The Income-Expenditure Identity

Last week I showed how economists calculate the value of everything produced in a national economy (Gross Domestic Product) by adding together the price of all goods and services purchased by household consumers, the public sector and other countries, adding the expenditure on investment, and subtracting the value of imports.  This gives us the value of expenditure on goods and service produced in a specific country for a particular year.  This is summarised in the equation:


The next thing to understand is that the expenditure on what is produced by that country must be equal to the income derived from production in that country.  Textbooks will usually state this as something obvious, without any explanation, but it is worth exploring why this is the case so that we understand the underlying dynamics properly.

It might seem obvious that expenditure by one person is income for someone else:  you buy something, and the business receives the payment.  However, the total amount received by a business in payments is revenue, not profit.  By definition, total expenditure must equal total revenue, because every penny spent is revenue for someone else.  But does all this revenue become profit or wages?  A business might have high revenues, but actually be making a loss (”revenue is vanity, profit is sanity”).

All revenue received by a business will be spent on its own costs or become profits (we can ignore business taxes for now as these are paid on profits).  Profits are income for the business and its shareholders.  Costs are either wages or expenditure on the products and services of other firms, and wages are income for workers.  So payments to other firms are the only part of one firm’s revenue that will not ultimately become income for the firm, its owners or its workers.  But these payments to other firms are revenue for those firms, so this calculation flows from firm to firm through the economy.  It’s not difficult to demonstrate that, in the end, total national expenditure, and therefore total national revenue, will equal total national income, but it would take too long to include in this post!  If you’re wondering about it, sit down and work it out yourself (that’s what I did).

But what about if goods purchased were manufactured last year?  Suppose, for example, a firm starts a year with an inventory of goods waiting to be sold, and in that year adds to its revenue by selling these goods off but not replacing them (so that its inventory goes down).  It finishes the year with much higher revenue than costs, because it has sold off and not replaced inventory produced in the previous year.  In our GDP calculation we want to know the value of what was produced this year, not what was sold.  But remember that an increase in inventory is counted as investment expenditure, and therefore a decrease in inventory is negative investment.  So the purchase by consumers of goods produced last year in the “C” element of our GDP calcuation will be offset by reduction in inventory in the “I” element.  The change in inventory reflected in “I” means that our GDP calculation is only capturing expenditure on goods produced in the year in question.

But what about income in this case, won’t the increased revenue lead to an increased income for the firm?  When an accountant prepares the profit and loss account for that firm for that year, they make an adjustment for the change in inventory so that these sales do not add to the in-year profits.  More specifically, they will record the reduction in inventory as a cost for the firm in that year (as if it was buying the inventory off itself).  This will be balanced by a negative entry in the capital account, showing the reduction in inventory as a reduction in the assets of the firm.

I hope that’s not too hard to follow – I’m trying to explain this as briefly as possible.  I might cover the accounting of profit and inventory in more detail in a few weeks, but what you can see here is the importance of how we account for changes in inventory, both in national income accounts and in the profit and loss accounts of a firm.

And this also highlights a broader point to note about this field of economic theory.  The equation for GDP and the income-expenditure identity are not hypotheses that have been tested empirically.  They are results that are true because of the definitions of the terms involved.  To understand what these equations are telling us we need to be crystal clear on what the definitions of these terms are, and be observant of how well they match up to the corresponding elements in the real world.  This insight is going to be vitally important over the next few weeks, so here are a couple of examples of how it applies here

First of all, there is a really important point about this identity that I’ve rarely seen in textbook or on-line explanations.  The “income” we’re talking about here that equals “expenditure” is the income generated by production in the country, not the total income earned by that country.  This is the “domestic product” bit in GDP – the value of domestic production.  We are saying that the income generated by production in a country will equal the expenditure on that production.  Some of these domestic businesses will be owned or part-owned by foreign individuals or companies, and hence when they distribute their profits these are distributed outside of the country in question.  Similarly, income will flow into that country from domestic ownership of foreign businesses. UK GDP is not the income of the UK, it is the income generated by production in the UK.  To calculate the income made by the UK we would need to adjust for profits of UK production flowing overseas, and income earned by foreign production owned by UK individuals and companies.  This calculation is known as National Income rather than Domestic Product, a fact that is obscured when we state that expenditure equals income if we are not clear on the definition of our terms.  This may be a small, technical point, but if not understood it can lead to erroneous thinking, and it highlights the importance of understanding the precise definition of the terms we are using.

Similarly, think more deeply about the importance of inventories, highlighted earlier.  The value of a firm is in part based on assumptions made about the value of its inventory.  But in rapidly changing markets, values of inventory can fall suddenly. The value of the music store HMV is reflected in part in the value of the stock of its CDs.  With the increasing rise in digital music, how confident are HMV accountants in the value of its current inventory?  There are many examples like this – right now anyone dealing in diesel cars is gambling that government tolerance for diesel pollution is not going to rapidly decrease, leading to punitive regulation and taxes.  In all these cases, if the value of the inventory falls, GDP falls, without the country physically producing anything less.  In the examples cited, the investors in these businesses did not accurately predict the fall in value of their products, and they simply have to watch the value of their inventory, and hence their business, fall before their very eyes.  This has knock-on effects to national income, because a share of the resources of the nation were invested in those businesses.  The impact of such errors in assessing the value of an investment will become critically important in about 5 weeks!

So finally, let’s return to our GDP equation and add in national income, which is denoted as “Y” (remembering that this is income generated by production, not total income of the country in question).  As a result of this identity we can now say:

GDP = C + I + G + (X-M) = Y

This is another building block that we need to understand – by definition, total expenditure will always equal total revenue, which will always equal total income – as I say, it seems so obvious that textbooks gloss over it, but this result and its implications will be vital over the coming weeks.  Next week we will get to the result that the entire blog has been leading up to.

2 Replies to “The Income-Expenditure Identity”

    1. I thought this was the straightforward stuff! I’m rushing through the introductory macro because I don’t just want to regurgitate textbooks. But we need to understand this basic theory, so that we can then understand its implications in reality (implications that the textbooks completely misunderstand).

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