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In
economics Economics () is the social science that studies the Production (economics), production, distribution (economics), distribution, and Consumption (economics), consumption of goods and services. Economics focuses on the behaviour and intera ...
, nominal
value Value or values may refer to: Ethics and social * Value (ethics) wherein said concept may be construed as treating actions themselves as abstract objects, associating value to them ** Values (Western philosophy) expands the notion of value beyo ...
is measured in terms of
money Money is any item or verifiable record that is generally accepted as payment for goods and services and repayment of debts, such as taxes, in a particular country or socio-economic context. The primary functions which distinguish money are as ...
, whereas real value is measured against
goods or services Goods are items that are usually (but not always) tangible, such as pens, physical books, salt, apples, and hats. Services are activities provided by other people, who include architects, suppliers, contractors, technologists, teachers, docto ...
. A real value is one which has been adjusted for
inflation In economics, inflation is an increase in the general price level of goods and services in an economy. When the general price level rises, each unit of currency buys fewer goods and services; consequently, inflation corresponds to a reductio ...
, enabling comparison of quantities as if the prices of goods had not changed on average; therefore, changes in real value exclude the effect of inflation. In contrast, a nominal value has not been adjusted for inflation, and so changes in nominal value reflect at least in part the effect of inflation but will not hold the same
purchasing power Purchasing power is the amount of goods and services that can be purchased with a unit of currency. For example, if one had taken one unit of currency to a store in the 1950s, it would have been possible to buy a greater number of items than would ...
.


Commodity bundles, price indices and inflation

A commodity bundle is a sample of
goods In economics, goods are items that satisfy human wants and provide utility, for example, to a consumer making a purchase of a satisfying product. A common distinction is made between goods which are transferable, and services, which are not tran ...
, which is used to represent the sum total of goods across the economy to which the goods belong, for the purpose of comparison across different times (or locations). At a single point of time, a commodity bundle consists of a list of goods, and each good in the list has a market price and a quantity. The market value of the good is the market price times the quantity at that point of time. The nominal value of the commodity bundle at a point of time is the total market value of the commodity bundle, depending on the market price, and the quantity, of each good in the commodity bundle which are current at the time. A price index is the relative price of a commodity bundle. A price index can be measured over time, or at different locations or markets. If it is measured over time, it is a series of values P_t over time t. A
time series In mathematics, a time series is a series of data points indexed (or listed or graphed) in time order. Most commonly, a time series is a sequence taken at successive equally spaced points in time. Thus it is a sequence of discrete-time data. Exa ...
price index is calculated relative to a base or reference date. P_0 is the value of the index at the base date. For example, if the base date is (the end of) 1992, P_0 is the value of the index at (the end of) 1992. The price index is typically normalized to start at 100 at the base date, so P_0 is set to 100. The length of time between each value of t and the next one, is normally constant regular time interval, such as a calendar year. P_t is the value of the price index at time t after the base date. P_t equals 100 times the value of the commodity bundle at time t, divided by the value of the commodity bundle at the base date. If the price of the commodity bundle has increased by one percent over the first period after the base date, then ''P''1 = 101. The inflation rate i_t between time t-1 and time t is the change in the price index divided by the price index value at time t-1: i_t = \frac := \frac - 1 expressed as a percentage.


Real value

The nominal value of a commodity bundle tends to change over time. In contrast, by definition, the real value of the commodity bundle in aggregate remains the same over time. The real values of individual goods or commodities may rise or fall against each other, in relative terms, but a representative commodity bundle as a whole retains its real value as a constant from one period to the next. Real values can for example be expressed in constant 1992 dollars, with the price level fixed 100 at the base date. The price index is applied to adjust the nominal value Q of a quantity, such as wages or total production, to obtain its real value. The real value is the value expressed in terms of
purchasing power Purchasing power is the amount of goods and services that can be purchased with a unit of currency. For example, if one had taken one unit of currency to a store in the 1950s, it would have been possible to buy a greater number of items than would ...
in the base year. The index price divided by its base-year value P_t / P_0 gives the growth factor of the price index. Real values can be found by dividing the nominal value by the growth factor of a price index. Using the price index growth factor as a divisor for converting a nominal value into a real value, the real value at time ''t'' relative to the base date is: :\frac


Real growth rate

The real growth rate r_t is the change in a nominal quantity Q_t in real terms since the previous date t-1. It measures by how much the buying power of the quantity has changed over a single period. :r_t = \frac / \frac - 1 ::= \frac - 1 ::= \frac / \frac - 1 ::= \frac - 1 where g_t is the nominal growth rate of Q_t, and i_t is the inflation rate. :1 + r_t = \frac For values of i_t between −1 and 1 (i.e. ±100 percent), we have the
Taylor series In mathematics, the Taylor series or Taylor expansion of a function is an infinite sum of terms that are expressed in terms of the function's derivatives at a single point. For most common functions, the function and the sum of its Taylor serie ...
:(1 + i_t)^ = 1 - i_t + i_t^2 - i_t^3 + ... so :1 + r_t = (1 + g_t)(1 - i_t + i_t^2 - i_t^3 + ...) :::= 1 + g_t - i_t - g_t i_t + i_t^2 + \text Hence as a first-order (''i.e.'' linear) approximation, :r_t = g_t - i_t


Real wages and real gross domestic products

The bundle of goods used to measure the
Consumer Price Index A consumer price index (CPI) is a price index, the price of a weighted average market basket of consumer goods and services purchased by households. Changes in measured CPI track changes in prices over time. Overview A CPI is a statistica ...
(CPI) is applicable to consumers. So for wage earners as consumers, an appropriate way to measure real wages (the buying power of wages) is to divide the nominal wage (after-tax) by the growth factor in the CPI.
Gross domestic product Gross domestic product (GDP) is a money, monetary Measurement in economics, measure of the market value of all the final goods and services produced and sold (not resold) in a specific time period by countries. Due to its complex and subjec ...
(GDP) is a measure of aggregate output. Nominal GDP in a particular period reflects prices that were current at the time, whereas real GDP compensates for inflation. Price indices and the U.S.
National Income and Product Accounts The national income and product accounts (NIPA) are part of the national accounts of the United States. They are produced by the Bureau of Economic Analysis of the Department of Commerce. They are one of the main sources of data on general econ ...
are constructed from bundles of commodities and their respective prices. In the case of GDP, a suitable price index is th
GDP price index.
In the U.S. National Income and Product Accounts, nominal GDP is called ''GDP in current dollars'' (that is, in prices current for each designated year), and real GDP is called ''GDP in ase-yeardollars'' (that is, in dollars that can
purchase Purchasing is the process a business or organization uses to acquire goods or services to accomplish its goals. Although there are several organizations that attempt to set standards in the purchasing process, processes can vary greatly between ...
the same quantity of commodities as in the base year).


Example


Real interest rates

As was shown in the section above on the real growth rate, :1 + r_t = \frac where :r_t is the rate of increase of a quantity in real terms, :g_t is the rate of increase of the same quantity in nominal terms, and :i_t is the rate of inflation, and as a first-order approximation, :r_t = g_t - i_t. In the case where the growing quantity is a
financial asset A financial asset is a non-physical asset whose value is derived from a contractual claim, such as bank deposits, bonds, and participations in companies' share capital. Financial assets are usually more liquid than other tangible assets, such as ...
, g_t is a
nominal interest rate In finance and economics, the nominal interest rate or nominal rate of interest is the rate of interest stated on a loan or investment, without any adjustments or fees. Examples of adjustments or fees # An adjustment for inflation(in contrast with ...
and r_t is the corresponding
real interest rate The real interest rate is the rate of interest an investor, saver or lender receives (or expects to receive) after allowing for inflation. It can be described more formally by the Fisher equation, which states that the real interest rate is approx ...
; the first-order approximation r_t = g_t - i_t is known as the
Fisher equation In financial mathematics and economics, the Fisher equation expresses the relationship between nominal interest rates and real interest rates under inflation. Named after Irving Fisher, an American economist, it can be expressed as real interest ...
. Looking back into the past, the ''ex post'' real interest rate is approximately the historical nominal interest rate minus inflation. Looking forward into the future, the expected real interest rate is approximately the nominal interest rate minus the expected inflation rate.


Cross-sectional comparison

Not only
time-series In mathematics, a time series is a series of data points indexed (or listed or graphed) in time order. Most commonly, a time series is a sequence taken at successive equally spaced points in time. Thus it is a sequence of discrete-time data. Exa ...
data, as above, but also
cross-sectional data Cross-sectional data, or a cross section of a study population, in statistics and econometrics, is a type of data collected by observing many subjects (such as individuals, firms, countries, or regions) at the one point or period of time. The analy ...
which depends on prices which may vary geographically for example, can be adjusted in a similar way. For example, the total value of a good produced in a region of a country depends on both the amount and the price. To compare the output of different regions, the nominal output in a region can be adjusted by repricing the goods at common or average prices.


See also

*
Aggregation problem An ''aggregate'' in economics is a summary measure. It replaces a vector that is composed of many real numbers by a single real number, or a scalar. Consequently there occur various problems that are inherent in the formulations that use aggregate ...
*
Classical dichotomy In macroeconomics, the classical dichotomy is the idea, attributed to classical and pre-Keynesian economics, that real and nominal variables can be analyzed separately. To be precise, an economy exhibits the classical dichotomy if real variables s ...
*
Constant Item Purchasing Power Accounting Constant purchasing power accounting (CPPA) is an accounting model that is an alternative to model historical cost accounting under high inflation and hyper-inflationary environments. It has been approved for use by the International Accounting St ...
*
Cost-of-living index A cost-of-living index is a theoretical price index that measures relative cost of living over time or regions. It is an index that measures differences in the price of goods and services, and allows for substitutions with other items as pric ...
*
Deflation In economics, deflation is a decrease in the general price level of goods and services. Deflation occurs when the inflation rate falls below 0% (a negative inflation rate). Inflation reduces the value of currency over time, but sudden deflation ...
*
Financial repression Financial repression comprises "policies that result in savers earning returns below the rate of inflation" to allow banks to "provide cheap loans to companies and governments, reducing the burden of repayments." It can be particularly effective a ...
*
Fisher equation In financial mathematics and economics, the Fisher equation expresses the relationship between nominal interest rates and real interest rates under inflation. Named after Irving Fisher, an American economist, it can be expressed as real interest ...
*
Index (economics) In Statistics, Economics and Finance, an index is a statistical measure of change in a representative group of individual data points. These data may be derived from any number of sources, including company performance, prices, productivity, and ...
*
Inflation In economics, inflation is an increase in the general price level of goods and services in an economy. When the general price level rises, each unit of currency buys fewer goods and services; consequently, inflation corresponds to a reductio ...
*
Inflation accounting Inflation accounting comprises a range of accounting models designed to correct problems arising from historical cost accounting in the presence of high inflation and hyperinflation. For example, in countries experiencing hyperinflation the Intern ...
*
Inflation hedge An inflation hedge is an investment intended to protect the investor against (hedge) a decrease in the purchasing power of money (inflation). There is no investment known to be a successful hedge in all inflationary environments, just as there is no ...
*
Interest In finance and economics, interest is payment from a borrower or deposit-taking financial institution to a lender or depositor of an amount above repayment of the principal sum (that is, the amount borrowed), at a particular rate. It is distinct ...
*
Money illusion In economics, money illusion, or price illusion, is a cognitive bias where money is thought of in nominal, rather than real terms. In other words, the face value (nominal value) of money is mistaken for its purchasing power (real value) at a previ ...
*
National accounts National accounts or national account systems (NAS) are the implementation of complete and consistent accounting techniques for measuring the economic activity of a nation. These include detailed underlying measures that rely on double-entry ...
*
Neutrality of money Neutral or neutrality may refer to: Mathematics and natural science Biology * Neutral organisms, in ecology, those that obey the unified neutral theory of biodiversity Chemistry and physics * Neutralization (chemistry), a chemical reaction in ...
*
Numéraire The numéraire (or numeraire) is a basic standard by which value is computed. In mathematical economics it is a tradable economic entity in terms of whose price the relative prices of all other tradables are expressed. In a monetary economy, acting ...
*
Real interest rate The real interest rate is the rate of interest an investor, saver or lender receives (or expects to receive) after allowing for inflation. It can be described more formally by the Fisher equation, which states that the real interest rate is approx ...
*
Real prices and ideal prices The distinction between real prices and ideal prices is a distinction between ''actual prices paid'' for products, services, assets and labour (the net amount of money that actually changes hands), and ''computed'' prices which are not actually cha ...
* Template:Inflation – for price conversions in Wikipedia articles


Notes


References

* * (
Adam Smith Adam Smith (baptized 1723 – 17 July 1790) was a Scottish economist and philosopher who was a pioneer in the thinking of political economy and key figure during the Scottish Enlightenment. Seen by some as "The Father of Economics"——— ...
's early distinction vindicated) * *


External links


DataBasics: Deflating Nominal Values to Real Values
from
Federal Reserve Bank of Dallas The Federal Reserve Bank of Dallas covers the Eleventh Federal Reserve District, which includes Texas, northern Louisiana and southern New Mexico, a district sometimes referred to as the Oil Patch. The Federal Reserve Bank of Dallas is one of 12 ...

CPI Inflation Calculator
from U.S.
Bureau of Labor Statistics The Bureau of Labor Statistics (BLS) is a unit of the United States Department of Labor. It is the principal fact-finding agency for the U.S. government in the broad field of labor economics and statistics and serves as a principal agency of t ...
{{economics Inflation Valuation (finance)