Economics in Two Lessons: Income Distribution

Here’s another excerpt from my book-in-progress, Economics in Two Lessons. Rather than work sequentially, I’m jumping between:

Lesson 1: Market prices reflect and determine opportunity costs faced by consumers and producers.


Lesson 2: Market prices don’t reflect all the opportunity costs we face as a society.

In the section over the fold, I’m looking at how opportunity cost reasoning applies to policies that change the distribution of income, wealth and other entitlements.

As usual, praise is welcome, useful criticism even more so. You can find a draft of the opening sections here.

Changes in the regulation of labor and capital markets and in taxation and expenditure policy since the 1970s have greatly enhanced the income and wealth of the best-off members of society (the so-called 1 per cent), and have yielded more modest, but still substantial, improvements in the position of those in the top 20 per cent of the income distribution (broadly speaking, professionals and business owners and managers).

On the other hand, incomes for the rest of the community have grown much more slowly than might have been expected based on the experience of the decades from 1945 to 1975. The substantial technological advances of recent decades have had little impact on the (inflation-adjusted) income of the median US household. For many below the median, incomes have actually fallen (real wages, welfare reform).

In the absence of the tax cuts of the 1980s, the associated cuts in public expenditure and financial and industrial relations policies that benefitted business, the incomes of the wealthy would not have increased as much as they have done. Those on median and lower incomes would have done substantially better[^1]. But how should we compare those gains and losses?

Economists and philosophers have been looking at this question for a long time and in many different ways. The answers most consistent with opportunity cost reasoning can be described by the following ‘thought’ experiment, developed explicitly by John Harsanyi and John Rawls in the mid-20th century, but implicit in the reasoning of earlier writers like Jeremy Bentham, John Stuart Mill and Friedrich von Wieser.

First consider yourself in the position of both the high income beneficiary and the low income loser from such a change. Next, imagine that you are setting rules for a society, of which you will be a member, without knowing which of these positions you might be in. One way to think of this is to imagine life as a lottery in which your life chances are determined by the ticket you draw.

Now consider a choice between increasing the income of the better off and the worse off person. Presumably, if the dollar increase were the same in both cases, you would prefer to receive it in the case where you are poor rather than in the case when you are rich.

The reasons for this preference are obvious enough. For a very poor person, an additional hundred dollars could mean the difference between eating and not eating. For someone slightly better off, it may mean the difference between paying the rent and being evicted. For a middle class family, it might allow an unexpected luxury purchase. For someone on a million dollars a year, it would barely be noticed.

Economists typically present this point in terms of the concept of marginal utility, a technical term for the benefits that are gained from additional income or consumption. As argued above, the marginal utility of additional income decreases as income rises. It follows that a policy that increases the income of the rich and decreases that of the poor by an equal amount will reduce the utility of the poor more than it increases the utility of the rich.

Few mainstream economists would reject this analysis outright[^2] . However, many prefer to duck the issue, relying on a distinction between ‘positive’ economics, concerned with factual predictions of the outcomes of particular economic policies and ‘normative’ economics, concerned with ‘value judgements’ like the one discussed above. The debate over the justifiability or otherwise of this distinction has been going on for decades and is unlikely to be resolved any time soon.

More importantly, constructs derived from economics are often used, implicitly or explicitly, in ways that imply that an additional dollar of income should be regarded as equally valuable, no matter to whom it accrues.

The most important of these constructs is GDP, the aggregate value of all production in the economy.GDP per person is the ordinary average (or arithmetic mean) income of the community. GDP per person treats additive changes in income equally no matter who receives them.

Used correctly, as a measure of economic activity, GDP can be a useful guide to the short-term management of the economy. In the short run, weak GDP growth is commonly an indicator of a recession, suggesting the need for expansionary monetary and fiscal policies.

Unfortunately, measures of GDP and GDP per person are commonly misused, as an indicator of living standards and economic welfare more generally. There are many reasons why this is inappropriate, but the failure to take account of the distribution of income is most important.
It is easy enough to see that, if the opportunity cost of a given increase the income of a better-off person is an equal increase in the income of a worse-off person, then the change is for the worse.

What about the case when we the choice is between a given increase for the worse off person and a larger increase for the better off person? How big does the opportunity cost have to be before it outweighs the benefit? This question, raising once again the thought experiment mentioned above, can be answered in many different ways

One answer, which seems close to the views typically elicited when people are asked questions of this kind, is to treat equal proportional increases in income as being equally desirable. That is, an increase of $1000 in the income of a person on $10 000 a year is seen as yielding a benefit comparable to that of an increase of $10 000 in the income of a person earning $100 000 a year. Conversely, if the opportunity cost of the $10 000 benefit to the high income earner is a loss to the low income earner of more than $1000, the cost exceeds the benefit.

It’s surprisingly easy to turn this way of looking things into a measure of living standards over time. If, instead, we want a measure that treats proportional changes equally, all that is needed is to replace arithmetic mean measures such as GDP per person with the geometric mean we all learned about in high school (and most of us promptly forgot).

The geometric mean has the property that, if all incomes increase by the same proportion, so does the geometric mean. So, it’s a better measure of the growth rate of incomes across the community than the usual arithmetic mean. It can also be justified mathematically, in terms of the theory of expected utility. For those interested, the details are spelt out in an optional section.

The geometric mean is equal to the arithmetic mean when incomes are distributed exactly equally. But the more unequal is the income distribution, the greater the gap between the arithmetic and geometric means. For this reason, the ratio of the arithmetic to the geometric mean is often used as a measure of income inequality.

We can look at the changes in these measures using data from the US Census Office, and some simple computations (details available on request). From 1967 to 2013, arithmetic mean income per household (in 2013 dollars) rose from $66 500 to $104 000, an increase of 56 per cent. But the geometric mean rose by only 34 per cent, from 50 000 to 67,500. The ratio between the two rose from 1.32 to 1.54, indicating a substantial increase in inequality.

The idea that equal proportional increases are equally valuable, and therefore that the geometric mean is a good measure of economic welfare or wellbeing is not the only answer to the question posed above. Another, leading to a strong version of egalitarianism, is always to prefer the increase to the worse off person[^3] . In this case, welfare is measured by the minimum income.

There’s no way of reaching a final resolution on questions like this. But it’s worth observing that a policy aimed at maximising the geometric mean of income would be substantially more egalitarian than anything that has ever been seen in a market economy.

For example, calculations by Peter Diamond and Emmanuel Saez, using a method equivalent to the geometric mean approach, suggest that the top marginal tax rate, after taking account of disincentive effects should be between 70 and 80 per cent.

These rates are far above those found in any country today. And while the top marginal rate was at or above this level in the 1950s, generous exemptions and other loopholes meant that the effective rate was much lower.

It’s not surprising that political outcomes are less egalitarian than an opportunity cost estimate would suggest. The thought experiment leading to the geometric mean gives everyone equal weight, as in an ideal democracy. In practice, however, the well off have more weight in democratic systems than do the poor; and of course the disparity is even greater in undemocratic and partly democratic systems. The disparity of political weight has increased with the growth of inequality over the past decades. So, while there are good arguments for more strongly egalitarian approaches, policies aimed at maximizing geometric mean income will inevitably be found well to the left of centre in any feasible political system.

[1^]: The claim that tax cuts for the rich will ultimately make people better off is discussed briefly in Section … and, at greater length, as one of the ‘zombie ideas’ in my book Zombie Economics
[2^]: The most notable exceptions, somewhat outside the mainstream, are members of the ‘Austrian School’, who have dismissed interpersonal comparisons as ‘unscientific’ and offered a variety of more or less spurious justifications for inequality. As discussed above, von Wieser, the originator of the opportunity cost analysis, was an exception to this exception.
[3^]: The ‘difference principle’ espoused by philosopher John Rawls is often interpreted to imply this view. However, scholars of Rawls work disagree on this, and much more.

44 thoughts on “Economics in Two Lessons: Income Distribution

  1. @Uncle Milton

    It doesn’t have to be very inelastic, just a bit less than 1. The aim is to put them just below the top of the Laffer (or ibn Khaldun) curve. It’s pretty obvious from Oz experience that the rate required to do that is well above 50 per cent, and from first principles that it’s below 100 per cent, so 70 to 80 sounds plausible to me.

  2. @John Quiggin

    70 is only 20 more than it is now.

    It’s funny that Tony Abbott and Joe Hockey have never received any credit for increasing the tax on high income earners in the 2014 budget 🙂

  3. It is easy enough to see that, if the opportunity cost of a given increase the income of a better-off person is an equal increase in the income of a worse-off person, then the change is for the worse.

    Was this supposed to be

    It is easy enough to see that, if the opportunity cost of a given increase the income of a better-off person is an equal indecrease in the income of a worse-off person, then the change is for the worse.

    Otherwise, I don’t see how that follows?

  4. @Andrae

    It’s a matter of how terminology is used.

    In your phrasing you’re referring to having to decrease one person’s income as a condition of increasing another person’s income, meaning that both things do happen.

    But in John Quiggin’s phrasing the reference is to not increasing one person’s income as a condition of increasing another person’s income, meaning that one thing happens and the other doesn’t.

    If ‘the cost of X is Y’ means that Y has to happen in order for X to happen, then ‘the opportunity cost of X is Y’ means something different, specifically that Y has to not happen in order for X to happen — at least, that’s how John Quiggin is using the terminology.

    Does that help at all to make it clearer?

  5. I don’t believe that high tax rates (70 – 80%) will be much of a disincentive for high income earners.

    Firstly, my observation of hard workers is that they like hard work, and the money is often a secondary consideration.

    Secondly, they are not battling to have a bigger house because they feel they need a bigger house. They want a bigger house than their neighbour, and a bigger boat etc.

    Thirdly, they’ll be running a business, and the success of their business adds to their status, so they’ll work hard for that, even if they don’t get a lot of extra money out of it. Indeed, high personal income tax rates might even encourage them to leave money in the business.

    As for income inequality, everyone having exactly the same income would obviously not work. One person having all the income and everyone else having nothing, is obviously not optimal. But one imagines that somewhere between the ludicrous extremes is the “best” distribution. I reckon its much too unequal already. And I reckon you could do a lot worse than starting by boosting the incomes of those at the very bottom. After all, even the right think that a rising tide lifts all boats.

  6. The geometric mean has the property that, if all incomes increase by the same proportion, so does the geometric mean. So, it’s a better measure of the growth rate of incomes across the community than the usual arithmetic mean. It can also be justified mathematically, in terms of the theory of expected utility. For those interested, the details are spelt out in an optional section.

    I am interested. Is that available?

  7. Interesting discussion, John. I look forward to the book (I was a huge fan of Zombie Economics). Do you think there is more to say on this topic or you said all you needed to say? I know I could have continued reading more.

    I think the “state of nature” thought experiment goes back further than Mill to Locke, Hobbes and Rousseau. Hobbes had a very dark view of the state of nature encapsulated in the oft-quoted passage “life was short, nasty, brutish and poor.” Rousseau’s state of nature was much more idyllic and encapsulated in the concept of the Noble Savage. Of course Locke’s state of nature was used to defend property rights and has echoes in the common law concept of terra nullius and the sad misapprorpiation of Australia. Rawls is following in the tradition of these philosophers. Anyway, the mention of Rawls got me thinking (I rarely get the opportunity to use a philosophy major).

  8. On this tax stuff I found the new book “Inequality” by Anthony Atkinson good. It reverses the arguments of his co-author Saez (who worked on the Mirrlees Review) and who had argued for a maximum MTR of 40% to instead propose a 65% top rate for the UK. It is a major shift from proposing to cut the top MTR a few years ago to substantially increasing it today.

    As Uncle Milton points out the result is so dependent on (to be exact) the elasticity of income w.r.t to the retention rate (1-MRT). Diamond-Saez assumed for the US it was 0.25 whereas Saez for the Mirrlees Review assumed 0.56. I have just read an Australian Treasury literature survey of this evidence and the evidence is all over the place – lots of variability and very dependent on the age & gender of the tax payer. With respect to the income measure used there is much devil in the detail – particularly, for wealthy people, such things as tax deductible charity contributions which rise when tax rates rise,

  9. @hc

    Someone should a study of how donations to charities vary when tax rates vary. It could be done as one of those quasi natural experiment studies.

  10. I guess it depends on where the top MRT kicks in. The current level of 180,000 would be absurd given the highest rate applies at approximately a mutliple of 3 time average weekly earnings and at 20-35% of median house prices and does have disincentive effects.

  11. I like this a lot, although I have a small quibble with log utility. If we use geometric means then all income distributions that have a zero value will be ranked equally in last place. Clearly it is better to live in Aust or the US (where presumably at least one household has no income) than say Zimbabwe, where zero incomes are common.

    Sen has a social welfare function which is output multiplied by one take the Gini coefficient. This has a lot of nice properties as a social welfare function and Wikipedia gives some country rankings based upon this method. As we would expect the rankings are dominated by Nordic countries with high GDP per capita and low inequality.

  12. My sentiments exactly. As a once senior manager in the International Motor Industry, I can vouch for the fact that money is not sole or even the main driver behind human endeavour once a certain level of affluence has been achieved, I am not at all sure that we behave in the ways economists think we do.

    Power, status, a sense of achievement are all motivational factors that are just as important or more important than income. I think it likely that a marginal rate of 70 – 80% at the highest income levels is not the disincentive to work that some believe it to be.

  13. @Aardvark
    What is the basis of your claim (in relation to the $180,000 income threshold level) that higher MRT would have disincentive effects?

  14. @Aardvark
    Isn’t it just as likely that, assuming income is the main concern of the individuals effected, that increasing the MRT might lead them to increasing their working hours? It would surely depend on how effort/hours worked relates to their income generation? For example, at present there is a freeze on Medicare rebates (something I know about) which in its effect is something similar to raising the tax rate in that there is a diminishing real income for the medical practitioner who bulk bills. The response from many practitioners is to find ways of increasing throughput by utilising non medical staff in innovative ways thereby allowing the practitioner to see more patients and increase income. Other ways may be to curtail appointment times to the minimum time allowed by medicare and make the patient come back to deal with issues not dealt with in that minimum time again allowing the practitioner to obtain more income for the same “time -effort”. Increasing the MRT could have much the same effect.

  15. @John Quiggin

    Professor, can you expand on
    (i) a refutation of the Austrian economists arguments (footnote 2
    (2) marginal tax rates -especially high rates help the economy- and give examples

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