Real and nominal value
In economics, nominal 'value refers to value measured in terms of absolute money amounts, whereas real value' is considered and measured against the actual goods or services for which it can be exchanged at a given time. Real value takes into account inflation and the value of an asset in relation to its purchasing power. In macroeconomics, the real 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.
Commodity bundles, price indices and inflation
A commodity bundle is a sample of goods, 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. 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. The nominal 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.A price 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 over time. A time series price index is calculated relative to a base or reference date. is the value of the index at the base date. For example, if the base date is 1992, is the value of the index at 1992. The price index is typically normalized to start at 100 at the base date, so is set to 100.
The length of time between each value of and the next one, is normally constant regular time interval, such as a calendar year. is the value of the price index at time after the base date. equals 100 times the value of the commodity bundle at time, 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, then P1 = 101.
The inflation rate between time and time is the change in the price index divided by the price index value at time :
expressed as a percentage.
Real value
The nominal value of a commodity bundle tends to change over time. In contrast, by definition, the real 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 in constant 1992 dollars, with the price level fixed 100 at the base date.The price index is applied to adjust the nominal value 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 at time t relative to the base date is:
Real growth rate
The real growth rate is the change in a nominal quantity in real terms since the previous date. It measures by how much the buying power of the quantity has changed over a single period.where is the nominal growth rate of, and is the inflation rate.
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 products
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 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 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.