Equation The equation looks like this:

real interest rate + inflation = nominal interest rate;

Here R is the real interest rate;
N is the nominal interest rate;
Pi - ;

The Greek letter Pi is commonly used to represent . It should not be confused with the pi constant used in geometry.

For example, if you put a certain amount of money in a bank at 10% per annum, with an inflation rate of 7%, then the nominal interest rate under such conditions will be 10%. The real rate will be only 3%.

Application of the Fisher Equation in Economics

If inflation is taken into account, then this is not a real interest rate, but a nominal rate that is adjusted or changes with inflation. The inflation rate used in evaluating the equation is the expected rate of inflation over the life of the loan. In Fisher's theory, the hypothesis was put forward that the count should be constant. The rate of inflation is taken into account differently when determining the interest rate of a loan within areas affected by current activities, technology and other world events that affect the real economy.

This equation can be applied both before the conclusion of the contract, and after the fact, that is, as a loan analysis. If the equation is used to evaluate credit ex post. For example, it can help determine purchasing power and calculate the cost of a loan. It is also used to help lenders determine what the interest rate should be. By using this formula, lenders can take into account the planned loss of purchasing power and therefore charge favorable interest rates.

The Fisher equation is commonly used in estimating investment amounts, bond yields, and ex post investment calculations.

Fisher also owns, which determines the dependence of the price and the amount of money in circulation. Many economic indicators depend on the amount of money. First of all, these are prices and rates on loans. Moreover, in conditions of stable economic development, the volume of money supply regulates prices. In the case of structural imbalances, the primary change in prices is possible, and only then there is a change in the cash supply. It turns out that depending on changes in various conditions in the economy, the political life of countries, the environment, prices can change, but vice versa, they can change due to an increase or decrease in prices. The formula looks like this:

Here M is the amount of money in circulation;
V is the rate of their turnover;
P - the price of the goods;
Q - volume, or quantity of goods

This formula is purely theoretical, since it does not contain a unique solution. However, we can conclude that the dependence of prices and money supply is mutual. In developed economies (a single country or a group of countries) with one currency, the amount of money in circulation must correspond to the level of the economy (production volume), the level of trade and income. Otherwise, it will be impossible to ensure price stability, which is the main condition for determining the amount of cash in circulation.

“Inflation is when with your money you can no longer buy as much as in those days when you had no money,” ironically American writer Leonard Louis Levinson.

Admit that no matter how sad, but it's true. Constant inflation eats away at our income.

We make investments, counting on certain percentages, but what do we have in reality?

To answer these and similar questions, the Fisher formula has been developed. inflation, money supply, price level, interest rates and real return- read about it in the article.

Relationship between money supply and prices - Fisher's equation

Regulation of the amount of money in circulation and the price level is one of the main methods of influencing the market-type economy. The relationship between the quantity of money and the price level was formulated by representatives of the quantity theory of money. In a free market (market economy) it is necessary to regulate economic processes to a certain extent (Keynesian model).

Fisher formula: inflation

The regulation of economic processes is carried out, as a rule, either by the state or by specialized bodies. As the practice of the 20th century showed, many other important economic parameters depend on the amount of money used in the economy, primarily the level of prices and the interest rate (the price of a loan). The relationship between the price level and the amount of money in circulation was clearly formulated within the framework of the quantity theory of money.

Prices and the amount of money are directly related. Depending on various conditions, prices may change due to changes in the money supply, but the money supply can also change depending on changes in prices.

Undoubtedly, this formula is purely theoretical and unsuitable for practical calculations. Fisher's equation does not contain any single solution; within the framework of this model, multivariance is possible. At the same time, under certain tolerances, one thing is certain: the price level depends on the amount of money in circulation. Usually two assumptions are made:

1. the speed of money turnover is a constant value;
2. All production capacities on the farm are fully utilized.

The meaning of these assumptions is to eliminate the influence of these quantities on the equality of the right and left sides of the Fisher equation. But even if these two assumptions are met, it cannot be unconditionally asserted that the growth of the money supply is primary, and the rise in prices is secondary. The dependence here is mutual.

Under conditions of stable economic development, the money supply acts as a regulator of the price level. But with structural imbalances in the economy, a primary change in prices is also possible, and only then a change in the money supply.

Fisher's formula (the equation of exchange) determines the amount of money used only as a medium of exchange, and since money also performs other functions, the determination of the total need for money involves a significant improvement in the original equation.

The amount of money in circulation

The amount of money in circulation and the total amount of commodity prices are related as follows:

The above formula was proposed by representatives of the quantity theory of money. The main conclusion of this theory is that in each country or group of countries (Europe, for example) there must be a certain amount of money corresponding to the volume of its production, trade and income. Only in this case price stability will be ensured. In the case of an inequality in the quantity of money and the volume of prices, changes in the price level occur:

• MV = PT - prices are stable;
• MV > PT - prices are rising (inflationary situation).

Thus, price stability is the main condition for determining the optimal amount of money in circulation.

Source: "grandars.ru"

Fisher Formula: Inflation and Interest Rates

Economists call bank interest the nominal rate of interest, and the increase in your purchasing power at the real rate of interest. If we designate the nominal interest rate as i, and the real interest rate as r, inflation as π, then the relationship between these three variables can be written as follows: r = i - π, i.e. The real interest rate is the difference between the nominal interest rate and the inflation rate.

Regrouping the terms of this equation, we see that the nominal interest rate is the sum of the real interest rate and the inflation rate: i = r + π. An equation written in this form is called the Fisher equation. It shows that the nominal interest rate can change for two reasons: due to changes in the real interest rate or due to changes in the inflation rate.

The quantity theory of money and Fisher's equation show how an increase in the money supply affects the nominal rate of interest. According to the quantity theory of money, a 1% increase in the money supply causes an increase in the inflation rate by 1%.

According to the Fisher equation, a 1% increase in the inflation rate, in turn, causes a 1% increase in the nominal interest rate. This relationship between the rate of inflation and the nominal rate of interest is called the Fisher effect.

It is necessary to distinguish between two different concepts of the real interest rate:

1. the real interest rate expected by the borrower and lender when issuing a loan (exante real interest rate) – i.e. expected, supposed;
2. the actual real interest rate is expost.

Lenders and borrowers are not in a position to predict the future rate of inflation with complete certainty, but they have certain expectations about this. Denote by π the actual rate of inflation in the future, and by e the expected future rate of inflation. Then the real interest rate exante will be equal to i - πе, and the real interest rate expost will be equal to i - π x v.

How is the Fisher effect modified to account for the difference between expected and actual future inflation rates? The Fisher effect can be more accurately represented as follows: i = r + πе.

The demand for money in real terms depends on both the level of income and the nominal interest rate. The higher the level of income Y, the greater the demand for cash reserves in real terms. The higher the nominal interest rate i, the lower the demand for them.

Source: "infomanagement.ru"

Nominal and real interest rate - Fisher effect

The nominal interest rate is the market interest rate without inflation, reflecting the current valuation of monetary assets.

The real interest rate is the nominal interest rate minus the expected rate of inflation.

For example, the nominal interest rate is 10% per annum and the projected inflation rate is 8% per annum. Then the real interest rate will be: 10 - 8 = 2%.

The difference between the nominal rate and the real one makes sense only in conditions of inflation or deflation.

The American economist Irving Fisher put forward an assumption about the relationship between the nominal, real interest rate and inflation, called the Fisher effect, which states that the nominal interest rate changes by the amount at which the real interest rate remains unchanged.

In formula form, the Fisher effect looks like this:

For example, if the expected inflation rate is 1% per year, then the nominal rate will increase by 1% in the same year, therefore, the real interest rate will remain unchanged. Therefore, it is impossible to understand the process of making investment decisions by economic agents without taking into account the difference between the nominal and real interest rates.

Consider a simple example: let's say you intend to give someone a loan for one year in an inflationary environment, what is the exact interest rate you set? If the growth rate of the general price level is 10% per year, then setting the nominal rate at 10% per annum with a loan of CU1000, you will receive CU1100 in a year.

But their real purchasing power will no longer be the same as a year ago. Nominal income increment of CU100 will be "eaten" by 10% inflation. Thus, the distinction between nominal and real interest rates is important for understanding exactly how contracts are made in an economy with an unstable general price level (inflation and deflation).

Source: "economicportal.ru"

Fisher effect

The effect, as a phenomenon, as a pattern, was described by the great American economist Irving Fisher in 1896. The general idea is that there is a long-term relationship between expected inflation and the interest rate (yield on long-term bonds). Content - an increase in expected inflation causes approximately the same increase in the interest rate and vice versa.

The Fisher Equation is a formula for quantifying the relationship between expected inflation and the interest rate.

Simplified equation: if the nominal interest rate N is 10, the expected inflation I is 6, R is the real interest rate, then the real interest rate is 4 because R = N – I or N = R + I.

The exact equation. The real interest rate will differ from the nominal one as many times as the prices change. 1 + R = (1 + N)/(1 + I). If we open the brackets, then in the resulting equation, the value of NI for N and I less than 10% can be considered tending to zero. As a result, we get a simplified formula.

Calculating the exact equation with N equal to 10 and I equal to 6 will give the following value of R.
1 + R = (1 + N)/(1 + I), 1 + R = (1 + 0.1)/(1 + 0.06), R = 3.77%.

In the simplified equation, we got 4 percent. It is obvious that the boundary of the application of the simplified equation is the value of inflation and the nominal rate of less than 10%.

Source: "dictionary-economics.ru"

Essence of inflation

Imagine that in a secluded northern village, all workers had their wages doubled. What will change in a local store with the same offer, for example, chocolate? How would its equilibrium price change? Why does the same chocolate become more expensive? The money supply available to the population of this village increased, and demand increased accordingly, while the amount of chocolate did not increase.

As a result, the price of chocolate has risen. But the rise in the price of chocolate is not yet inflation. Even if all foodstuffs in the village rise in price, this will still not be inflation. And even if all goods and all services in this village rise in price, this will not be inflation either.

Inflation is a long-term sustained increase in the general price level. Inflation is the process of depreciation of money, which occurs as a result of the overflow of circulation channels with the money supply. How much money must circulate in the country in order for the price level to be stable?

The equation of exchange - Fisher's formula - allows you to calculate the money supply needed for circulation:

where M is the amount of money in circulation;
V is the velocity of money, which shows how many times 1 ruble changes hands in a certain period of time;
P is the average price per unit of output;
Y - real gross domestic product;
RU - nominal GDP.

The equation of exchange shows that every year the economy needs the amount of money that is required to pay for the value of the GDP produced. If more money is put into circulation or the velocity of circulation is increased, then the price level rises.

When the growth rate of the money supply exceeds the growth rate of the mass of commodities: MU > RU,
equilibrium is restored as a result of rising prices: MU = R|U.

An overflow of money circulation channels can occur if the velocity of money circulation increases. The same consequences can be caused by a reduction in the supply of goods on the market (a drop in production).

The degree of depreciation of money is determined in practice by measuring the rate of price growth.

In order for the price level in the economy to be stable, the government must maintain the growth rate of the money supply at the level of the average growth rate of real GDP. The amount of money supply is regulated by the Central Bank. Emission is the issuance of an additional amount of money into circulation.

Depending on the rate of inflation, inflation is conditionally distinguished:

• moderate
• galloping
• high
• hyperinflation.

If prices rise slowly, up to about 10% per year, then one usually speaks of moderate, “creeping” inflation.

If there is a rapid and abrupt increase in prices, measured in double digits, then inflation becomes galloping. With such inflation, prices rise no more than twice.

Inflation is considered high when prices rise by more than 100%, that is, prices rise several times.

Hyperinflation occurs when the depreciation of money becomes self-sustaining and uncontrollable, and the growth rates of prices and the money supply become exceptionally high. Hyperinflation is usually associated with war, economic disruption, political instability, and erroneous government policies. The rate of price growth during hyperinflation exceeds 1000%, i.e., during the year, prices rise by more than 10 times.

The intensive development of inflation causes distrust of money, and therefore there is a massive desire to turn it into real values, the "flight from money" begins. There is an increase in the velocity of circulation of money, which leads to an acceleration of their depreciation.

Money ceases to fulfill its functions, and the monetary system comes into complete disorder and decline. This is manifested, in particular, in the introduction into circulation of various monetary surrogates (coupons, cards, other local monetary units), as well as hard foreign currency.

The collapse of the monetary system as a result of hyperinflation, in turn, causes the degradation of the entire national economy. Production is falling, normal economic ties are being disrupted, and the share of barter transactions is growing. There is a desire for economic isolation of various regions of the country. Growing social tension. Political instability is manifested in the lack of trust in the government.

This also reinforces distrust of money and its depreciation.

A classic example of hyperinflation is the state of German money circulation after the First World War in 1922-1923, when the rate of price growth reached 30,000% per month, or 20% per day.

Inflation manifests itself differently in different economic systems. In a market system, prices are formed under the influence of supply and demand; depreciation of money is open. In a centralized system, prices are formed by directives, inflation is suppressed, hidden. Its manifestations are the shortage of goods and services, the growth of monetary savings, the development of the shadow economy.

Factors causing inflation can be both monetary and non-monetary. Let's consider the main ones. Demand-pull inflation is the result of excessive growth in government spending, consumers and private investment. Another cause of inflation in demand may be the issue of money to finance government spending.

In cost inflation, prices rise as firms increase their costs of production. For example, growth wages if it outpaces the growth of labor productivity, it can cause cost inflation.

• Inflation is a general rise in prices. It is caused by the excess of the growth rate of the money supply over the mass of commodities.
• According to the rate of price growth, four types of inflation are distinguished, of which the strongest is hyperinflation, which destroys the economy.
• Inflation is unpredictable. People with fixed incomes suffer the most from its consequences.

Source: "knigi.news"

How to correctly calculate the real yield adjusted for inflation

Probably everyone knows that the real yield is the yield minus inflation. Everything rises in price - products, goods, services. According to Rosstat, over the past 15 years, prices have increased 5 times. This means that the purchasing power of money that has just been lying in the nightstand all this time has decreased by 5 times, before they could buy 5 apples, now 1.

In order to somehow preserve the purchasing power of their money, people invest it in various financial instruments: most often these are deposits, currency, real estate. More advanced ones use stocks, mutual funds, bonds, precious metals. On the one hand, the amount of investments is growing, on the other hand, they are depreciating due to inflation.

If you subtract the inflation rate from the nominal rate of return, you get the real rate of return. It can be positive or negative. If the return is positive, your investment has multiplied in real terms, that is, you can buy more apples, if it is negative, it has depreciated.

Most investors calculate real returns using a simple formula:

Real Return = Nominal Return - Inflation

But this method is inaccurate. Let me give you an example: let's take 200 rubles and put them on a deposit for 15 years at a rate of 12% per annum. Inflation over this period is 7% per year. If we consider the real yield using a simple formula, we get 12-7=5%. Let's check this result by counting on the fingers.

For 15 years, at a rate of 12% per annum, 200 rubles will turn into 200 * (1 + 0.12) ^ 15 = 1094.71. Prices during this time will increase by (1+0.07)^15=2.76 times. To calculate the real profitability in rubles, we divide the amount on the deposit by the inflation coefficient 1094.71/2.76=396.63. Now, to translate the real yield into percentages, we consider (396.63/200)^1/15 -1 * 100% = 4.67%. This is different from 5%, i.e. the test shows that the calculation of the real yield in the "simple" way is not accurate.

where Real Rate of Return - real yield;
nominal rate - nominal rate of return;
inflation rate - inflation.

We check:
(1 + 0.12) / (1 + 0.07) -1 * 100% \u003d 4.67% - Converges, so the formula is correct.

Another formula that gives the same result looks like this:

RR=(nominal rate-inflation)/(1+inflation)

The greater the difference between nominal yield and inflation, the greater the difference between the results calculated by the "simple" and "correct" formula. This happens a lot in the stock market. Sometimes the error reaches several percent.

Source: "activeinvestor.pro"

Calculation of inflation. Inflation indices

The inflation index is an economic indicator that reflects the dynamics of prices for services and goods that the population of the country pays for, that is, for those products that are purchased for further use, and not for overproduction.

The inflation index is also called the consumer price index, which is an indicator of measuring the average level of prices for consumer goods over a certain period of time. Different methods and formulas are used to calculate the inflation index.

Calculation of the inflation index using the Laspeyres formula

The Laspeyres index is calculated by weighing the prices of 2 time periods according to the same consumption volumes of the base period. Thus, the Laspeyres index reflects the change in the cost of services and goods of the base period that has occurred over the current period.

The index is defined as the ratio of consumer spending on the purchase of the same set of consumer goods, but at current prices (∑Qo×Pt), to spending on the purchase of goods and services in the base period (∑Qo×Po):

where Pt - prices in the current period, Qo - prices for services and goods in the base period, Po - the number of services and goods produced in the base period (as a rule, 1 year is taken for the base period).

It should be noted that the Laspeyres method has significant drawbacks due to the fact that it does not take into account changes in the structure of consumption.

The index only reflects changes in income levels, not taking into account the substitution effect, when the prices of some goods fall and this leads to an increase in demand. Consequently, the method of calculating the inflation index according to the Laspeyres method in some cases gives a slightly overestimated value.

Calculation of the inflation index using the Paasche formula

Another way to calculate the inflation index is based on the Paasche formula, which also compares the prices of two periods, but in terms of consumption volumes of the current period:

where Qt are prices for services and goods in the current period.

However, the Paasche method also has its own significant drawback: it does not take into account price changes and does not reflect the level of profitability. Therefore, when prices for some services or products decrease, the index overestimates, and when prices increase, it underestimates.

Calculation of the inflation index using the Fisher formula

In order to eliminate the shortcomings that are inherent in the Laspeyres and Paasche indices, the Fisher formula is used to calculate the inflation index, the essence of which is to calculate the geometric mean of the 2 above indices:

Many economists consider this formula to be ideal, as it compensates for the shortcomings of the Laspeyres and Paasche formulas. But, despite this, experts in many countries prefer the choice of one of the first two methods.

For example, for international reporting, the Laspeyres formula is used, since it takes into account that some goods and services may, in principle, fall out of consumption in the current period for one reason or another, in particular during the economic crisis in the country.

Gross domestic product deflator

An important place among inflation indices is occupied by the GDP deflator - a price index that includes all services and goods in the consumer basket. The GDP deflator allows you to compare the growth in the general level of prices for services and goods over a certain economic period.

This indicator is calculated in the same way as the Paasche index, but measured as a percentage, that is, the resulting number is multiplied by 100%. As a rule, the GDP deflator is used by the state statistical offices for reporting.

Big Mac Index

In addition to the above official methods for calculating the inflation index, there are also such unconventional ways its definitions, such as the Big Mac index or the hamburger index. This method of calculation makes it possible to study how the same products are valued in different countries today.

The well-known hamburger is taken as the basis, and all because it is sold in many countries of the world, it has a similar composition almost everywhere (meat, cheese, bread and vegetables), and the products for its manufacture, as a rule, are of domestic origin.

Thus, the most expensive hamburgers today are sold in Switzerland ($6.81), Norway ($6.79), Sweden ($5.91), the cheapest ones are in India ($1.62), Ukraine ($2.11), Hong Kong ($2.12). As for Russia, the cost of a hamburger here is $2.55, while in the US a hamburger costs $4.2.

What does the hamburger index say? The fact that if the cost of a Russian Big Mac in terms of dollars is lower than the cost of a hamburger from the United States, then the official exchange rate of the Russian ruble is underestimated against the dollar.

Thus, it is possible to compare the currencies of different countries, which is a very simple and easy way to recalculate national currencies.

Moreover, the cost of a hamburger in each country directly depends on the volume of production, prices for raw materials, rent, labor and other factors, so the Big Mac index is one of best ways see the discrepancy between the value of currencies, which is especially important in a crisis, when a "weak" currency provides some advantages in terms of prices and costs for products, and an expensive currency becomes simply unprofitable.

Borscht index

In Ukraine, after carrying out, to put it mildly, unpopular reforms, an analogue of the Western Big Mag index was created, which has the patriotic name "borscht index". In this case, the study of price dynamics is carried out exclusively on the cost of the ingredients that make up the national Ukrainian dish - borscht.

However, if in 2010-2011 the borscht index could “save the situation” by showing the people that a plate of borscht now costs a little less, then in 2012 the situation changed dramatically. So, the borscht index showed that in September 2012 the average borscht set, consisting of vegetables, costs as much as 92% more than in the same period last year.

This rise in prices has led to the fact that the volume of purchases of vegetables by the population in Ukraine has decreased by an average of 10-20%.

As for meat, on average it has risen in price by 15-20%, but by this winter a rapid rise in price up to 30-40% is expected due to the increase in prices for fodder grain. On average, borscht made from potatoes, meat, beets, carrots, onions, cabbage, tomatoes and a bunch of greens is taken as the basis for assessing changes in the price level according to the borscht index.

Source: "provincialynews.ru"

Exchange rate and inflation

Inflation is the most important indicator of the development of economic processes, and for the currency markets - one of the most significant benchmarks. Currency dealers are watching inflation data very carefully. From the perspective of the foreign exchange market, the impact of inflation is naturally perceived through its relationship with interest rates.

Since inflation changes the ratio of prices, it also changes the benefits actually received from the income generated by financial assets. This impact is usually measured using real interest rates (Real Interest Rates), which, unlike conventional (nominal, Nominal Interest Rates) take into account the depreciation of money that occurs due to the general rise in prices.

An increase in inflation reduces the real interest rate, since some part must be deducted from the income received, which will simply go to cover the price increase and does not give any real increase in the benefits (goods or services) received.

The simplest way formal inflation accounting and consists in the fact that the nominal rate i is considered as the real interest rate minus the inflation coefficient p (also given as a percentage),

A more accurate relationship between interest rates and inflation is provided by Fisher's formula. For obvious reasons, government securities markets (interest rates on such securities are fixed at the time of their issue) are very sensitive to inflation, which can simply destroy the benefits of investing in such instruments.

The effect of inflation on government securities markets is easily transferred to closely related currency markets: the dumping of bonds denominated in a certain currency crs, which occurred due to rising inflation, will lead to an excess in the cash market in this currency crs, and consequently, to a fall in it. exchange rate.

In addition, the inflation rate is the most important indicator"health" of the economy, and therefore it is carefully monitored by central banks.

The means of combating inflation is to raise interest rates. Rising rates divert part of the cash from business turnover, as financial assets become more attractive (their profitability grows along with interest rates), loans become more expensive; as a result, the amount of money that can be paid for goods and services produced falls, and consequently the rate of price growth also decreases.

Because of this close relationship with central bank rate decisions, foreign exchange markets closely monitor inflation indicators. Of course, individual deviations in inflation levels (for a month, a quarter) do not cause the reaction of central banks in the form of changes in rates; central banks follow trends, not individual values.

For example, low inflation in the early 1990s allowed the FED to keep the discount rate at 3%, which was good for economic recovery. But in the end, inflation indicators ceased to be essential benchmarks for the currency markets.

Since the nominal discount rate was small, and its real version generally reached 0.6%, this meant for the markets that only upward movement of inflation indices made sense. The downtrend in the US discount rate was broken only in May 1994 when the FED raised it, along with the federal funds rate, as part of a pre-emptive inflation control measure. True, raising rates then could not support the dollar.

The main published indicators of inflation are the consumer price index (consumer price index), the producer price index (producer price index), and the GDP deflator (GDP implicit deflator). Each of them reveals its own part of the overall picture of price growth in the economy. Figure 1 illustrates the growth of consumer prices in the UK over the past 12 years.

Figure 1 UK consumer prices

This figure directly represents the cost of some consumer basket; the growth rate of this basket value is the commonly published consumer price index. On the chart, the growth rate is depicted by the slope of the trend line, along which the main upward trend in prices goes.

It is clearly seen that after overcoming the problems of 1992, which led to the exit of England from the European monetary union, the reforms carried out brought the economy to a different growth line, along which the price increase (the slope of the right trend line) is much less than it was at the end of the previous decade and in features - in 91-92 years.

An example of the actions of the central bank, based on its position on inflationary processes, and the reaction of the foreign exchange market caused by them, is shown in Figure 2, which shows a chart of the British pound against the dollar.

Figure 2. Chart of the British pound; Bank of England rate hike on September 8, 1999 and reaction to rumors of another hike

On September 8, 1999, a meeting of the Bank of England Monetary Policy Committee was held. None of the experts predicted then an increase in interest rates, since economic indicators did not show clear signs of inflation, and the pound was already estimated too high. True, on the eve of the meeting there were many comments that the increase in rates of the Bank of England in 1999 or early 2000 is inevitable.

But no one predicted it for this meeting. Therefore, the decision of the Bank to raise its main interest rate by a quarter of a percent came as a surprise to everyone, which shows the first sharp rise in the pound.

The Bank explained its decision by the desire to prevent further price increases, signs of which he saw in the overheated housing market, strong consumer demand and the possibility of inflationary pressure from wages, since unemployment in England was at a fairly low level. Although it is possible that the Bank's decision was influenced by the recently implemented FED rate hike.

The second rise in the chart the next day was caused by active discussion in the market about the inevitability of a new rate hike soon (rate hike is a common term for raising central bank rates in market slang); there were, apparently, many willing not to be late to buy a pound before it rose even more. The fall of the pound at the end of the week was due to the reaction to the US inflation data, which will be discussed later.

Inflation and interest rates

The connection between inflation and the conditions of money circulation can be demonstrated on the basis of the basic equation of the theory of money, if we write it for the relative changes in its constituent values, which shows that under these conditions, price growth (inflation) is completely determined by the regulatory actions of the central bank through a change in the money supply.

In reality, of course, the causes of inflation are quite complex and numerous, the growth of the money supply is only one of them.

Suppose some amount S was invested for the same period at an interest rate i (which is called the nominal interest rate, nominal interest rate), that is, the amount S will turn over the same period into S -> S(l + i). At the beginning of the period under review (at the old prices), it was possible to purchase the amount of goods Q=S/P for the amount S.

The real interest rate is called the interest rate in real terms, that is, determined through the increase in the volume of goods and services. In accordance with this definition, the real interest rate r will give for the same period under consideration the change in the volume Q,

Collecting all the above relations, we get,

Q(l + r) = S(l + i)/ P(l + p) = Q * (1 + i)/ (1 + p),

whence we obtain the expression for the real interest rate in terms of the nominal interest rate and the inflation rate,

r=(l+i)/(l+p)-l.

The same equation, written in a slightly different form,

characterizes the well-known Fisher effect in macroeconomics.

Fisher formula and monopoly price increase

Apparently, there are two types of prices: competitive and monopoly. The mechanism of competitive pricing is well researched. With a stable money supply, it never leads to an irrevocable rise in prices. When there is a market shortage of a commodity, the enterprises that produce it may temporarily raise prices.

However, after a certain period of time, capital will flow into this sector of the economy, that is, where a high rate of profit has temporarily formed. The influx of capital will make it possible to create new capacities for the production of scarce goods, and after a certain time an excess of this goods will form on the market. In this case, prices may even fall below the general level, as well as below the cost level.

Ideally, with the complete absence of monopolies in the market and with some constant technological progress, in the absence of an excess money supply in circulation, the market economy does not produce inflation. On the contrary, such an economy is characterized by deflation.

Monopoly is another matter. They discourage competition and can inflate prices at will. The growth of monopolies is often a natural consequence of competition. When weak competitors die and only one winner remains in the market, it becomes a monopolist. Monopolies are general and local. Some of them are natural (unremovable).

Other monopolies are established temporarily, but this does not make it easier for consumers and the entire economy of the country. They fight monopolies. All countries with developed market economies have antitrust laws. However, this is a recognition of the fact that monopolies cannot be dealt with by market methods alone. The state forcibly divides large monopolies. But in their place, oligopolies can form.

Price collusion is also pursued by the state, but it is not easy to prove. Sometimes certain monopolies, especially those engaged in energy, transport and military production, are placed under strict state control, just as was done in the socialist countries.

Arbitrary price increases by monopolies are important point in cost inflation theory.

So, suppose there is a certain monopoly that intends to use its position in the market to raise prices, that is, in order to increase its share of income in the country's total NI. It could be an energy, transport or information monopoly.8 It could be a trade union, which can be considered a de facto monopoly in the sale of labor. (John Keynes himself considered trade unions to be the most aggressive monopolies in this respect).

Monopolies can also include the state, which collects taxes as a payment for the services it provides to maintain security, order, social security, and so on. Let's start with one of the possible cases. Let's say a private monopoly raised its tariffs (either the government increased taxes, or the unions won higher wages). In this case, we accept the condition that the money supply M remains constant.

Then, for one turnover of the money supply, the following condition is satisfied:

Thus, all changes in the equation, if they occur at all, will have to occur on the right side of the equation (p * q). There is a change - it is an increase in the weighted average price p. Therefore, an increase in price will necessarily lead to a decrease in the volume of q sold.

• Under conditions of invariance of the money supply for one period of circulation, a monopoly increase in prices leads to a reduction in the sale (and production) of goods.
• However, one more, more optimistic conclusion can be drawn: Inflation caused by monopolies, given a constant money supply, cannot last as long as inflation caused by the printing of money. A complete halt in production cannot be beneficial to the monopolies. There is a limit to which it is advantageous for a private monopoly to raise tariffs.

In support of the conclusions of the Fisher formula, we can find any number of examples in the history of economics. Strong inflation is usually accompanied by a reduction in production. However, in this case, almost always, money emission was also added to the monopoly increase in prices. At the same time, with strong inflation, there is often a relative contraction in the money supply.