Real versus nominal value

From Wikipedia, the free encyclopedia

In economics, the nominal value of a bundle of goods is its money-value for the relevant year (or period). For a series of years, different nominal values in the series do not distinguish whether the differences are from changes in quantities comprising the bundles or from changes in prices of the goods. The real value of the bundle does make that distinction. The real value is a number that indexes the size of the bundle in each year. The real values so stated are as if prices had remained constant in the different years. Any changes in real values of the bundles in different years are then attributed to changes in quantities.

Contents 1 Illustration and generalization 2 Uses and examples of nominal and real values 3 Real and nominal interest rates 4 See also

[edit] Illustration and generalization

Consider the simplest case of a bundle the has only one commodity, i. Let:

P_i = the unit price of i, say, $5

Q_i = the quantity of i, say, 10 units.

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

nominal value of i = P_i x Q_i = $5 x 10 = $50.

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

real value of bundle i = P_i x Q_i/P_i = Q_i = 50/5 = 10.

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

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

real value of bundle i in year t = nominal value of Q_i^t/P_i^t = Q_i^t

This example generalizes for nominal values relative to real values across different years for which P, a price index comparing the general price level across years, is available. Consider a nominal value (say of the hourly wage rate) in each different year t. To derive a real-value series from a series of nominal values in different years, divide nominal value in each year by the price index P^t in that year:

real value in year t = nominal value in year t/P^t.

Numerical example: If for years 1 and 2 (say 20 years apart) the nominal wage and P are respectively $10 and $16 1.00 and 1.333, real wages are respectively: $10 (= 10/1.00) and $12 (= 16/1.333). The real wage so constructed in each different year indexes the amount of goods in that year that could be purchased relative 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 goods the nominal wage could purchase.

The generalizaation of a commodity bundle from the illustration above is to a set of quantities of different commodities. A sum of nominal values for each of the different commodities is also called a nominal value. For a set of n different commodities, the nominal value of that bundle is the sum of the respective nominal values:

P₁ x Q₁ + . . . + P_n x Q_n

[edit] Uses and examples of nominal and real values

Nominal values -- such as nominal wages or nominal gross domestic product -- refer to amounts that are paid or earned in money terms.

Real value, such as real wages, or real gross domestic product, are derived by dividing the relevant monetary value by the price of a relevant good, or a price index of a bundle of goods (in this case, the bundle may change over time). Real values represent the purchasing power of wages, interest, or total production. That is, they calculate the quantity of the given good or bundle of goods a given nominal wage, or nominal domestic income will buy.

In the simple case of a single good, output or consumption may be measured either in terms of monetary value (nominal) or actual physical quantity (real).

In most cases, price indexes are calculated relative to some base year. If, for example, the base year is 1992, real values may be expressed in constant 1992) dollars)

The price index or infation measure that is used to normalize the purchasing power unit can vary.

For wage earners, the relevant bundle of goods is that used to compute the Consumer Price Index in some given base year for which the CPI is set to 1. So, the real wage is the nominal wage divided by the CPI.

For measures of national product, such as Gross Domestic Product the relevant bundle of goods is that which makes up national product, and the price of this bundle is measured by the GDP Deflator.

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

There are other measures of inflation used in other situations.

Nominal values are the default in most real life situations. Taxes are applied to nominal income, mortgages are written with nominal interest rates, wage agreements are written with nominal rate increases. These nominal rates are likely to have an inflation presumption built in, and only time will tell if the presumption was correct.

[edit] Real and nominal interest rates

• Real interest rates are measured as the difference between nominal interest rates and the rate of inflation
  • The expected real interest rate is the nominal interest rate minus the inflation rate expected over the term of the loan.
  • The realized (ex post) real interest rate has the actual inflation rate subtracted from the nominal interest rate.

[edit] See also

• Inflation
• Deflation
• Real interest rate