Home > Economics in Two Lessons > Economics in Two Lessons: Income Distribution

Economics in Two Lessons: Income Distribution

September 7th, 2015

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.

and

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.

Categories: Economics in Two Lessons Tags:
  1. Uncle Milton
    September 7th, 2015 at 18:11 | #1

    The geometric mean is equal to the arithmetic mean when incomes are distributed exactly unequally

    Unequally?

  2. Uncle Milton
    September 7th, 2015 at 18:15 | #2

    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.

    Do they reach this conclusion or is it implied by their calculations? And, either way, what’s the reference?

  3. John Quiggin
    September 7th, 2015 at 18:43 | #3

    The Case for a Progressive Tax: From Basic
    Research to Policy Recommendations
    Peter Diamond
    Emmanuel Saez
    CESIFO WORKING PAPER NO. 3548
    CATEGORY 1: PUBLIC FINANCE
    AUGUST 2011

    They give a bunch of estimates up to 80 per cent.

  4. John Quiggin
    September 7th, 2015 at 18:43 | #4

    @Uncle Milton
    D’oh! Fixed now I hope.

  5. Uncle Milton
    September 7th, 2015 at 18:52 | #5

    @John Quiggin

    Two questions:

    1. At what income level does this tax rate kick in?
    2. A high marginal rate is the opposite of what comes out of Diamond-Mirrlees. Why is Diamond-Saez different?

  6. rog
    September 7th, 2015 at 19:03 | #6

    Not sure that market prices are or were an efficient reflection of true costs; Abbots dumping of renewables in favour of LNG projects has been a costly exercise.

    http://rogermontgomery.com/now-the-international-energy-agency-tell-us-profits-are-a-pipe-dream-from-200-billion-worth-of-australian-lng-projects/

  7. Ikonoclast
    September 7th, 2015 at 19:28 | #7

    Why not attack inequality at its source rather than seek to correct it with taxes after it happens? Gross inequality occurs as an outcome of the ownership setup of our production system. The only way to address this properly is to ensure enterprises are worker owned and worker managed. Anything less than this is the “same old same old” and we are going to keep on getting exactly what we are getting now. What we are getting now is increasing inequality and increasing economic and social instability with no end in sight except serious crises. This system is past its use-by date. There is no point tinkering with it. The point is to replace it.

  8. J-D
    September 7th, 2015 at 21:04 | #8

    @Ikonoclast

    If your only tool is a hammer, then every problem looks like a nail.

  9. Ikonoclast
    September 7th, 2015 at 21:35 | #9

    @J-D

    Fun game, let’s play it.

    If your only tool is the market system, then every problem is assumed to be solvable by markets.

  10. September 7th, 2015 at 22:36 | #10

    Bernoulli’s lottery ticket? I hope you can find space for this in the appendix. Of more interest would be a reference to experimental evidence for diminishing marginal utility. It’s been demonstrated in rats working for chocolate. There must be psych experiments on students, perhaps involving tradeoffs between beer, TV and sex.

  11. September 7th, 2015 at 22:42 | #11

    The first paragraph does not make it clear what is the universe of reference: Australia, the USA, OECD countries, all current market economies, all known market economies in history? Perhaps this would be best explained in the introduction. I would use the OECD frame, with variations specified.

  12. hc
    September 8th, 2015 at 05:19 | #12

    Have not seen the Diamond – Saez paper but the claim is at variance with most of the optimal income tax literature which seeks low MTRs on high incomes. The reason is that 10% disincentive effects on high incomes are expensive compared to 10% disincentive effects on low incomes – this is so both for efficiency reasons and for reasons linked to ability to make income transfers to the poor. You just lose a lot. The empirical work I have seen testing the Mirrlees model (including work by Saez) confirms this – a fairly flat optimal tax schedule with high average but low marginal rates of tax on the wealthy.

    I think it would be reasonable to include an explanation of their result.

    My read on the applied Mirrlees work is that of Uncle Milton.

  13. John Quiggin
    September 8th, 2015 at 05:20 | #13

    @Ikonoclast

    I agree. This point is made in a section I’m currently drafting.

  14. John Quiggin
    September 8th, 2015 at 05:28 | #14

    @Milton and HC

    The top rate is meant to apply to the top 1 per cent, above 400k

    The low income result is largely an artifact of bad assumptions about the distribution of income. With a finite set of earners you get the zero marginal tax rate conclusion for the highest earner, because there is no one above them. But (especially if you want a reasonably high threshold) quite a large proportion of the tax base consists of income in excess of the 1 per cent cutoff (400 k in this case), and, with a Pareto distribution there is no cutoff at which it’s sensible to lower the rate.

    As a reminder, the top 1 per cent get something like 25 per cent of all income.

  15. Geoff Edwards
    September 8th, 2015 at 06:59 | #15

    1. I only wish that Prof J’s explanation of opportunity cost could be embedded more widely into policy. Given that it is central to mainstream economics teaching, I don’t understand why it features so sparsely in mainstream economic commentary in respect of public budgets. One of my personal current enthusiasms is to advocate for clear-sighted analysis of the opportunity cost of building expensive transport mega-projects. Prof John spoke lucidly on this at a recent seminar http://www.royalsocietyqld.org.au/events/events_2015.htm but I wait impatiently for most other economics commentators to pressure governments to abandon projects with benefit-cost ratios of less than 2 to 1 in favour of spending on research, education infrastructure and environmental repair with BCAs several multiples of this. Opportunity cost is probably a better way of presenting this argument than BCA.

    2. Above, Prof J writes “Assuming that market prices are equal to opportunity costs” … but in the pdf most refs are that “Market prices reflect and determine opportunity costs”. This second construction would seem preferable, as the set of cases where nominal values are exactly equal would seem small, even if the general principle applies.

    3. “the top marginal rate was at or above this level in the 1950s”. Indeed. And the economy was not thereby wrecked from the 1950s to the 1970s. The change – and the reasons for it and the consequences of it – holds many lessons for a debate about inequality, and deserve a chapter.

    4. “found well to the left of centre in any feasible political system.” This is a gloomy statement. Is it not possible that in the forthcoming global transition, this might happen? Maybe put “any contemporary political system in the neoliberal-dominated world” or similar.

    5. In a couple of places, e.g. in the pdf the most important macroecconomic problem is mass unemployment, a sociological view is taken. But the environmental destruction is arguably even more fundamental, more insidious, less well recognised and more threatening to economic and societal welfare.

    6. Yes, trade is widely recognised as not necessarily a zero-sum game, but viewed globally, and over time, then world trade arguably is a zero-sum game. There seems no basis for imaging that all countries will always benefit and that transport (fuel) costs will always be negligible?

    7. “Technological innovations that allow us to produce a given output with less of
    every kind of input, including labour, provide us with the classic example of
    free lunch.” Maybe, but most such equations disregard or assume as negligible the input of biophysical energy. Industrialisation has been a process of replacing animal muscle power with fossil fuel power. This is unsustainable and has an opportunity cost. Solow’s equations that he presumed gave a central place to innovation omitted energy and resources.

  16. J-D
    September 8th, 2015 at 07:31 | #16

    @Ikonoclast

    If your only tool is the single remark that ‘there is nothing to do except change the system’, then no matter what John Quiggin posts on the subject of economics you will take it as an appropriate opportunity to respond with the endlessly repeated (and therefore tedious) comment that ‘there is nothing to do except change the system’; unless, that is, you decide that the comment has been repeated often enough and decide to give it a rest.

  17. Ikonoclast
    September 8th, 2015 at 08:06 | #17

    @John Quiggin

    I assume you agree with the basic concern of my first rhetorical question.

    “Why not attack inequality at its source rather than seek to correct it with taxes after it happens?

    However, I cannot safely assume that you agree with my claimed solution which is in effect a recommendation for thorough-going socialism. So, I am wondering what you mean or would recommend in detail on this point?

    One can assume there is a kind of continuum of measures.

    (1) Greater regulation of finance and financial transactions.
    (2) More counter-cyclical spending.
    (3) Improved minimum wage rates.
    (4) Improved labour rights over “profit rights”.
    (5) Laws to limit large individual private accumulation of production capital or shares.
    (6) Laws mandating transfers of capital ownership from capitalists to workers.
    (7) Laws mandating full worker co-operative ownership and management of all enterprises.
    (8) Laws mandating nationalisation of natural monopolies.

    These are examples on a continuum which more or less gets more socialist as it goes. I assume you would recommend measures down to point 4. I am not sure you would be prepared to go any further but perhaps you might like to clarify.

  18. BilB
    September 8th, 2015 at 08:08 | #18

    This is one of your best pieces, JQ. You have nailed so many buttons it is difficult to respond.

    So where we all innately understand…..

    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……… 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….

    ….it is good to see it written down.

    It is vital to understand this in the current rhetorical assault on progressive taxation. I am a mechanical guy and I fully understand leverage. I once moved a 24 tonne boat out of a hole with simple levers and rollers where expensive machinery had failed, I can recognise the mechanisms of wealth leverage at work. So when I saw Howard reduce the top tax rate at a time when no one would question it (tax flattening), later successfully install a GST (tax flattening) taking advantage of the politically inept Democrats, and later when the balloon of wealth that enabled Howard’s actions had vanished Hockey attempts to adjust upwards the GST (tax flattening) taking advantage of his own party’s failings as the justification, I know precisely what is underway. The “heavy weight” of taxation is being lifted off the shoulders of the already wealthy and moved to the shoulders of everyone else. Progressive leverage is a very powerful process. Putin understands this very well.

    I have been struggling with the whole notion of opportunity cost for some time going back to the definition a number of times. I found this item which I like for its graphic simplicity you tube pkEiHZAtoro.

    Something about opportunity cost as a primary evaluation mechanism does not ring true, and I finally figured out what it is. I will summarise the flaw in the term “net casting”.

    Taking up an opportunity definitely has entry level economic parameters, but those parameters rarely define the outcome. Bank managers know full well that a “business plan” is simply a document to be used as the reason why he handed over money to a customer. The percentage that actually define what happened next would be in the margin of error. Business is driven mostly by the “being there” factor. “I just happened to be in the right place at the right time”, and the unspoken part is that “and had everything needed to do the job”. It is this very reality that makes economics such a very difficult field. I will put forward the notion that economics fails predictively because it is lead to quantify the billions rather than the units.

    A metric I like to ponder is one billion. These days we fling the word around with gay abandon rarely stopping to comprehend its form. To the end of appreciating what one billion meant I visualise this in terms of factors and the ones I use are that one billion dollars is 10,000 time $100,000. And to give that some visual perspective, $100,000 will buy a fairly respectable CNC (Computer Numerical Control) machine that would have a ground base of 2 meters by 3 meters, be 2.5 meters high and weigh around 3 tonnes. Your billion dollars will buy 10,000 of these which will fill some 6 hectares with no space between them.

    The next time a politician rattles off the cost of a submarine or a motorway think of the opportunity cost of that billion dollars in terms or 600 meters by 200 meters of precision machinery 2.5 meters high weighing 30,000 tonnes. That is the opportunity cost of that sort of decision. But the opportunity loss of that decision is the productive capacity of those machines times the employment not created times the economic multiplier, moderated by the net casting factor.

    http://patch.com/illinois/lagrange/a-dollar-spent-locally-worth-more-study-shows

  19. Julie Thomas
    September 8th, 2015 at 08:49 | #19

    “Something about opportunity cost as a primary evaluation mechanism does not ring true”. It rings true as an equation and a way of thinking that would be wonderful if it was possible, but for me it is unrealistic.

    The thing about opportunity cost that confuses me is that most of my life I have been a single mother and I have never had the luxury of being able to evaluate opportunity cost for just myself; there has always been another person or more who has needs that I have to be aware of and accommodate the best way that I can.

    I’d be in the “slightly better off” category although I do not have to worry about paying rent – and this is the most serious problem for many people who live on my level of income – and the choice of how I would spend the extra money would be based on needs.

    I would have to evaluate who needed new shoes the most and how much I should spend on his new shoes – of course the demand is for the most expensive – when another child needs a haircut and I need to see a dentist.

    Calculating the opportunity cost of what I buy in any case in which I have been blessed by an extra payment from Centrelink is just a waste of time from my point of view – I cannot possibly have full knowledge of the outcomes of my choices – and sometimes I think I may as well just write a list of all the things we ‘need’ and throw darts at it.

  20. Aardvark
    September 8th, 2015 at 08:58 | #20

    I find the argument that 70-80% marginal tax to be counterintuitive to the idea that the marginal dollar is far less valuable to a higher income earner than a low income earner. Surely the gains from effort, human capital and entrepreneurship would then need to be signficantly large for the high income earner to want to expand the size of their income if the marginal utility of additional earning is low. Wouldn’t the preferable model be to address the root cause inequality rather than the inequality itself if we are to increase the total value of the social welfare function (rather than redistribute a lower value of net wealth).

  21. Nevil Kingston-Brown
    September 8th, 2015 at 09:23 | #21

    How does the difference between geometric and arithmetical means correlate with the more commonly used gini coefficient as an inequality measure?

  22. Uncle Milton
    September 8th, 2015 at 09:31 | #22

    @John Quiggin

    The derivation of the optimal top rate does seem to turn on an assumption that the labour supply of high income earners is quite inelastic. That might be true, or they might all emigrate to Hong Kong if you tax them heavily. Who knows?

    The DS paper incidentally was published in Journal of Economic Perspectives—Volume 25, Number 4—Fall 2011—Pages 165–190

  23. Nevil Kingston-Brown
    September 8th, 2015 at 09:47 | #23

    A problem with demands to address the “root cause” of inequality is that this usually translates into demands for much higher wages. Certainly in the US there is scope to substantially increase wages in line with productivity without much altering the amount of jobs, but here, rather less so.
    The problem is that very high wages at the lower end will greatly accelerate the automation of the remaining human-intensive industries (e.g. service industries) and the offshoring of manufacturing and other tradable sectors. We saw bank tellers largely replaced with ATMs a long time ago, we are now seeing supermarket checkout jobs replaced with DIY machines, video library staff replaced with vending machines, etc. It doesn’t take much imagination to see robot shelf stackers in supermarkets, mechanization of fast food preparation and serving, etc. Worker ownership is not a solution to high-wage-driven mechanisation as they will not compete effectively with mechanized capitalist systems, unless they underpay themselves.
    Unless we are prepared to complement mass mechanization with a high guaranteed minimum income or something of the sort (which would require high high-end taxes anyway), taxing high incomes and redistributing the proceeds after the production process occurs will preserve many more jobs than the large alterations in workplace relations required to not just slow but reverse trends in inequality. Again, the US and maybe UK are probably exceptions in this regard, where low-end wages could be substantially increased due to their historical lag behind labour productivity. Wages in Australia and Europe have by and large kept pace with labour productivity IIRC.

  24. Bruce Bradbury
    September 8th, 2015 at 09:49 | #24

    “is to treat equal proportional increases in income as being equally desirable”. This is confusing (it is easy to read it as if the ‘equally’ were missing). It would be better to spell it out as saying that equal proportionate increases will increase the welfare of rich and poor equally. Similarly in the following sentences, ‘benefit’ should be ‘benefit to them’.

  25. Nevil Kingston-Brown
    September 8th, 2015 at 09:49 | #25

    @Uncle Milton
    Given that a majority of the top 1% high income earners have got their income from rent (broadly defined) rather than anything useful, perhaps a relevant question is whether we would actually lose anything if they migrated to Hong Kong.

  26. John Quiggin
    September 8th, 2015 at 10:01 | #26

    @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.

  27. Uncle Milton
    September 8th, 2015 at 10:22 | #27

    @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 🙂

  28. Uncle Milton
    September 8th, 2015 at 10:25 | #28

    @Uncle Milton

    … or for not undoing Labor’s doubling of the tax on the super contributions of very high income earners.

  29. BilB
    September 8th, 2015 at 10:29 | #29

    Aardvark,

    Above a certain income level creating new income requires not additional physical effort. Here is an example of unpredictable net casting outcomes

    http://www.smh.com.au/business/smart-investors-reap-windfall-from-power-meters-20121223-2btk1.html

  30. Andrae
    September 8th, 2015 at 10:31 | #30

    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?

  31. J-D
    September 8th, 2015 at 14:28 | #31

    @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?

  32. J-D
    September 8th, 2015 at 14:29 | #32

    Those italics are a mistake; sorry about that.

  33. September 8th, 2015 at 17:00 | #33

    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.

  34. September 8th, 2015 at 18:42 | #34

    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?

  35. James
    September 8th, 2015 at 21:37 | #35

    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).

  36. hc
    September 8th, 2015 at 22:56 | #36

    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,

  37. Uncle Milton
    September 9th, 2015 at 09:59 | #37

    @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.

  38. Aardvark
    September 9th, 2015 at 10:50 | #38

    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.

  39. John Quiggin
    September 9th, 2015 at 11:42 | #39

    @Uncle Milton

    I gave them credit

    if Abbott wants to increase income tax on high earners, I’ll support him. And, if he wants to call this policy a “debt reduction levy”, I don’t have a problem with that.

  40. NickR
    September 9th, 2015 at 12:03 | #40

    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.

    https://en.wikipedia.org/wiki/List_of_countries_by_Sen_social_welfare_function

  41. John Turner
    September 9th, 2015 at 12:49 | #41

    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.

  42. John Turner
    September 9th, 2015 at 13:08 | #42

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

  43. John Turner
    September 9th, 2015 at 13:19 | #43

    @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.

  44. Peter Kirsop
    September 10th, 2015 at 06:49 | #44

    @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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