# Real versus nominal value (economics)

(Redirected from Nominal dollars)
Further information: Real versus nominal value

In economics, a nominal value is an economic value expressed in historical nominal monetary terms. By contrast, a real value is a value that has been adjusted from a nominal value to remove the effects of general price level changes over time and is thus measured in terms of the general price level in some reference year (the base year). For example, changes in the nominal value of some commodity bundle over time can happen because of a change in the quantities in the bundle or their associated prices, whereas changes in real values reflect only changes in quantities. The process of converting from nominal to real terms is known as inflation adjustment.

Real values are a measure of purchasing power net of any price changes over time. For example, nominal income is often restated as real income, thus removing that part of income changes that merely reflect inflation (a general increase in prices). Similarly, for aggregate measures of output, such as gross domestic product (GDP), the nominal amount reflects production quantities and prices in that time period, whereas the differences between real amounts in different time periods reflect only changes in quantities. A series of real values over time, such as for real GDP, measures quantities over time expressed in prices of one year, called the base year (or more generally the base period). Real values in different years then express values of the bundles as if prices had been constant for all the years, with any differences due to differences in underlying quantities.

The nominal/real value distinction can apply not only to time-series data, as above, but also to cross-section data varying by region. For example, the total sales value of a particular good produced in a particular region of a country is influenced by both the physical amount sold and the selling price, which may be different from that of the country as a whole; for purposes of comparing the economic activity of different regions, the nominal output of the good in that region can be adjusted into real terms by repricing the goods at national-average prices.

## Calculation

The nominal value of a commodity bundle in a given year depends on both quantities and then-current prices, namely, as a sum of prices times quantities for the different commodities in the bundle. In turn nominal values are related to real values by the following arithmetic definition:

nominal value / real value = (P x Q) / Q = P.

Here P is a price index, and Q is a quantity index of real value. In the equation, P is constructed to equal 1.00 in the base year. Alternatively, P can be constructed to equal 100 in the base year:

(nominal value / real value) x 100 = P.

The base year can be any year, and comparisons of quantities are valid provided all values are adjusted to their values in the same base year. After a number of years have passed in which government statistics have been reported in terms of a particular base year, a new base year for comparisons is typically adopted; for the next several years all new data as well as all pre-existing data will be reported in terms of the new base year.

## Illustrations

The simple case of a bundle of commodities (goods) is one that has only one commodity. In that case, output or consumption may be measured either in terms of money value (nominal) or physical quantity (real). Let i designate that commodity and let:

Pi = the unit price of i, say, \$5
Qi = the quantity of good i, say, 10 units.

The nominal value of the good would then be price times quantity:

nominal value of good i = Pi x Qi = \$5 x 10 = \$50.

Given only the nominal value and price, derivation of a real value is immediate:

real value of good i = (Pi x Qi)/Pi = Qi = 50/5 = 10.

The price "deflates" (divides) the nominal value to derive a real value, the quantity itself.

Similar for a series of years, say five, given only nominal values of the good and prices in each year t, a real value can be derived for each of the five years:

real value in year t = (nominal value in year t) / (price relative to base year) = Qit.

The following example generalizes from an individual good to a bundle of goods across different years for which P, a price index comparing the general price level across years, is available. Consider a nominal value (say of an hourly wage rate) in each different year t. To derive a real-value series from a series of nominal values in different years, one divides the nominal wage rate in each year by Pt, the price index in that year. By definition then:

real value in year t = (nominal value in year t) / Pt.
 Numerical example: If for years 1 and 2 (say 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 so constructed in each different year indexes the amount of commodities in that year that could be purchased, for comparison to other years. Thus, in the example the price level increased by 33 percent, but the real wage rate still increased by 20 percent, permitting a 20 percent increase in the quantity of commodities the nominal wage could purchase.

The above generalization to a commodity bundle from the previous sing-good illustration has practical use, because price indexes and the National Income and Product Accounts are constructed from such bundles of commodities and their respective prices.

A sum of nominal values for each of the different commodities in the bundle is also called a nominal value. A bundle of n different commodities with corresponding prices and quantities for each year t defines:

nominal value of that bundle in year t = P1t x Q1t + . . . + Pnt x Qnt.

From the above:

Pt = the value of a price index in year t.

The nominal value of the bundle over a series of years and corresponding Pt define:

real value of the bundle in year t = Qt = (nominal value of the bundle in year t) / Pt.

Alternatively, multiplying both sides by Pt:

nominal value of the bundle in year t = Pt x Qt.

So, every nominal value can be dichotomized into a price-level part and a real part. The real part Qt is an index of the quantities in the bundle.

## Price indices

Real values (such as real wages or real gross domestic product) can be derived by dividing the relevant nominal value (e.g., nominal wage rate or nominal GDP) by the appropriate price index. For consumers, a relevant bundle of goods is that used to compute the Consumer Price Index (CPI). So, for wage earners as consumers a relevant real wage is the nominal wage (after-tax) divided by the CPI. A relevant divisor of nominal GDP is the GDP price index.

Real values represent the purchasing power of nominal values in a given period, such as wages or total production. In particular, price indexes are typically calculated relative to some base year. If for example the base year is 1992, real values are expressed in constant 1992 dollars, referenced as 1992=100, since the published index is usually normalized to have the price index equal 100 in the base year. To use the price index as a divisor for converting a nominal value into a real value, as in the previous section, the published index is first divided by the base-year price-index value of 100. 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). In effect the price index of 100 for the base year is a numéraire for price-index values in other years.

The terminology of classical economics used by Adam Smith used a unit of labour as the purchasing power unit, so monetary quantities were defined by the cost of an hours of labour required to produce or purchase a given quantity.

## Interest rates

Main article: Fisher equation

Since interest rates are measured as percentages rather than in terms of units of some currency, real interest rates are measured as the difference between nominal interest rates and the rate of inflation. The expected real interest rate as of the starting time of a loan is the nominal interest rate minus the inflation rate expected over the term of the loan. The realized (ex post) real interest rate is computed by subtracting the actual inflation rate that ends up prevailing during the life of the loan from the nominal interest rate, and reflects what actually happened during the life of the loan.

The relationship above is approximate only. The actual relationship is as follows:[1]

(1+IRN)=(1+IRR)x(1+I),

where:

IRN is the nominal interest rate,
IRR is the real interest rate, and
I is the inflation rate.