Income (2)

Making sure income is measured consistently

We’ve seen what income is for the simple case of an employee who’s paid money for their work. What about for other people?

Imagine three similar scenarios involving Alice, a farmer. In the first, Alice harvests 100 apples, and keeps them for herself:

In the second, Alice harvests 100 apples (transaction 1), then sells them to Bob for £10 (transaction 2). But she decides she wants them for herself after all, and buys them back, also for £10 (transaction 3):

The third is the same as the second except that Alice sells them to Bob for £20. Then she decides she wants them for herself after all, and buys them back, also for £20:

If we think of income as being an amount of money which someone is paid, it looks like Alice’s income is either nothing, £10 or £20 in the three difference scenarios. But the outcome is exactly the same in all 3 cases! There’s surely something very wrong if our definition of income can give different results for exactly the same outcome — what useful information would that give us? So we need to do better. But is it possible to define income so that the same outcome gives us the same measure of income?

Actually it’s pretty easy using the ideas of the One Lesson:

Raw net worth, like plain net worth, is just assets minus liabilities, where:

• assets are what you own plus what you’re owed

• liabilities are what you owe

The difference compared to plain net worth is that assets and liabilities aren’t converted to a quantity of money first. So if someone owns a house, and is owed a car (e.g. they’ve paid for it, but it hasn’t been delivered yet), and owes an apple to their neighbour, then their raw net worth, like in the One Lesson image above, is:

Their house + the car - an apple.

If you’ve come across vector arithmetic in maths, that’s what we’re dealing with here.

RNW and “raw” income

Let’s stop thinking of someone’s income as being how much money comes in, and instead look at how much RNW “comes in” — that is, how much their RNW increases. As I was writing this, it occurred to me that we could call this their “Raw Income”¹.

Going back to the 3 scenarios above with farmer Alice, let’s see what her raw income is in each case.

Alice keeps her output

As always, to see how Alice’s RNW changes, add the arrows pointing towards her (and subtract any pointing away from her). In this case, the production arrow pointing towards her shows that her RNW increases by 100 apples.

So her raw income is 100 apples.

Bob isn’t involved in any economic actions, so his raw income is 0.

Alice sells and buys back her output for £10

There are 3 transactions here. The first is identical to scenario 1. Alice’s raw income at this point is 100 apples. Bob’s raw income is 0.

In the second transaction, Alice sells the 100 apples to Bob for £10. What’s Alice’s income over the whole scenario so far? Well she’s gained 100 apples, then lost 100 apples, but gained £10. Gaining and losing 100 apples cancel each other out, leaving her with a gain of £10, so that’s her raw income at this stage.

Notice that transferring the apples to Bob (the purple arrow of transaction 2) is negative raw income for Alice. It wouldn’t make sense only to count the increases, because then it would appear that Alice’s raw income at this stage was £10 plus 100 apples. That wouldn’t recognise that, compared to where she started, she only has £10 extra.

What about Bob? He’s lost £10, but gained 100 apples. So his raw income after transaction 2 is 100 apples - £10.

In the 3rd transaction, Alice buys the 100 apples back from Bob for £10. So her raw income over the whole scenario is:

And Bob’s raw income over the whole scenario is:

So in scenario 2, despite the two transactions involving buying and selling, both Alice’s and Bob’s raw incomes are exactly the same as for the first scenario. We’re getting the same result for the same outcome, which is exactly what we want from a meaningful definition of raw income.

Alice sells and buys back her output for £20

Compared to the second scenario, the only difference here is that £20 changes hands temporarily instead of £10. The ultimate change to everyone’s RNW is exactly the same as for both the first two scenarios. Alice’s raw income is 100 apples, and Bob’s raw income is 0.

So it looks like “raw income” is easy to calculate, and gives us a consistent result when the outcome is the same. We’re almost finished, but there’s one more thing to consider: consumption.

Consumption and Income

If Alice eats one of the apples, she now owns one less apple, and nobody else has one more apple. This is a consumption action, and her RNW decreases by 1 apple.

When she sold the apples to Bob, the action of transferring the apples to him decreased her RNW by 100 apples and was also negative raw income (- 100 apples). Alice had transferred some of her income to Bob (in exchange for Bob transferring £10 of his income to Alice). Is the decrease in Alice’s RNW when she eats an apple also negative raw income (- 1 apple)?

The answer is no. We’ll look at this further in the next article, but for now, I’ll just say that the idea of income is about increasing someone’s ability to consume. Consumption is making use of income, not undoing it or transferring it to someone else.

Summary

Last week, we looked at the income for an employee, who is paid money for their work. In that simple case, we could say that their income is the amount of money they are paid for their work, and that works fine. But for people whose income isn’t only in the form of money, this isn’t really good enough: it can give inconsistent results for the same outcome, so it’s not well-defined.

Instead we can talk about someone’s raw income: the change in their RNW as a result of their economic activity (apart from some types of consumption, as we’ll see next time). That gives us a meaningful way to measure how much someone’s ability to consume has increased.

1. None of these scenarios includes any consumption. Next time, we’ll see that when there is consumption, raw income isn’t quite the same as the change in RNW.