Uncharted Territory

May 30, 2009

The Wine, The Widgets and The Wardrobe

Filed under: Complex decisions, Concepts, Economics, Energy policy, Global warming, Reflections — Tim Joslin @ 12:14 am

The blogging medium generally operates in reverse-chronological 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 sense whatsoever.

Previously I glossed over what are in fact two distinct cases:
1. When the product for which it is proposed to use taxes to reduce consumption is produced internally to the economy – alcoholic drink for example.
2. When the product has to be imported, e.g. oil or other fossil fuel.

Case 1: Internally produced products
I assumed last time that all income over the 50 units p.a. needed for essentials would be spent on drink. I’d now like to consider a refined example where there is a limit to how much can be drunk – 60 units worth p.a. say, at the untaxed price. Any income over that amount is spent on massages, say, as suggested in the comment by Dr Adrian Wrigley.

I suppose I should address Adrian’s point directly. He argues that the higher the price of drink, the less will be consumed relative to massages. I seriously doubt it. This may well be “classical economics”, but in real life value is determined socially, not just in terms of utility. In this case, the social consideration is paramount. People will only spend on massages what they have left after peer-pressure has forced them to drink with their mates until they fall over.

Now let’s do the math. Remember our population of 100 people earn from 50 to 149 units per year. Necessities in this economy cost 50 units/year and the most that can be spent on drink is 60 units. As before, the guy earning 50 can afford no drink. Those earning 110 or over can afford to imbibe the full 60 units worth. So the total amount spent on drink is 40*60 + 60*(0+59)/2 = 2400 + 1770 = 4170 units.

Only the top 39% (earning from 111 to 149) can afford massage. So 39*(1+39)/2 = 780 units are spent on massage.

Now let’s impose our tax on drink at (say) 100%, redistributing the revenue to the whole population. We can only approximate by simple arithmetic (we have to use a more sophisticated technique such as iteration to find an exact solution), but let’s assume roughly the same amount of drink is consumed as before – around 4200 units worth, before tax, so 8400 units in total with the 100% tax.

The 4200 units raised by the taxman are distributed evenly, so that now the population has from 92 to 191 units to spend each year. But drink costs twice as much, so only those earning 170 units or more can afford to spend the maximum 120 units a year. The rest can spend from 42 to 119 units. The total amount now spent on drink is therefore 22*120 + 78*(42+119)/2 = 2640 + 6279 = 8910 units. But this buys only half as much drink as without the tax. Nevertheless the total amount of drink bought is equivalent to 4455 units, a significant increase over the 4170 units drunk prior to the introduction of the tax regime. (Really we should iterate by feeding the tax revenue of 4455 back into the calculation but this clearly won’t affect the result massively…).

As a sanity check, note that only the top 21% (earning 171 or more units) can now afford massage, so a mere 21*(1+21)/2 = 231 units is spent on that activity. Massage professionals change career to start wineries all over the country.

Of course, if we believe so much in our drink tax policy that we respond by raising the tax to (say) 500%, and redistributing the approximate 25000 units of tax raised (there are just under 5000 units available to be spent on all except essentials, before tax), then the population will have from 300 to 399 units to spend. But with the maximum intake of drink now costing 360 units, no-one will be able to afford a massage. The maximum salary of 399 units is only enough to spend 50 units on essentials and 349 units on drink. Everyone will spend all their disposable income down the boozer!

In real life, of course, the situation would be considerably worse, because there are far more people on low wages than high ones, not equal numbers on each unit of salary as I’ve modelled.

I fear that the implication extends beyond the vice taxes. For example, policies such as increasing taxes on heating fuel and distributing the money directly or indirectly (i.e. by just adding it to the general pool of money raised by taxation) to the poor and elderly would be socially just, but ineffective in reducing carbon emissions. The effect of such policies is to reduce the constraint on consumption for those who were constrained by price, whilst failing to limit consumption of the targeted product by the majority of those who weren’t previously constrained. Dear, oh dear!

An even bigger point is that surely we want everyone to become better off in the future. Productivity is increasing all the time, so this should be the natural outcome. Policies to restrict consumption of products unhealthy to individuals or the environment simply by taxing them should therefore be considered suspect at the outset. It doesn’t really make a lot of sense to keep the majority of the population poor just so that their consumption of harmful products can be limited by taxing said products! Such policies only make sense if the goal is to increase the price of a harmful option above that of a desirable option. If no desirable substitute exists (as for drink) then this result suggests that perhaps we should be thinking more about alternatives to taxation policies to reduce consumption – public education initiatives, for example.

Case 2: Imported products
This is the true Man in the Wardrobe Fallacy. The point is that taxation is a change internal to the economy, but the amount we can afford to import is an external parameter, independent of internal taxes.

It’s not entirely clear to its inhabitants how the UK pays its way in the world these days. But we must be selling something in order to fund our imports. Possibly our main export is now financial services snake-oil, but let’s pretend we make widgets and export £10bn of these a year. We can therefore afford £10bn worth of imports a year, and let’s say we spend the dosh on oil and products that contain “embodied” emissions. [See an interesting recent piece by Monbiot on embodied emissions, and note the comment by SteelyGlint].

Let’s say we impose an import tax on these nasties making them more expensive to the consumer. Why might this be ineffective?

1. Remember we will still be able to import £10bn worth of goods because nothing has changed on the export side – the world still wants £10bn worth of our widgets. And practically everything we might import has at least “embodied” carbon. If we use (say) less oil, because the tax encourages us to use it more efficiently, but import manufactures produced using coal-based power from (say) China instead, then we could find we’re responsible for even more carbon emissions than before! [OK, an explanation: I know the consumer pays tax on the embodied emissions (actually I consider such a tax to be entirely impractical, but let’s be hypothetical for a moment), but if the scarcity value of oil is high, the cost of manufacture low and the carbon import tax not too high, the embodied emissions in £1000 worth (even after applying a carbon import tax) of Chinese manufactures could easily exceed the potential emissions in £1000 worth (after the carbon import tax) of oil! Oops!!].

2. Hang onto that point about efficiency. If we’re using less oil, but achieving the same economic output, perhaps by driving smaller cars, then – oops – we’ve improved the efficiency of the UK economy per unit of output! This will allow us to undercut our competitors and export more. We’ll therefore have more than £10bn to spend on imports. Oh dear!

3. OK, let’s get serious. We’ve taxed the oil we’re importing from Saudi, so that we import less. Instead, we blow the money on something containing no embodied carbon (for the sake of argument) – Indian Premier League cricket, for example. Now all we’ve done is put pounds into someone else’s hands (or perhaps dollars if we use that for such trade) – i.e. Indians working in the cricket industry. Now Saudi has this oil to sell and Indians have the pounds the Saudis were happy to take from us in return for their oil… All we’ve done is move the problem and put another link in the trade merry-go-round.

I seriously doubt that demand-side financial engineering (such as carbon taxes) will alone have any positive effect at all in reducing global carbon emissions. In fact, it could easily make the problem worse!

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…

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