Uncharted Territory

May 27, 2009

The Man in a Wardrobe Fallacy

Filed under: Complex decisions, Concepts, Economics, Energy policy, Global warming, Reflections — Tim Joslin @ 5:44 pm

Perhaps it was the Beano where I first read of the Man in a Wardrobe Fallacy. Two guys are struggling with a heavy wardrobe. “I thought there were three of you”, the customer says. Punchline: “The other guy is inside carrying the clothes!”

The Man in a Wardrobe Fallacy relates to one of the numerous problems likely to stymie attempts to use the price mechanism to limit consumption. In a nutshell, everyone forgets that money is just a way of distributing resources.

It may not look like it at first sight, but here is a pertinent example of the Man in a Wardrobe Fallacy : if an economy can produce or afford to import enough fuel (say) for (say) 5% of the possible desires of the population, then 5% of the possible desires of the population will be satisfied, whatever nominal price you put on fuel. [This case relies on the possible desires of the population being large relative to the potential supply of fuel, but has anyone looked at the real world lately? Noticed how much more we all need to fly than we did 25 years ago? Anyone heard of The Reverend Thomas Malthus?].

Don’t believe me? Try a thought-experiment:

(1) Imagine a population of 100 people with incomes varying from 50 to 149 units a year. Everyone spends all their income each year (a total of 9950 units).

(2) Spending is such that all will use up to the first 50 units of their income – a total of 5000 units – to buy essentials such as food. Anything left over is spent on something that you (the government) want people to spend less on – let’s say drink, but the argument is the same for unnecessary fuel.

(3) One poor sod can’t afford even one pint all year, but, with no tax on drink, everyone else spends the remainder of their income in excess of 50 units – from 1 to 99 units – on drink. A total of 49.5*100 = 4950 units are spent on drink.

(4) Can’t have this, says the government. Tax drink at 25%, 50%, 100%! The tax rate makes no difference.

(5) The critical point is that the tax raised is distributed, let’s say evenly across the population. Now, a little thought will show that the government can do nothing more effective with the tax revenue. It could destroy it, but this would simply raise the value of the money remaining in circulation. It could spend it on imports, or even give it away as overseas aid, but then the money must (eventually) be spent on products denominated in units – and returned to our own besotted population!

(6) When we raise and redistribute the drink tax, it’s obvious that the amount of money spent in the economy each year increases from 9950 units to (9950 + x) units where x is the amount raised by the drink tax. As before, 5000 units are spent on essentials, leaving (4950 + x) units to be spent on drink. Whatever x is, (4950 + x) units buys exactly the same amount of drink as 4950 units did before the need to pay x units in tax to the government! Of course, because of the redistributive tax, even the poorest guy can now afford to drink – he had been earning 50 units a year, but this is now supplemented from the tax revenues – but the total amount drunk is the same!

The real world is a little more complicated. For example, as the price of drink is raised, people might choose to buy a substitute product instead. Heroin, say.

If we substitute for drink something more fundamental – fossil fuels (“carbon”), which are embodied in almost everything we consume – we see that the effectiveness of trying to limit consumption with a tax depends (in the first approximation*) entirely on the availability of substitute products. Absent planning permission for nuclear power stations, tidal energy barrages and wind-turbines, imposing a tax on carbon in the UK would have very little effect on overall fossil-fuel consumption. Such a tax would be a case of shuffling the deckchairs on the Titanic. It affects internal patterns of fossil fuel consumption, but not overall consumption, because it has no effect on the amount of carbon the UK can afford to import!

This is the Man in a Wardrobe Fallacy. Even if the Man has imaginary superpowers – like a modern-day Maxwell’s Daemon – in this case including weightlessness, redistributing the weight of the clothes in the wardrobe would not reduce the overall load by one single gram.


Note: Further fallacies (not for the faint-hearted!).

*Actually, it gets worse, but I want to stick to an explanation of the Man in a Wardrobe Fallacy here. Producing (as opposed to importing) renewable energy in the UK would simply allow us to increase our total energy consumption – we could afford to import the same amount of “carbon” as before!**

** Actually it might get even worse, as the economy would become more efficient than any others which don’t invest in renewables. We could undercut others on pricing of exports and therefore afford to import even more carbon than before…



  1. I don’t geddit.

    In your example, people aim to spend the first 50 units of money on essentials. Presumably the rest they choose to spend on a variety of discretionary products.

    Let’s simplify it to just two discretionary products, drink and massage.

    The ratio of drink to massage depends on the prices and private values of the two products. Isn’t it fairly standard economic theory that raising the price (eg through tax) of drink in relation to massage will generally result in lower consumption of drink and higher consumption of massage?

    If you construct a model where the entire economy is devoted to producing drink, then of course the entire economy is dedicated to consuming drink too (after the “fixed” cost of food)! Financial transfers (eg tax, welfare, subsidy) are irrelevant in this case. But this is not remotely realistic nor informaive. Try again, Tim!

    Comment by Adrian Wrigley — May 29, 2009 @ 2:26 pm

  2. Good to hear from you, Adrian.

    I based my original post on the observed behaviour of myself and friends when I first started work. At first I earnt just about enough to pay for the essentials (rent, food, student debt repayments). As I earnt more I simply spent more and more on entertainment, principally beer and pool in the Tumbledown Dick (those were the days!). The point is that social factors override any rational assessments of value, determining spending patterns once necessities are paid for. So, for example, you happily buy a round of beers for a sum that (because of tax) could buy you something else that absent the social context appears to have more value.

    Another observation to bear in mind is that the proportion of income people spend on different things varies dramatically over time. We “yuppies” as we used to be called back in the day spent as much on not only booze but also likely music (and in some cases ciggies) as on food. This would have been unthinkable for someone starting out in working life 50 years earlier.

    Nevertheless, I have been wondering whether there are limits to how much one can spend on booze. The trouble is that I think this makes the situation even worse – taxes on drink could be even LESS effective! I’ll explain why in the next post…

    Comment by Tim Joslin — May 29, 2009 @ 7:43 pm

  3. […] order. The reader encounters the most recent post first. If anyone has not already read my previous post outlining the Man in a Wardrobe Fallacy, then I suggest now would be a good time to do so. Otherwise the following will likely make no […]

    Pingback by The Wine, The Widgets and The Wardrobe « Uncharted Territory — May 30, 2009 @ 12:14 am

  4. […] worry whether my previous attempts to explain the Man in the Wardrobe Fallacy, here and then here, were too theoretical. So I’m going to try to work through the argument, step […]

    Pingback by The Nature of Money, the Consequent Likely Ineffectiveness of Carbon Taxes – Revisiting the Man in the Wardrobe Fallacy « Uncharted Territory — November 19, 2009 @ 12:57 pm

  5. “It is upon the Trunk that a gentleman works.”
    —Analects of Confucius, I.2

    This is a wonderful analogy! But, I would argue, there are both good arguments and bad arguments associated with it; and a good analogy associated with at least one bad argument (if that be so) is to be avoided.

    Let me deal with what I think are the good arguments.
    Carbon taxes and Cap and trade schemes have, potentially, two major ways in which they can ‘leak’, if they are not global.

    1) First, industry could relocate from the West to non-capped/taxed countries, leading to more emissions. Actually, this may not as bad as expected. The price change for industry on average is likely to be 3% for a carbon tax of $30, and few sectors are both carbon- and export- intensive: see [1]. For higher carbon prices, ‘Border tax’ adjustments are designed to prevent this leakage, and provide a meaningful lever in negotiations, so long as they are done sensitively and with collaboration (i.e. cooperatively) with our partners such as China. Of course invoking trade is a ‘hard’ tool: but that may not be a bad thing. We can’t negotiate without some sort of stick; there are various trade wars that already exist and civilization has not yet collapsed.

    2) Secondly, you could argue that the reduction in fossil fuel consumption in the West, will lead to reductions in the world price of fossil fuel and therefore emissions increases elsewhere. This is a serious point in favour of carbon taxes for the west (and third world) prosperity (see ‘The Resource Curse’ for how high oil prices enrich elites and not the population). It is also a point against the climate-effectiveness of such a scheme. The obvious point is just to say that we need to make the carbon prices higher than expected to achieve the same goal.

    It must also be said that the oil/coal exporting countries will be more keen to keep the oil/coal in the ground if the reward for digging it up now is low. So even any incentives for keeping in the ground will require demand reductions. (Furthermore demand reductions by the west have political legitimacy – we have the right to control outr own consumption behaviour; and we probably don’t have the cash to do anything else).

    3) Third, there is a leakage associated even with a global scheme. If we do not burn fossil fuel now, we may burn it at a later date. This is true enough, but presumably a scheme which continually keeps it in the ground is exactly what is needed.

    All of this is a matter of scale. We have not dealt with matters of scale. But there are reasons to suppose that an increase in end-user prices would reduce demand and, if high enough, encourage alternatives on a large scale.

    Let me deal now with the poor arguments.

    A) Carbon emissions are completely inelastic to price.
    NOT TRUE. It is true of course that energy demand is pretty insensitive to price (I’d guess a 20% reduction for a doubling in prices). But above a certain (carbon) price, it is likely that alternative non-carbon sources would come in. There is ample supply of at least some of these alternatives (e.g. solar internationally).

    B) If a country spends less on fossil fuels they could afford to spend more on other, potentially more carbon intensive, imports.
    The arguments leading to this are confused in more ways than one .

    We need to deal with two presuppositions, both of which are questionable:
    Bi) A countries balance of trade in goods and services is in long term balance.
    This is FALSE. Some countries run up deficits and sell financial assets to finance the deficit.

    A second presupposition is the following:
    Bii) Imports from other countries (possibly including a multiplier effects of the use of revenue) could be comparatively carbon intensive to imports of fossil fuels (possibly including a multiplier). I think this is extremely unlikely. (see diagram in [1]).

    Putting all this together, I am therefore deeply unconvinced by what you call ‘Man in the Wardrobe’. The problem I have is the use of a good analogy to deal with both good and bad arguments. A concept that includes aspects that one agrees with and those that one disagree with is doubly difficult, because it is hard to attack the analogy without attacking parts which, conceptually at least are correct.

    Among the parts that I conceptually agree with, there is a need to assess the scale of the effect. That will have to come for another day.

    [1] Stern Review, Chapter 11, p8, http://www.hm-treasury.gov.uk/d/Chapter_11_Structural_Change_and_Competitiveness.pdf

    Comment by Stephen Stretton — November 21, 2009 @ 5:42 pm

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