Purchasing power. Consumer price and purchasing power indices of the ruble Calculation of the purchasing power of money
Conditions.
The average monthly salary of the regional consumer cooperation workers in current prices was 2000 rubles in the base year, and 2400 rubles in the reporting year. Consumer prices in the reporting year increased by 25% compared to the baseline. The share of taxes in wages was 12% in the base year and 14% in the reporting year.
Define:
) Index of nominal wages;
) Index of real wages.
) The purchasing power index of money is determined by the formula:
where PC is the consumer price index in the reporting year, according to the condition, it is equal to 1 + 25% / 100% = 1.25.
The purchasing power index will be:
.
where is the average nominal wage in the base and reporting periods.
In the calculation, we take into account the share of taxes in wages (w), then the formula will take the form:
.
We get:
.
We get:
.
It can be concluded that the purchasing power of money has decreased by 0.8 times. Nominal wages, in turn, increased by 1.173 times, while real wages decreased by 0.938 times.
Taxes and inflation
5.2 Inflation. IN the above methods of building up all dMonetary values were measured at par. In other words, notthe decrease in real purchasing power was taken into account. ability of money for the period covered by the operation. Oneto in modern conditions inflation in monetary relations plays a significant role, and without taking it into account, the final results are often notional.
Inflation must be taken into account in at least twocases: when calculating the accumulated amount of money and when measuring real efficiency (profitability) of a financial transaction.Let us dwell on these problems.
Let us introduce the notation:
S - the accumulated amount of money, measured at par,
C - the accrued amount, taking into account its impairment,
J p- price index,
J c- an index characterizing the change in the purchasing power of money over a period.
It's obvious that
Money purchasing power index is known to beis the reciprocal of the price index - the higher the prices, the lower the purchasing power:
The indicated indices, of course, should refer to the same time intervals. Suppose, for example, today received 150 thousand rubles. It is known that in the previous two years prices increased 1.5 times (or 50% increase),J p = 1,5, the purchasing power index of money is 1 / 1.5. Sledova Therefore, the real purchasing power is 150 thousand rubles. will be 150 / 1.5 = 100 thousand rubles. in the money with a purchasing way property two years ago.
It is not difficult to relate the price index and the inflation rate. Under pace inflationh is understood the relative increase in prices for the period; it is usually measured as a percentage and is defined as
In turn
For example, if the inflation rate for the period is 30%, then this ismeans that prices have risen 1.3 times.
Inflation is a chain process. Therefore, the price index over several periods is product chain in dex prices:
(5.4)
where h t –Inflation rate in the period t.
· Example 5.2
Now let it be about the future. If h - constant the expected (or projected) inflation rate per period, then for NS of such periods we get
(5.5)
A gross mistake that, unfortunately, occurs inRussian practice is the summation (!) of the rates ofinflation of individual periods to obtain a generalized inflation indicator for the entire period. What, we note, is essential forlowers the value of the resulting indicator.
Let us return to the problem of the depreciation of money as it accumulates.If the increase is made at a simple rate, then it is increasedthe total amount, taking into account the purchasing power, is
(5.6)
As you can see, an increase in the accrued amount, taking into account its ininflationary impairment occurs only when 1 + ni > J p
· Example 5.3
Let us now turn to the increase in compound interest. On thethe increased amount, adjusted for inflationary depreciation, is
(5.7)
The quantities multiplied by R in formulas (5.6) and (5.7), represent the growth factors, I take into accountthe expected inflation rate. Now let's see how jointly influence compound ratei and inflation rate h on the value the increase of this factor. Obviously, if the average annual rateinflation is equal to the interest rate, interest rate, then the growth of the real amountwill not happen - the buildup will be absorbed by inflation, and,Consequently, C = P. If h / 100> i, then there is an "erosion" of capital - its real amount will be less than the first moan. Only in a situation where h / 100< i, the real happensgrowth, real accumulation. It's obvious thatwhen calculating simple interest, the rate compensatingthe influence of inflation, corresponds to the value
A rate exceeding a critical valuei’(When accrued leery of compound interesti’= H ), are called positive interest rate.
Money owners, of course, cannot put up with their money.inflationary impairment and take varioustorture compensation for losses. The most common is the adjustment of the interest rate at which the accrual is made, i.e. increase in the rate by the amount of the so-calledinflationary premium. The total value can be called brute then-rate.(In Western financial literature, such a ratesometimes referred to as nominal.However, this term is already “for nyat ”.
We define the gross rate (we denote it as r) subject to full compensation for inflation. When building up a complex the interest rate, we find the gross rate from the equality
Where
(5.8)
In practice, the inflation-adjusted rate is often easier to calculate, namely:
(5.9)
· Example 5.4
In the case when the inflation index is applied for the entire term of the loan, the interest rate, taking into account inflation, is determined by the formula
· Example 5.5
When increasing by simple interest simple interest we have
where J p - price index for the period under consideration.
· Example 5.6
Obviously, at high inflation rates,how the bet is only meaningful for short or lastfor medium-term operations.
Another way to compensate for losses from a decrease in the purchasing power of money is the index of the original amount. In this case, the amount P
General purchasing power index (IPS) – economic indicator, most often used to assess the attractiveness of one or another.
Purchasing power index shows how many goods and services can be purchased for a unit of currency. Accordingly, changes ISI index indicate the dynamics of inflation in the country and the stability of the currency in general. The higher the prices, the lower the purchasing power of the currency, and vice versa.
Why is a purchasing power index needed?
The purchasing power index is used to analyze changes in the volume of goods and services that the population can afford to purchase for the same amount in the current year and what is being researched. Also, this index reflects how the nominal and real wages of the population relate to each other. The value of the purchasing power index is the inverse of the index of prices for goods or tariffs.
The purchasing power of the money of a particular state depends on the level of wealth of one person and at the same time is an indicator of the well-being of the entire population of the country. When purchasing power begins to grow sharply, the country experiences a wave of deficit, when demand becomes greater than supply, and people, feeling the opportunity to buy more, begin to actively use it. Therefore, the growth of purchasing power is not an unambiguously positive phenomenon. When there is a deficit, there is a tendency towards equilibrium, to achieve which it is necessary either to increase production volumes or to raise prices. As you can imagine, increasing is much more difficult than just raising prices, so the second option is much more common when there is a shortage.
When the purchasing power of money decreases, this, of course, also does not bring anything good with it, affecting both the economy of a particular country and the economy of the whole world. Unlike the process of increasing purchasing power, decreasing it leads to inflation. And in a particularly "neglected" case, the monetary unit may simply depreciate. Then the consumer will be able to purchase less goods or services for the same amount. The depreciation of some world currencies will create problems for the entire world economy. So, for example, it can happen with the dollar, the world.
Many the developed countries conduct research using inflation statistics and price dynamics. These studies are designed to provide information that is necessary for a prompt response to possible in different countries world crises. Together with the statistics of prices, an indicator of the purchasing power of money is also given.
How is the purchasing power index (formula) calculated?
The following formula is used to calculate the purchasing power index:
Its value shows the relative change in the purchasing power of money held by the population. If, for example, inflation in the consumer sector was 12.5% over the year (prices for consumer goods and services increased by 12.5% on average), this means that the CPI = 1.125, and the IRI = 1 / 1.125 = 0.889.
The result shows that the purchasing power of money has decreased on average by 11.1%, i.e. for the same amount of money, the population will buy goods by 11.1% less than in the base period, or, otherwise, maintaining the same standard of living costs 11.1% more today than yesterday.
Composite indices characterize the change in the aggregate. There may be several aggregates, but the aggregate that changes is put under the index sign, and the index acquires the corresponding name for the aggregate.
Aggregate form is the main form of summary indexes. To calculate aggregate indices, you need to know quantitative characteristics each unit.
Aggregate index is a complex relative indicator that characterizes the average change in a socio-economic phenomenon, consisting of disparate elements.
Numerator and Denominator the aggregate index is the sum of the products of two values, one of which changes (indexed value), and the other remains unchanged in the numerator and denominator of the index (weight).
Indexed value is called the feature, the change of which is being studied.
Index weight Is a value used for the purpose of comparing indexed values.
Aggregate index of the physical volume of production:
In this index, the indexed value will be the quantity of products in physical terms (q), and the weight will be the price (p).
The numerator of the fraction shows the notional value of goods produced in the current period in prices of the base period.
The denominator is the actual value of goods produced in the reference period.
The index shows how many times the cost of a product will increase or decrease due to an increase or decrease in the volume of its production, or how many percent is an increase (decrease) in the cost of a product as a result of a change in the physical volume of its production.
The difference between the numerator and denominator - shows how many rubles the cost of production has changed as a result of an increase or decrease in the volume of its production.
Aggregate price index:
Paasche index
- Laspeyres index
The index shows how many times the cost of production has increased or decreased due to price changes, or how many percent is the increase (decrease) in the cost of production as a result of price changes.
Typically, the values of these two indices do not match. The difference in values is explained by the fact that the indices have different economic content.
Paasche index shows how much goods in the current period have become more expensive or cheaper than in the baseline.
Laspeyres Index a shows how many times the goods of the base period would rise in price or fall in price due to the change in prices for them in the reporting period.
The Paasche index tends to underestimate, while the Laspeyres index tends to overestimate the inflation rate. The Laspeyres index is used to calculate the consumer basket, otherwise called the "cost of living index". Paasche index - an index of retail prices, used to analyze their changes.
When identifying a trend in the study of price dynamics, the Fisher price index is used for smoothing.
To account for changes in the consumer basket over time, the Marshall Price Index is calculated:
The product of the Laspeyres price index and the Pasche volume index is turnover index.
The formula for the relationship of indices or the simplest multiplicative factor model.
Multiplicative models consider the influence of factors in their product.
Thus, the index of the cost of production, or the index of turnover, is the ratio of the value of production of the current period to the value of production in the base period and is determined by the formula:
This index shows how many times the cost of production (turnover) of the reporting period has increased (decreased) compared to the baseline, or how many percent is the increase (decrease) in the cost of production.
If 100% is subtracted from the value of the cost index, then the difference will show how many percent the cost of production has increased (decreased) in the current period compared to the baseline.
The difference between the numerator and denominator shows how many rubles the cost of production has changed in the current period compared to the baseline.
In practice, when studying the influence of factors on the result, it is often necessary to determine not the percentage, but the cost. In this case, the analysis is carried out using additive models or by the method of sum differences. To do this, in the multiplicative model, subtract the denominator from the numerator.
Additive model of turnover.
A change in turnover occurs under the influence of a change in two factors: price and quantity of goods.
– savings or cost overruns that the population will receive due to price changes.
One of the most important indicators of price statistics is the consumer price index. This index is widely used in revisions social programs, serves as the basis for increasing minimum sizes wages and reflects the real purchasing power of money.
Purchasing power index Is the reciprocal of the price index.
Purchasing power- the ability to purchase any goods for one monetary unit... It is calculated through the purchasing power index.
Example. Let the price index = 1.43 or 143%. Consequently, the price has increased by 43%. Determine the change in the purchasing power of the ruble.
The purchasing power index is 1 / 1.43 = 0.6993 or 69.93%.
Consequently, the purchasing power of the ruble decreased by 30.07% (100% - 69.93%).
The way in which average prices are calculated depends on the availability of information. When choosing a formula for calculating the average price, proceed from the logical formula for the average price:
where - average price per unit of goods, rub.,
Q - revenue from the sale of goods, rub.
q - the amount of goods sold in physical terms.
If there is data on prices and quantities of goods sold, the average price is calculated as the arithmetic weighted average:
,
where p is the price of the product.
If there is data on the turnover in monetary terms and on the selling prices of the goods, the harmonic weighted average is used:
In the absence of data on the quantity and value of goods sold and there is only data on price levels for two or more dates, the average price can be calculated in two ways:
Simple arithmetic mean:
,
where p Н, p К are prices at the beginning and end of the period, respectively.
On the average for the moment series of dynamics:
Calculating the average using this formula gives more accurate results and should be preferred.
If neither the number of sales nor the revenue is known, then the average prices are calculated using the number of time periods during which the given price existed. In such cases, when calculating average prices, a simple formula can be used as an arithmetic mean formula, if during this period of time the daily amount of sales was uniform:
,
and the average harmonic weighted, if the daily proceeds from sales were uniform:
,
where n is the number of time periods during which this price existed.
The average price for a group of goods (meat of different sorts, etc.) can be calculated knowing the relative indicators of the sales structure:
,
where
- the share of the sale of each type of product in the total sales.
The average price of a product for the region is also calculated, and the specific weight of the population in the aggregate of regions is used as the weight d.
The price level indicator can be calculated as a relative value expressing purchasing power of money income of the population(the ability to buy any quantity of goods for the value of the average per capita monetary income, average wages, average pensions, etc.). Purchasing power is the value of money expressed in goods, i.e. it shows how many goods can be bought for one currency unit. The calculation can be carried out both for the entire population and for individual groups in the whole country or for individual regions:
,
where PS is purchasing power,
D is the average per capita money income.
When calculating the purchasing power of money, only consumer prices are used. When calculating, they mean:
the type and quality of the goods remain unchanged,
the price structure does not change, the price ratio within the product group remains stable,
goods can be bought without restriction,
price equilibrium prevails (no black market).
Under such conditions, purchasing power depends only on prices and is the reciprocal of the price level.
Consumer price and purchasing power indices for the ruble. Methods for their calculation
The consumer price index (CPI) characterizes the change over time in the general level of prices for goods and services purchased by the population for non-productive consumption. CPI is one of the most important indicators characterizing the standard of living of the population.
CPI applies:
to assess changes in the cost of living and inflation in the country;
to revise government social programs (the basis for raising the minimum wage, indexing living wage, indexing the minimum pension, justifying subsidies and subsidies to prices that do not allow a decrease in the level of consumption by the population of essential goods and services);
in defining public policy in the field of finance, regulation real rate national currency, analysis and forecast of price processes;
for recalculation of indicators of the system of national accounts from current to comparable prices.
To characterize changes in prices for consumer goods and services, a system of indices is used, which can be used to solve various problems. This system is formed by:
consolidated CPI, which characterizes the change in a fixed (basic) full set of goods and services purchased on average per family;
consolidated CPI, which characterizes the change in the cost of a fixed set of goods and services, excluding unwanted goods (alcoholic beverages and tobacco products);
consolidated CPI, showing the change in the cost of a fixed set of goods and services excluding non-essential goods (luxury goods, gold jewelry, cars, as well as especially fashionable goods);
the cost of living index, which characterizes the change in the cost of a fixed set of 25 basic foodstuffs;
the index of the control cost of the necessary social set, which characterizes the change in the cost of a fixed set of basic consumer goods and services traditional for the population of the Russian Federation, the composition and volumes of consumption of which are necessary to ensure human life and preserve his health (37 items);
CPI for certain socio-demographic groups of the population.
The CPI measures the change in the value of a fixed set of goods and services in the current period compared to its value in the previous (reference) period.
The basket of basic consumer goods and services is fixed so that changes in the CPI only cause changes in prices, but not changes in consumption patterns due to changes in income or the purchase of other goods. Therefore, the CPI is also called the cost of living index.
The consumer “basket” for calculating the CPI includes representatively:
goods and services of mass consumer demand,
certain non-essential goods and services (jewelry, furs, cars, maintenance of a car, etc.).
For international comparisons, the CPI is used for the entire range of consumed goods.
The CPI is used to measure inflation, excluding non-essential goods.
The CPI calculation includes the following steps:
sampling of geographical boundaries of observation;
selection of basic trade and service enterprises;
selection of representative goods and representative services;
registration of prices for goods and tariffs for paid services;
formation of the structure of weights for calculating the consumer market price index;
calculation of the consumer price index;
calculation of average prices (tariffs) for goods and services.
Two sources of information are used to calculate the CPI:
a) statistical observation of changes in prices and tariffs in the consumer market;
b) sample surveys of household income, expenditure and consumption (provide data on the structure of actual consumer spending of the population for the previous year).
To determine the weights in the CPI, in addition to the household survey, additional information is also used: data on the structure of retail turnover, on production certain types products, expert assessments.
In 1991, a special state service for monitoring and registering changes in prices and tariffs was created under the State Statistics Committee. Russian Federation... Within the framework of this service, regular non-continuous monitoring of the level and dynamics of consumer prices and the calculation of CPI were organized throughout Russia.
In each region, in addition to the administrative center, the most important from the point of view of socio-economic development and geographical location, regional centers with a sufficiently high degree of saturation of the consumer market are selected.
Regional bodies of state statistics, using the main array method, select basic trade and service enterprises in their region. The scope of supervision includes representative enterprises of all forms of ownership and organizational and legal forms.
Prices are registered for a set of goods (services) that is the same for all regions of the Russian Federation - the representatives most frequently consumed by the population.
The consumer set for calculating the CPI consists of three large groups:
Foodstuffs,
Non-grocery goods,
paid services rendered to the population.
Each group is represented by goods (services) or small product subgroups.
This consumer mix is formed at the federal level and remains unchanged for a long time (usually at least a year).
In each specific region, the general description of the product group is detailed by those representative goods that occupy a significant volume in the regional consumer market and will be offered for a long time. The selection of a representative product from the product group it represents is made taking into account the massive demand (the share of this product in the sales volume of the product group) and the regularity of its sale at the base enterprise.
To calculate the CPI, the formula is used Laspeyres price index, but not an aggregate form, but the arithmetic average weighted from individual price indices, calculated according to the indicators of the structure of expenses. The weight is the share of consumer spending of the population for a certain representative product.
The Laspeyres pricing formula is transformed as follows:
,
where Q 0 - the cost of an individual product in the consumer "basket" of the base period;
- the share of household spending on a specific j-th product in the total volume of consumer spending in the base period;
- individual basic price index for the j-th representative product,
,- the average prices of the goods, respectively, of the current and base periods. They are calculated as simple arithmetic averages of the prices recorded at the selected base outlets:
,
where M is the number of outlets.
The index shows how many times (or by what percentage) the consumer spending of the population would change in the current period compared to the previous one, if the level of consumption remained the same when prices changed.
The formula with individual base indices is difficult to use because over long periods of time, the range of goods sold changes, goods are replaced, the structure of commodity flows changes. Therefore, the individual basic price index is calculated as the product of chain individual price indices:
The use of chain price comparisons makes it easier to introduce new products or replace them when the need arises.
When calculating the price index using the Laspeyres formula, three questions need to be addressed:
selection of the base year for constant weights,
determination of the term of use of weight coefficients without revising them,
linking the index calculated after the revision of the weights with the previously existing time series of price indices.
The consolidated CPI is calculated monthly, quarterly, and on an accrual basis for the period from the beginning of the year. The CPI is calculated monthly for the previous month of the current year and for the corresponding month of the previous year, as well as on an accrual basis from the beginning of the year to the corresponding period of the previous year. The calculation of price indices for a quarter, half-year, period from the beginning of the year is carried out by the chain method, i.e. by multiplying monthly consumer price indices.
Statistics show that using the Laspeyres formula tends to inflate real price changes. So, if the prices for some consumer goods increase in relation to the rest of the goods, then consumers reduce the cost of these goods. By replacing more expensive goods with some cheaper ones, consumers can buy a set of goods and services that is adequate to the previous one, but it will cost them less than buying the previous set at new prices.
The consumer price index calculated according to this formula does not take into account qualitative changes either. If the quality of goods and services improves, so should their prices rise. However, it is assumed that the entire increase in the monetary value of the consumer “basket” is entirely caused by inflation, and not by an improvement in the quality characteristics of goods and services. Consequently, the calculation on a fixed set is correct only for a short period of time, if during this time there are no significant quantitative and qualitative changes in the structure of consumer spending. Under these conditions, the CPI will adequately reflect the change in the cost of living.
The consumer price index according to the modified Laspeyres formula is calculated at the regional and federal levels.
The composite price index for Russia is calculated as a weighted average of regional indices, the weight is the share of the population of the corresponding region in the total population:
,
where - consumer price index in the k-th region;
- the share of the number of the k-th region in the total population of Russia.
This methodology for calculating the CPI is common for many countries, which allows for international comparisons. All major industrial countries publish their own consumer price indices on a regular basis.
In Great Britain, this index is called the retail price indices, has been calculated since 1914 and is published monthly by the Central Statistical Office. Weight characteristics change annually based on the results of the survey of the expenses of the “average family”. Two “pensioner” indices are calculated separately, which take into account the weight characteristics of the expenses of single pensioners or families with two pensioners, respectively.
In the United States, the consumer price index has been calculated since 1919. Its main purpose is to reflect the level of inflation in the country and serve as a basis for negotiating wages. Moreover, two versions of the consumer price index are calculated. One is for employees living in urban areas, the other is for those who do not live in urban areas. In addition, indices are calculated that take into account changes in the field of taxation, social insurance and protection.
Money purchasing power index calculated as the inverse of the CPI:
Its value shows the relative change in the purchasing power of money held by the population. If, for example, inflation in the consumer sector was 12.5% over the year (prices for consumer goods and services increased by 12.5% on average), this means that the CPI = 1.125, and
... The result shows that the purchasing power of money has decreased on average by 11.1%, i.e. for the same amount of money, the population will buy goods by 11.1% less than in the base period, or, otherwise, maintaining the same standard of living costs 11.1% more today than yesterday.
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