Real versus nominal value (economics)

Economics
A supply and demand diagram, illustrating the effects of an increase in demand.
Index Outline Category
History Types Classification
History of economics Economic history (academic study) Schools of economics Microeconomics Macroeconomics Methodology Heterodox economics JEL classification codes
Concepts Theory Techniques
Econometrics Economic growth Economic system Experimental economics Mathematical economics Game theory Post-scarcity Market National accounting
By application
Agricultural Behavioral Business Computational Cultural Demographic Development Digitization Ecological Education Environmental Evolutionary Expeditionary Geography Health Industrial organization Information International Knowledge Labour Law Managerial Monetary / Financial Natural resource Organizational Personnel Public / Welfare economics Regional Rural Service Urban Welfare
Lists
Economists Publications (journals)
Business and economics portal

In economics, a real value of a good or other entity has been adjusted for inflation, enabling comparison of quantities as if prices had not changed. Changes in real terms therefore exclude the effect of inflation. In contrast with a real value, a nominal value has not been adjusted for inflation, and so changes in nominal value reflect at least in part the effect of inflation.

Prices and inflation

A representative collection of goods, or commodity bundle, is used for comparison purposes, to measure inflation. The nominal (unadjusted) value of the commodity bundle in a given year depends on prices current at the time, whereas the real value of the commodity bundle, if it is truly representative, remains the same. The real value 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 over time.

A price index is calculated relative to a base year. Indices are typically normalized at 100 in the base year. Starting from a base (or reference) year, a price index P_t represents the price of the commodity bundle over time t. In base year zero, P₀ is set to 100. If for example the base year is 1992, real values are expressed in constant 1992 dollars, based at 100 for 1992. Also imagine for example, that the price of the commodity bundle has increased in the first year by 1%, then P_t rises from P₀ = 100 to P₁ = 101.

The inflation rate $i_{t}$ between year t - 1 and year t is:

change in price / price in year t - 1

={\frac {P_{t}-P_{t-1}}{P_{t-1}}}

={\frac {P_{t}}{P_{t-1}}}-1

Real value

Comparison of real and nominal gas prices 1996 to 2016, illustrating the formula for conversion. Here the base year is 2016.

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 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 in year t relative to the base year 0 is:

{\frac {P_{0}\cdot Q_{t}}{P_{t}}}

Real growth rate

The real growth rate $r_{t}$ is the change from one period to the next of a nominal quantity $Q_t$ in real terms. It measures by how much the buying power of the quantity has changed.

r_{t}={\frac {P_{0}\cdot Q_{t}}{P_{t}}}/{\frac {P_{0}\cdot Q_{t-1}}{P_{t-1}}}-1

={\frac {P_{t-1}\cdot Q_{t}}{P_{t}\cdot Q_{t-1}}}-1

={\frac {Q_{t}}{Q_{t-1}}}/{\frac {P_{t}}{P_{t-1}}}-1

={\frac {1+g_{t}}{1+i_{t}}}-1

where:

g_{t}

is the nominal growth rate of

Q_t

and:

i_{t}

is the inflation rate.

1+r_{t}={\frac {1+g_{t}}{1+i_{t}}}

For values of $i_{t}$ between -1 and 1, we have the Taylor series

(1+i_{t})^{-1}=1-i_{t}+i_{t}^{2}-i_{t}^{3}+...

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{higher order terms.}}

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

r_{t}=g_{t}-i_{t}

Real wages and real gross domestic product

The bundle of goods used to measure the Consumer Price Index (CPI) is applicable to consumers. So for wage earners as consumers, an appropriate way to measure real 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 which 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 the 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 [base-year] dollars (that is, in dollars that can purchase the same quantity of commodities as in the base year).

Example

If for years 1 and 2 (possibly a span of 20 years apart), the nominal wage and price level P of goods are respectively

nominal wage rate: $10 in year 1 and $16 in year 2

price level: 1.00 in year 1 and 1.333 in year 2,

then real wages using year 1 as the base year are respectively:

$10 (= $10/1.00) in year 1 and $12 (= $16/1.333) in year 2.

The real wage each year measures the buying power of the hourly wage in common terms. In this example, the real wage rate increased by 20 percent, meaning that an hour's wage would buy 20% more goods in year 2 compared with year 1.

Real interest rates

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

1+r_{t}={\frac {1+g_{t}}{1+i_{t}}}

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, $g_{t}$ is a nominal interest rate and $r_{t}$ is the corresponding real interest rate; the first-order approximation $r_{t}=g_{t}-i_{t}$ is known as the Fisher equation.^[1]

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 data, as above, but also cross-section 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.

Notes

↑ Benninga, Simon; Oded Sarig (1997). Corporate Finance: A Valuation Approach. The McGraw-Hill Companies. p. 21. ISBN 0-07-005099-6.

References

W.E. Diewert, "index numbers," ([1987] 2008)The New Palgrave Dictionary of Economics, 2nd ed. Abstract.
R. O'Donnell (1987). "real and nominal quantities," The New Palgrave: A Dictionary of Economics, v. 4, pp. 97–98 (Adam Smith's early distinction vindicated)
Amartya Sen (1979). "The Welfare Basis of Real Income Comparisons: A Survey," Journal of Economic Literature, 17(1), p p. 1-45.
D. Usher (1987). "real income," The New Palgrave: A Dictionary of Economics, v. 4, pp. 104–05

External links

Economics
Economic theory Econometrics Applied economics
Macroeconomics	Adaptive expectations Aggregate demand Balance of payments Business cycle Capacity utilization Capital flight Central bank Consumer confidence Currency Demand shock Depression (Great Depression) DSGE Economic growth Economic indicator Economic rent Effective demand General Theory of Keynes Hyperinflation Inflation Interest Interest rate Investment IS–LM model Microfoundations Monetary policy Money NAIRU National accounts PPP Rate of profit Rational expectations Recession Saving Shrinkflation Stagflation Supply shock Unemployment Macroeconomics publications
Microeconomics	Aggregation problem Budget set Consumer choice Convexity Cost–benefit analysis Deadweight loss Distribution Duopoly Economic equilibrium Economic shortage Economic surplus Economies of scale Economies of scope Elasticity Expected utility hypothesis Externality General equilibrium theory Indifference curve Intertemporal choice Marginal cost Market failure Market structure Monopoly Monopsony Non-convexity Oligopoly Opportunity cost Preference Production set Profit Public good Returns to scale Risk aversion Scarcity Social choice theory Sunk costs Supply and demand Theory of the firm Trade Transaction cost Value Uncertainty Utility Microeconomics publications
Applied fields	Agricultural Business Demographic Development Economic history Education Environmental Financial Health Industrial organization International Knowledge Labour Law and economics Monetary Natural resource Public Service Urban Welfare
Methodology	Behavioral economics Computational economics Econometrics Economic systems Experimental economics Mathematical economics Methodological publications
Economic thought	Ancient economic thought Austrian school of economics Chicago school of economics Classical economics Feminist economics Heterodox economics Institutional economics Keynesian economics Mainstream economics Marxian economics Neoclassical economics Post-Keynesian economics Schools overview
Notable economists and thinkers within economics	Kenneth Arrow Gary Becker Francis Ysidro Edgeworth Milton Friedman Ragnar Frisch Friedrich Hayek Harold Hotelling John Maynard Keynes Tjalling Koopmans Paul Krugman Robert Lucas Jr. Jacob Marschak Alfred Marshall Karl Marx John von Neumann Vilfredo Pareto David Ricardo Paul Samuelson Joseph Schumpeter Amartya Sen Herbert A. Simon Adam Smith Robert Solow Léon Walras more
International organizations	Asia-Pacific Economic Cooperation Economic Cooperation Organization European Free Trade Association International Monetary Fund Organisation for Economic Co-operation and Development World Bank World Trade Organization
Category Index Lists Outline Publications Business and economics portal

This article is issued from Wikipedia. The text is licensed under Creative Commons - Attribution - Sharealike. Additional terms may apply for the media files.