Short & Simple 7 – A Fundamental National Accounting Identity

A prominent flow measure for the economy as a whole is Gross Domestic Product (GDP). This is a measure of the total output produced within the domestic economy over a year.

In the National Accounts, total output is evaluated at market prices. Conceptually, it is as if the quantity of each good or service produced is multiplied by its price, with the products then summed to give a figure for total output or ‘nominal GDP’.

The figure for nominal GDP can be adjusted for changes in the average price level to arrive at a measure of ‘real GDP’. This measure is intended to give us a sense of how the physical output of goods and services compares with other periods.

Although real GDP is intended to shed light on the level of physical production, clearly it is a monetary measure just like nominal GDP. It is just that real GDP is a monetary measure that has been corrected for price changes.

The reason real output (or real GDP) is measured in monetary terms is that there is no good way to add up physical quantities of different goods and services to arrive at a single number. For example, imagine an economy that produces just three goods with the following physical output:

Physical Output = 50 computers + 75 motor vehicles + 40,000 apples

We cannot add up these quantities to arrive at a single measure of physical output. The goods have different units of measurement. They are incommensurable.

But if we know prices, we can express the output of each good in monetary terms. All output will then be measured in a common monetary unit and can be added together. Suppose the prices are $1,000 for a computer, $10,000 for a car and $1 for an apple. Given these prices, nominal output can be calculated as:

Nominal Output = $1,000 x 50 + $10,000 x 75 + $1 x 40,000 = $840,000

This is our measure of nominal GDP.

Perhaps it is known that prices on average rose by 5 percent over the year. The figure for nominal GDP can then be converted into real GDP by deflating the nominal figure by 5 percent. This is done by dividing the nominal figure by 1+p, where p is the rate of increase in prices over the period. Accordingly:

Real GDP = $840,000 / (1 + 0.05) = $800,000

If we denote real output by Q and the average price level by P, then nominal output is PQ.

There is a very important connection – in fact, an identity – between total output and two other major macroeconomic flows, namely total income and total spending.

First, total output Q is identically equal to total income Y. The reason for this is that output priced in monetary terms generates income of an equal monetary amount.

It is easy to see why this must be true in the case of output that is sold. The amount paid for the output goes as income to the sellers.

The identity is not so obvious in the case of unsold output. It holds because in the National Accounts this unsold output is treated, for accounting purposes, as if it has been purchased by the firms that produced it. This accounting treatment ensures that total output equals total income, even though some output is unsold.

Second, we know from part 4 that total spending equals total income. Put simply, all spending goes to somebody as income.

Putting these observations together enables us to arrive at an important accounting identity:

GDP = Total Output = Total Income = Total Spending

Since total output Q and total income Y are the same when measured in monetary terms, both are often denoted simply by Y.

This identity is at the heart of National Accounting. In particular, it informs various methods of measuring GDP. One of these methods will be the focus of part 8.

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