Society & Culture & Entertainment Education

The Production-Expenditure-Income Identity

Understanding Macroeconomic Theory

Understanding much of basic macroeconomic theory tacking the notion that, at an aggregate level in an economy, production, expenditure, and income are quantitatively equivalent in an economy.  Notationally speaking, the variable Y could refer to any one of these three concepts (in real rather than nominal terms) depending on context, so things get very confusing very quickly if you don't understand this equivalence!

To see why this equivalence holds, let's start with the macroeconomic measure of production.

GDP as the Measure of Domestic Production

An economy's gross domestic product is defined as the market value of all final goods and services produced within an economy's borders within a period of time.  Real GDP, represented by Y, refers to the value of an economy's output in real, i.e. constant dollar, terms, in order to take inflation out of the measure of output.  (Nominal GDP, which is production measured in current dollar terms, is generally represented by P x Y, where P is a measure of the average or overall price level in an economy.)  

This measure of real GDP, Y, must also equal the amount of aggregate expenditure in an economy simply because aggregate expenditure is defined as the amount that the world spends on the economy's goods and services.  This becomes more clear once we recall the expenditure categories of GDP:

Y = C + I + G + (X - IM)

where C represents expenditure on household consumption, I represents investment in domestic capital, G represents government purchases (as opposed to transfer payments), X represents exports, and IM represents imports.

 As members of households, we know that we can consume both things that were produced domestically and that were produced in other countries (i.e. imported).  Since we're trying to measure expenditure on domestic goods and services only, we want to subtract out the imports part of consumption, which this equation does.  We also want to add in foreign purchases of domestically-produced goods and services, which is why exports are added in the equation.  Similarly, if the government buys something that is not produced domestically, it is counted as an import and netted out to zero in the equation.

You may have noticed that the equivalence of production and expenditure requires that everything that an economy produces is actually sold within the same period as it is produced.  This doesn't always happen, of course- firms often accumulate or divest inventory- but the assumption that is made for accounting purposes is that the inventory that is not sold in the market is "bought" by the firm itself as inventory investment.

 Under this convention, it does in fact have to be the case that the market value of domestic production and worldwide expenditure on domestically produced goods and services must be equal.

This value of Y, or real GDP, must also equal the aggregate income of everyone in that economy (before taxes and such, of course).   This is simply a result of the fact that every transaction has a buyer and a seller, and, under the preceding assumption about firms buying unsold inventory as investment, all output results in a transaction.

This intuition is illustrated best by an example.  consider a very small economy with just one producer that sells one television per year.

 If that television has a market value of $500, then the market value of aggregate production, i.e. GDP, is $500.  In addition, the producer got paid $500 for the TV by definition, so income is equal to $500 as well.  In more complex economies, producers aren't a single entity, but it is still the case that the market value of the domestically produced output gets distributed to parties in the economy either as labor income or as profit, which is just income on capital.

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