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So a tax on income, rather than helping fulfill my first preference, is likely to stymie my second because of the bait and switch you've identified.
Of course the two goals hypothesized are distinct. Do you really think Layard cannot see this? He's making the factual claim that both of these two goals are combined and that addressing the relative income "problem" will address the other. Maybe he's right. Maybe he's wrong. But he's not stupid.
Now, I have absolutely no committment to defending Layard's views. My position is that relative income explains little in itself, but is connected to things that explain lots. (Out of wack work/life balance may or may not be one thing that it partially explains.)
I guess you could put it this way: If I unilaterally choose to work less, my relative income goes down. But if I have a meddlesome preference for higher position (really just a preference that other people have lower position), I will expose myself to the "pollution" of folks who do not opt out of the race. (But notice that the pollution isn't caused by others doing anything to increase their position, just by my choice to reduce mine.) If the loss from the pollution swamps the gain of extra leisure, I won't opt out. But if everybody opted out (because of the tax), we'd all be better off.
So these questions are clearly are not unrelated. We get into the arms race because of the our meddlesome preferences. It seems Layard is framing it as though mutual disarmament in the race is the evaluative baseline. If someone defects from the agreement, and starts working longer hours to move up in relative income, then that's "pollution."
But, first, Layard needs to show that disarmament would indeed be part of some kind of ideally rational agreement to fix it as the baseline, deviations from which need special justification. He doesn't show that.
Second, the defection question and the pollution question are separate. My defection from a multi-party cooperative agreement may cause the entire cooperative endeavor to crumble, and the cooperative surplus with it. So you lose if I defect. But the defection is not a negative externality, unless one has an extremely un-orthodox notion of an externality. It can just show that the agreement is out of equilibrium.
Second, the pollution argument just isn't set up as a collective action problem. It just says that upward moves cause a utility loss to other parties, simply in virtue of reducing their relative position, NOT in virtue having an effect on work/leisure balance. The pollution argument needs to address the utility loss from reduced position independent of the argument for utility loss do to the inability to enforce a collective agreement on work/leisure balance.
I think Layard may treat the problems separately in the lectures on which his book is based. I need to check. But in the book, Layard gets, in effect, halfway through the pollution/externalities argument, and then just switches to the related but logically distinct work-life collective action problem.
I think that this is wrong. Income is the pollution. Every dollar that I make is good for me but bad for everyone else, since it makes my relative income higher than it would have been if I had not made that dollar.
That said, income taxes do not seem to be the solution to the pollution. This is easiest to see with a flat tax. In a world with a uniform 50% flat tax on all income, an extra hour of work helps me in terms of relative income just as much as it would if there was no tax at all. The whole income distribution is now just scaled down by 50%, so someone who had an income of x now has an income of .5x. Since your added gains are now scaled down by the same amount, they impact your relative position just as much as they would have.
Could another kind of tax do better? That depends on some of the details of Layard's belief about how relative income disparities lead to unhappiness. In any plausible income distribution, income is going to vary from the first percentile to the 99th percentile. The question is if the unhappiness created by income disparities depends on the details of the distribution or not. If not, then no tax could change the total amount of "pollution". If the distribution does matter (e.g. with a more equal distribution creating less disutility) then the tax could reduce pollution by improving the distribution. Since some units of income pollute more than others, the tax would need to be higher on the income that pollutes more. For instance, a progressive income tax might be a more efficient pollution tax, if additional income for richer people creates more pollution than additional income for poorer people (which would be the case if there is less total pollution in a more equal distribution).
The arms race argument, as you said, is a separate argument, and I think a clearer and better one.
Also, I think it's incorrect to say the pollution is caused by income *mobility*. Some forms of mobility increase the income gap and others shrink it, as stated above.
The whole discussion of Layard is a red-herring though. Income-envy is so low on the list of reasons to favor "left-wing" things like CEO salary limits, decentralization of economic power, wealth transfers, minimum incomes, public spending favoring the less wealthy, etc. that its almost disingenous to discuss it exclusively. Even consumption-envy, for example, is a considerably more formidable reason. Livlihood/status security and status/power imbalances caused by wealth inequality are much bigger issues. Layard seems to have some inkling of how income inequality (he should discuss wealth inequality) threatens the status security of those with less (making them jealous, not envious). But he obviously does not get this across very well, since Will can convince people that the status-jealous impoverished should just "get over it".
(To his credit, Will just says that this is a possibility. Of course it is THAT.)
Possible reasons:
(1) Wealth inequalities are endemic in any highly productive economy. We could find no way to equalize wealth without ruining the economy, thus costing the low/middle income people so much consumption-possibility that it's better for them just to deal with their wealth-inferiority complexes.
(2) High wealth people get so much benefit from being such that redistributing their wealth to the less wealthy would have overall costs to average utility.
(3) High wealth people have so much political power, that it would cost more to organize a way of redistributing their wealth than the benefit to the redistributees.
(4) Most everybody accept for the REAL LOSERS thrives on "the rat race" and a more egalitarian arrangement would plunge everyone into existential dread... a utility crusher.
If I were ranking those possible reasons, I would say that (1) and (3) are by far the most plausible and that its quitedifficult to decide between them. (4) also plays an important role. (2) is a piss poor justification of inequality.
Also, the study does cannot encompass all of the ways that wealth inequality negatively impacts the poor. Studies like that (few and number and incomplete as they are) make good intellectual ammunition and food for thought, but do little to justify world views.
There's another possible reason against state efforts to reduce economic equality. It could be that the policies that the state would embark upon in order to reduce inequality are morally unacceptable on other grounds, aside from economic considerations.
For instance, one way to reduce inequality in American society is to crack down on immigration, as immigration is a sizable source of domestic economic inequality. But to do so seems counterproductive because the United States might successfully reduce domestic inequality, but global inequality would increase.
Similarly, conservatives frequently argue that welfare programs that redistribute income encourage dependency, crowd out civil society and social capital, or promote some other bad outcome. Thus, we might reject state efforts to reduce inequality because of harmful effects that specific redistributive policies generate and these effects might be harmful for the economy, as you suggest in (1), or harmful for other reasons.
How could policy makers know that the rate race is actually immiserating us if social science is incapable of detecting the immiseration? Or do you define immiseration in terms distinct from subjective well-being?
As you point out, I did not by any means provide an exhaustive list of "possible reasons" that the wealth-poor should "get over it" for Coasian reasons. But notice that many of your conservatives' concerns have to do with effects on the economy.
It would probably be foolish for policy makers to set out uninformed to save us from a purportedly immiserating rat race. But social scientists could do relevant studies. So far happiness studies tend to just ask people roughly "How happy are you?" We could ask more nuanced questions. Also, the study Will cites just studies beliefs about income mobility. We could study a sample of people who actually have achieved inter-quintile mobility (or suffered downward movement). Was downward movement as bad as feared? Did income-position gains correlate with expected happiness gains? One of the first happiness studies, by Easterlin, found (to the contrary) that individuals predicted accurately that they would get wealthier but inaccurately that they would get more happy throughout their lives.
Mathematically, the crucial assumption for Layard's argument to hold is that other people's income increases the marginal utility of my consumption. Technically, you're correct to say that this is distinct from the "pollution" argument, because the latter requires only that others' income decrease my utility - it doesn't necessarily have anything to say about the marginal utility of my own consumption. However, it turns out that in the most of the standard ways of parameterising the utility function, the "pollution" assumption does in fact imply that my marginal utility of consumption increases. Indeed, it's more the case that you have to make special assumptions about the form of the utility function to avoid this implication, than to generate it - which is why (even if it's not completely transparent) Layard isn't being utterly ridiculous here.
Also, FWIW in these standard formulations, income is the pollution, so I don't quite know why you're taking such issue with that. Again, it's possible to argue for alternative formulations, but the standard one is far from obviously implausible.