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Ineconomics,nominalvalue refers to value measured in terms of absolutemoney amounts, whereasreal value is considered and measured against the actualgoods or services for which it can be exchanged at a given time. Real value takes into account inflation and thevalue of an asset in relation to itspurchasing power. In macroeconomics, thereal gross domestic product compensates for inflation so economists can exclude inflation from growth figures, and see how much an economy actually grows. Nominal GDP would include inflation, and thus be higher.

Acommodity bundle is a sample ofgoods, 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. Thenominal 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.

Aprice 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${\displaystyle P_t}$ over time${\displaystyle t}$. Atime series price index is calculated relative to abase orreference date.${\displaystyle P_0}$ is the value of the index at the base date. For example, if the base date is (the end of) 1992,${\displaystyle P_0}$ is the value of the index at (the end of) 1992. The price index is typicallynormalized to start at 100 at the base date, so${\displaystyle P_0}$ is set to 100.

The length of time between each value of${\displaystyle t}$ and the next one, is normally constant regular time interval, such as a calendar year.${\displaystyle P_t}$ is the value of the price index at time${\displaystyle t}$ after the base date.${\displaystyle P_t}$ equals 100 times the value of the commodity bundle at time${\displaystyle t}$, 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, thenP₁ = 101.

Theinflation rate${\displaystyle i_t}$ between time${\displaystyle t-1}$ and time${\displaystyle t}$ is the change in the price index divided by the price index value at time${\displaystyle t-1}$:

${\displaystyle i_t=\frac{P_t-P_{t-1}}{P_{t-1}}}$

${\displaystyle =\frac{P_t}{P_{t-1}}-1}$

expressed as a percentage.

The nominal value of a commodity bundle tends to change over time. In contrast, by definition, thereal 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 inconstant 1992 dollars, with the price level fixed 100 at the base date.

The price index is applied to adjust the nominal value${\displaystyle Q}$ 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 in the base year. The index price divided by its base-year value${\displaystyle P_t/P_0}$ 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 timet relative to the base date is:

${\displaystyle \frac{P_0\cdot Q_t}{P_t}}$

The real growth rate${\displaystyle r_t}$ is the change in a nominal quantity${\displaystyle Q_t}$ in real terms since the previous date${\displaystyle t-1}$. It measures by how much the buying power of the quantity has changed over a single period.

${\displaystyle r_t=\frac{P_0\cdot Q_t}{P_t}/\frac{P_0\cdot Q_{t-1}}{P_{t-1}}-1}$

${\displaystyle =\frac{P_{t-1}\cdot Q_t}{P_t\cdot Q_{t-1}}-1}$

${\displaystyle =\frac{Q_t}{Q_{t-1}}(\frac{P_t}{P_{t-1}}{)}^{-1}-1}$

${\displaystyle =\frac{1+g_t}{1+i_t}-1}$

where${\displaystyle g_t}$ is the nominal growth rate of${\displaystyle Q_t}$, and${\displaystyle i_t}$ is the inflation rate.

${\displaystyle 1+r_t=\frac{1+g_t}{1+i_t}}$

For values of${\displaystyle i_t}$ between −1 and 1 (i.e. ±100 percent), we have theTaylor series

${\displaystyle (1+i_t{)}^{-1}=1-i_t+i_t^2-i_t^3+...}$

so

${\displaystyle 1+r_t=(1+g_t)(1-i_t+i_t^2-i_t^3+...)}$

${\displaystyle =1+g_t-i_t-g_t{i}_t+i_t^2+\text{higher order terms.}}$

Hence as a first-order (i.e. linear) approximation,

${\displaystyle r_t=g_t-i_t}$

The bundle of goods used to measure theConsumer Price Index (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 (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 theGDP price index. In the U.S. National Income and Product Accounts, nominal GDP is calledGDP in current dollars (that is, in prices current for each designated year), and real GDP is calledGDP in [base-year] dollars (that is, in dollars that canpurchase the same quantity of commodities as in the base year).

As was shown in the section above on the real growth rate,

${\displaystyle 1+r_t=\frac{1+g_t}{1+i_t}}$

where

${\displaystyle r_t}$ is the rate of increase of a quantity in real terms,

${\displaystyle g_t}$ is the rate of increase of the same quantity in nominal terms, and

${\displaystyle i_t}$ is the rate of inflation,

and as a first-order approximation,

${\displaystyle r_t=g_t-i_t.}$

In the case where the growing quantity is afinancial asset,${\displaystyle g_t}$ is anominal interest rate and${\displaystyle r_t}$ is the correspondingreal interest rate; the first-order approximation${\displaystyle r_t=g_t-i_t}$ is known as theFisher equation.^[1] Looking back into the past, theex 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.

Not onlytime-series data, as above, but alsocross-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.

• Diewert, W. E. (2008) [1987]. "Index Numbers".The New Palgrave Dictionary of Economics (2nd ed.). pp. 1–32.doi:10.1057/978-1-349-95121-5_940-2.ISBN 978-1-349-95121-5.
• O'Donnell, R. (1987). "Real and Nominal Quantities".The New Palgrave: A Dictionary of Economics. Vol. v. 4. pp. 97–98. (Adam Smith's early distinction vindicated)
• Sen, Amartya (1979). "The Welfare Basis of Real Income Comparisons: A Survey".Journal of Economic Literature.17 (1):1–45.JSTOR 2723639.
• Usher, D. (1987). "Real Income".The New Palgrave: A Dictionary of Economics. Vol. v. 4. pp. 104–05.

• DataBasics: Deflating Nominal Values to Real Values fromFederal Reserve Bank of Dallas
• CPI Inflation Calculator from U.S.Bureau of Labor Statistics

• Inflation
• Valuation (finance)

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