Balance Mechanics 3.1: More on income

We had previously defined income and consumption as the transactions that change a unit’s net worth, i.e.:

y-c=\Delta nw \

Now I want to explain in more detail what income is because income can be different things that have to be kept apart. Also what income is is often not sufficiently well explained in normal textbooks.

First we should define income. Income is defined as a unit’s consumption plus its change in net worth:

y=c+\Delta nw \

Further, changes in net worth can be separated into changes in tangible assets (\Delta ta \) and changes in net financial assets (\Delta nfa=\Delta ofa -\Delta l \ ) so that:

y=c+\Delta ta +\Delta nfa \

The change in tangible assets is also called investment (\Delta ta \equiv=i \ ); and you can change your net financial assets (as we had defined in the previous post) by having an expenditure surplus or deficit (r-e=\Delta nfa \). Putting all that together we can write income thus:

y=c+i + r-e \

Using this definition we can distinguish between three kinds of income: production as income, revenues as income and capital gains as income.

Production as income

The things that you produce and then either consume or invest are also your income. For instance, if you have a garden where you grow potatoes, the potato is your production and as such your income. When you eat the potato, you consume your product and your income is equal to your consumption:

y=c \

When you do not eat the potato but just keep it, you increase your stock of tangible assets — because you can plant the potato and have more potatoes later on:

y=i\

You can also produce services: if you cook your dinner yourself (having found and not planted the potato) this service is also your income and your consumption. While this kind of service is not counted in the national accounts (whereas going out for dinner is), it still is income and consumption. There is no reason one should not count it in the national accounts because other strange but comparable things are.

Take the implicit rent of people who own their house and do not rent it. The housing service which in value is equivalent to the rent you would pay the landlady to live in the house is counted in the national accounts. Otherwise economies with a high rate of home owners would have a much lower GDP than economies where most people rent.

As far as investment as income is concerned, in the real world this is mostly important for companies. Companies which build their own machines and other tangible assets increase their income (which is their profit) one-by-one with their investment — if no expenditures are associated with the investment.

Income as revenue

For most of us, the main source of our income are our revenues, mostly from wages, but for some also from interest and dividends (capital income). Companies receive revenues from their sales (but this is not yet companies‘ income).

There are three things that you can do with those revenues: you can use them for consumption, investment or to increase your net financial assets if you do not spend as much as you receive in revenues.

If you receive some revenues (for instance wages) and consume part of its, the consumption occurs on two places in the income equation:

y=c+r_{wage}-e_{consumption} \

Consumption occurs both as c as a positive entry and as an expenditure e_{consumption} as a negative entry. This is different from the consumption goods that you produce and consume yourself and which directly increase your income. Here, consumption does not change your income because you buy your consumption good somewhere. Your income is thus equal to your wage. If we did not add the term c, income would be equal to the expenditure surplus only and not the full amount of your wage income. To the extent that you buy all your consumpion goods, c - e_{consumption} is always zero. When you also produce some of your consumption goods, consumption will be higher than consumption expenditures. This is why it is important to keep consumption and consumption expenditures apart.

The same principle applies if you buy tangible assets with your income:

y=i+r_{wage}-e_{investment} \

As long as you buy your tangible assets (houses, machines etc.) your expenditures are as high as your investment and your income is again equal to your wages as it should be.

Lastly, whatever you buy, you change your net financial assets by the amount of your revenue supluses / deficits so that:

y=c+i+r-e=c+i+\Delta nfa \

Income as capital gains

The third kind of income is if your net worth changes due to capital gains. Capital gains change the value of your assets. We can write:

y=\Delta nw=\Delta gfa_{capgains}+ \Delta ta_{capgains}-\Delta l \

Since we had defined income as consumption plus the change in capital gains, capital gains are also income. Normally liabilities do not change in value so that capital gains only apply to changes in the value of assets.

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