In

_{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 $t-1$:
$i\_t\; =\; \backslash frac$
:$=\; \backslash frac\; -\; 1$
expressed as a percentage.

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 the same quantity of commodities as in the base year).

DataBasics: Deflating Nominal Values to Real Values

from

CPI Inflation Calculator

from U.S.

economics
Economics () is the social science that studies the production, distribution, and consumption of goods and services.
Economics focuses on the behaviour and interactions of economic agents and how economies work. Microeconomics analyz ...

, nominal value 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. 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 ofgoods
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 t ...

, 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. Ex ...

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''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 ofpurchasing 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:
:$\backslash frac$
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. :$r\_t\; =\; \backslash frac\; /\; \backslash frac\; -\; 1$ ::$=\; \backslash frac\; -\; 1$ ::$=\; \backslash frac\; /\; \backslash frac\; -\; 1$ ::$=\; \backslash frac\; -\; 1$ where $g\_t$ is the nominal growth rate of $Q\_t$, and $i\_t$ is the inflation rate. :$1\; +\; r\_t\; =\; \backslash frac$ For values of $i\_t$ between −1 and 1 (i.e. ±100 percent), we have theTaylor 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 seri ...

:$(1\; +\; i\_t)^\; =\; 1\; -\; i\_t\; +\; i\_t^2\; -\; i\_t^3\; +\; ...$
so
:$1\; +\; r\_t\; =\; (1\; +\; g\_t)(1\; -\; i\_t\; +\; i\_t^2\; -\; i\_t^3\; +\; ...)$
:::$=\; 1\; +\; g\_t\; -\; i\_t\; -\; g\_t\; i\_t\; +\; i\_t^2\; +\; \backslash text$
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 theConsumer 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 statisti ...

(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 monetary 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 subjective nature this measure is of ...

(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 are constructed from bundles of commodities and their respective prices. In the case of GDP, a suitable price index is thGDP 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 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, :$1\; +\; r\_t\; =\; \backslash frac$ 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 afinancial 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 a ...

, $g\_t$ is a nominal interest rate 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.
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 onlytime-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 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
* Constant Item Purchasing Power Accounting
*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 pri ...

*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
* Index (economics)
*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 hedge
*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 disti ...

*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 i ...

* Numéraire
*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
* 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 1 ...

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)