How We Account for Price Changes (Inflation)

When working with GDP data, one must be certain to determine whether the figures are constant dollar or current dollar figures, or as they appear in the textbooks, real or nominal GDP. GDP can be thought of as a weighted sum of all goods and services produced in the economy, where the weights are prices. By using prices as a common denominator, we need not keep a lengthy record of how many goods and services including toasters and apples and cars were produced. We simply need to find the value of all these goods and add them together to arrive at a dollar denominated measure of output. A simple example has been constructed to clarify the distinction between the various output measures and prices.

Real vs. Nominal GDP

Given that GDP is defined as the value of currently produced goods and services, changes in GDP can result from changes in prices and/or changes in outputs.  Positive growth in GDP due to increases in output is generally recognized as a Good, while increases in GDP due to price increases is generally recognized as a Bad. To distinguish between the two effects, the government generates two measures of GDP, Constant $ GDP and Current $ GDP.

To better understand the differences, the following example has been constructed.  There are two goods being produced (X and Y) on two dates (1987 and 1997). Step one involves choice of a base year for the calculations, a decision made by the Commerce Department. The current base year is 1987, which has been used in the current example. The calculation of GDP for the base year is quite straightforward. GDP in the base year is $90, $60 worth of good X and $30 worth of good Y. In 1997, the value of GDP is $170.

A Simple Example

NOMINAL GDP (1987) Px₈₇*X₈₇ + Py₈₇*Y₈₇ = 6*10 + 2*15 = 90

NOMINAL GDP (1997) Px₉₇*X₉₇ + Py₉₇*Y₉₇ = 6*15+ 4*20=170

But how much of the change was accounted for by the price changes, and how much by output changes? To separate out the two effects, a third, hypothetical calculation must be made. This calculation is the value of the goods and services produced in 1997 assuming the prices had not changed since 1987. The result is a value of GDP in 1997, expressed in 1987 $s, which equals $130.

REAL GDP (1997) Px₈₇*X₉₇ + Py₈₇*Y₉₇ = 6*15 + 2*20 =130

By comparing this $130 with the $90 figure for 1987, we conclude that the level of output increased 44 percent between 1987 and 1997.

Given our measures of real GDP (R) and nominal GDP (N), the specification of the relationship between them gives us a measure of the price level - the GDP price deflator (P). The relationship between real GDP, nominal GDP, and the price deflator (P) is given by the following equation.

R = N/P

It is useful if you think of this as one equation with three unknowns - with the value of two unknowns one could solve for the other unknown. The three forms of the equation are:

(1) N = R*P

(2) P = N/R

(3) R = N/P

In this simple example we have the following values:

(1)' Nominal GDP in 1997 N(97) = R97*P97 = 130*1.31 = 170

(2)' Price Level in 1997 P(97) = N97/R97 = 170/130 = 1.31*

(3)' Real GDP in 1997 R(97) = N97/P97 = 170/1.31 = 130

With the value of the price deflator we could calculate the inflation rate as the annual percentage change in the deflator. In this example what we can say is that in the base year (1987) the deflator equaled 1 so that between 1987 and 1997 the price level has increased 31 percent.