# Real versus nominal value (economics)

In economics,

**nominal**value is measured in terms of money, whereas

**real**value is measured against goods or services. A real value is one which has been adjusted for inflation, enabling comparison of quantities as if the prices of goods had not changed on average. Changes in value

**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**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, in aggregate remains the same. 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 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 year, a price index

*P*represents the price of the commodity bundle over time

_{t}*t*. In base year zero,

*P*

_{0}is set to 100. If for example the base year is 1992, real values are expressed in constant 1992 dollars, with the price level defined as 100 for 1992. If, for example, the price of the commodity bundle has increased in the first year by 1%, then

*P*rises from

_{t}*P*

_{0}= 100 to

*P*

_{1}= 101.

The inflation rate between year

*t*- 1 and year

*t*is:

## Real value

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, 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:

## Real growth rate

The real growth rate is the change from one period to the next of a nominal quantity in real terms. It measures by how much the buying power of the quantity has changed.where:

and:

For values of between −1 and 1, we have the Taylor series

so

Hence as a first-order approximation,

## Real wages and real gross domestic product

The bundle of goods used to measure the Consumer Price Index is applicable to consumers. So for wage earners as consumers, an appropriate way to measure real wages is to divide the nominal wage by the growth factor in the CPI.Gross domestic product 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 In the U.S. National Income and Product Accounts, nominal GDP is called

*GDP in current dollars*, and real GDP is called

*GDP in dollars*.

## Example

## Real interest rates

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

and as a first-order approximation,

In the case where the growing quantity is a financial asset, is a nominal interest rate and is the corresponding real interest rate; the first-order approximation 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.