Declining marginal utility of income and the utilitarian argument for income redistribution
Update: A number of the arguments I have made in this post are highly problematic (I always publish too hastily). However, I still consider the basic point to be correct and will hopefully publish a follow-up soon.
What do economists mean when they are talking about the phenomenon of declining marginal utility of income? It’s pretty simple, really. If you earn £10k a year, an extra £1,000 is worth a lot more to you than if you earn £100k a year. Another way of putting it is: the world is better off ‘happiness-wise’ (ceteris paribus) if the extra £1,000 goes to the less well-off. I used to believe that this generates a simple argument from utilitarian premises for widespread income redistribution.
But a few months ago, I had a thought that actually this isn’t so obviously the case. Declining marginal utility of income has an interesting corollary, namely that those who work jobs that require long hours should be paid more per hour in order to maintain the same level of happiness. I have made this point to a number of people in discussion and I don’t feel I have made myself clear, so I thought I would have a stab in written form.
Imagine a prime specimen of homo economicus whom I shall gender-neutrally term ‘Alex’. Now, let us first suppose that for Alex, the marginal utility of income is constant. Alex is deciding whether to take a job for £20k that requires 40 hours per week, or £30k that requires 60 hours per week. Alex would be indifferent to these two options, for if we understand the decision on how much he/she wishes to work as a trade-off between income and leisure, then as he/she is being equally compensated for his foregone leisure in each case, Alex would be neither better nor worse off with either job.
However, we know that marginal utility of income is not constant. The first 20k is more important, and of the first 20k the first few thousand is even more important as this is what will feed and clothe our imaginary prospective employee. The things we buy with our extra income as we get richer are less important than the things we would buy first. That’s the declining marginal utility of income. There is also a second effect, which is the declining marginal utility of leisure. In this example, the marginal hours Alex works (say he/she works 9-9 rather than 9-5) are more valuable than the marginal hours worked by the 9-5 employee. This is because if you get out of work at 5, you still have time in the day to do things like have hobbies and go and see friends. Getting out at 4 rather than 5 doesn’t make much of a difference to your ability to have extensive hobbies outside of work or to your social life, but the difference between getting out at 8 and 9 makes a very large difference – not only in terms of the time you have, but in how much energy you have to spend that time fruitfully. Therefore, in order to be compensated for all that Alex loses by working longer hours, Alex gets paid more for that time. In fact, declining marginal utility is everywhere. Working is (at least in one way) like cheesecake: the next slice is never as good as the previous one, and there would come a point where I would actually pay to not have an extra slice.
So, we have Alex working a 60 hour a week job for (say) £40k p.a., and suppose we have Casey working a 40 hour a week job for (say) £20k p.a. It is entirely plausible that, in terms of their actual welfare, Alex and Casey are equally well off. Alex may be able to buy box seats at the theatre, but Casey has the time to do amateur theatre. So if we were considering what justice would require in terms of redistribution of the income of Alex and Casey towards someone else, ‘Morgan’ who cannot earn income due to disability or illness, it
would be may well be inegalitarian to require Alex to give more a higher proportion of income to Morgan than Casey. People who choose to work longer hours should not automatically be considered better off just because they have more income, and when you combine the two effects of working more and being compensated more highly for those marginal hours due to the declining marginal utility of income the amount of extra income required to equalize their well being could be considerable.
Let me make one thing perfectly clear: for income in excess of that required to compensate workers with long hours I think the redistribution argument holds – but with the ceteris paribus assumption. And there are lots of things that matter (from a utilitarian perspective) that would need to be taken into account such as the effect of high marginal taxes on work incentives. If you don’t think that work incentives matter, think about this: an economy is fundamentally about exchange – trades made between two or more parties for their mutual benefit. If I buy a sandwich at M&S for £3, what is basically happening is that I would rather have the sandwich than the £3, and M&S would rather have the £3 than the sandwich. Everyone is better off. Now, the people who run M&S are much richer than I am. But I want them to make the sandwich and trade with me rather than not. It is too easy to think of those who earn more as being parasitic on society’s resources – but a crucial part of society’s resources is labour itself, people taking resources and turning them into something more useful, desirable and, indeed, valuable.
The economist Tyler Cowen recently wrote an excellent essay in The American Interest entitled ‘The Inequality That Matters’, in which he makes the following point:
“The funny thing is this: For years, many cultural critics in and of the United States have been telling us that Americans should behave more like threshold earners. We should be less harried, more interested in nurturing friendships, and more interested in the non-commercial sphere of life. That may well be good advice. Many studies suggest that above a certain level more money brings only marginal increments of happiness. What isn’t so widely advertised is that those same critics have basically been telling us, without realizing it, that we should be acting in such a manner as to increase measured income inequality. Not only is high inequality an inevitable concomitant of human diversity, but growing income inequality may be, too, if lots of us take the kind of advice that will make us happier.”
If it is the case that much of what is really valuable is that which cannot be priced and exchanged in a market, then this makes a considerable difference to optimal public policy from the perspective of an egalitarian – let alone a utilitarian.
Update: if you are of an egalitarian mindset, and have not read Elizabeth Anderson’s fantastic ‘What is the Point of Equality?’ paper, please do. You are missing out on both a superb critique and impassioned defence
Update 2: That Alex and Casey should be taxed in direct proportion to their income does not at all follow, as has been pointed out to me. Strictly speaking what should happen from an egalitarian perspective is that each should be taxed in such a way that their welfare loss is equal. It is a completely open question as to what this would actually look like, because it depends on the exact way in which the marginal utility of income varies with income. If I was attempting to argue against progressive taxation/redistribution this would be a problem, but I’m not. I’m just attempting to show that arguing for progressive taxation/redistribution merely on the basis of declining marginal utility of income doesn’t do the necessary work. I have therefore adjusted the strength of my claim accordingly.
 File under ‘totally fucking obvious to everyone who isn’t an economist’
 Again, only an economist would call everything that isn’t gainful employment ‘leisure’, but I’ll stick to the convention here
 I’m going to start running out of gender-neutral names soon…
 Still going strong
 My original point was incorrect, as the declining marginal utility of income means that any given £1 taken from Alex is worth less to Alex than £1 from Casey is worth to Casey. However, if you take £1 from Alex and not from Casey, then Casey is better off than Alex since I assumed they are equally well off. The tax should therefore be proportionate, and proportion of income is as good a proxy as any for how to keep their welfare constant, even if it isn’t perfect
 There is also a third substantial effect, which is cost of living and relative rates of inflation. I would point the reader in the direction of two excellent essays from a couple of American conservative writers whom I enjoy reading (it’s not an extensive list) – the first is from Reihan Salam at the NRO, on variations in income and cost of living across the US, and the second is from Will Wilkinson, a.k.a. the sole redeeming feature of the CATO institute. Also very much worth reading is Steve Waldman’s response to Wilkinson, which can be found here. I link, you decide.