The carbon tax and compensation

You know how people sometimes cut down their 3rd year politics essay and submit it for publication in Woroni? Well today I’m doing just that (only this is my blog, not Woroni). We did the carbon tax in class a few weeks ago and I want to write about it, mostly because it is surprisingly simple, and makes for a nice horse to flog about the inadequacies of our public discourse.

A great many people argue that the carbon tax is a pointless policy because the compensation it incorporates means that nobody will actually shift their consumption away from carbon. This is wrong. Allow me to explain using my newfound economics skills. I will use a graph first, which might be a bit complex. I will then use a hypothetical example.  

Figure 1 shows an individual’s consumption between two categories of goods—carbon intensive goods (the x-axis) and carbon-neutral goods (the y-axis). It shows the effect of an increase in the price of carbon intensive goods, as you would get under a carbon tax.

The curves marked U₁ & U₂ represent different levels of utility derived from the same set of preferences. That is to say, throughout this exercise, the preferences of the individual do not change; that is why the U curves are identical, U₁ is just higher than U₂. It is higher because at the original price of carbon (PX₁) the individual can afford more of both goods than at PX₂, and this gives them a higher level of utility. As you move towards the north-east corner of the graph you move towards higher (better) levels of utility.

The red lines represent the individual’s budget constraints—their income. Under the original conditions the individual consumes at point A. Here, the individual’s utility function touches their budget constraint. Point A is an optimum point because it is the highest point on the U₁ curve that can be reached within the budget constraint. 

After the carbon tax, the price of carbon increases, so the consumer can now afford less carbon intensive goods. This is represented by the budget constraint shrinking away from the x-axis to PX_2. The individuals ‘real income’ is now lower. Their nominal income has not changed, but it can afford less of the goods in question.

At this level of income, the individual can no longer reach U₁, so the individual attains a lower level of utility—U₂. This optimisation process on the part of the individual is captured in point B, which is the point at which U₂ can be reached with the least expenditure.

 Notice that at B the individual is consuming less carbon intensive goods than at point A. Win if your objective is to move people away from carbon. However, the individual is also worse off because they are at a lower level of utility. So the government compensates them with money to get them back to their original level of utility, U₁.

But note that the compensation moves their consumption to point C, not back to A. Why? Because prices have changed! Under the new price regime the individual’s budget constraint is captured by the lime line (the ‘substitution effect’, which shows the impact of a price change while holding real income constant). Notice that the lime line has the same slope as the budget constraint at B. 

Under this price regime and budget constraint the point where the individual can reach U₁ is no longer A, but C. Note that C involves less carbon consumption than A. This is so because prices have changed and individuals are rational—they will optimise away from relatively expensive goods.

Let’s try and relate all this complex graphical analysis to a real world example. Consider an individual, Bob, who can tick the ‘I want to use green energy sources’ box on his electricity bill for a price of $20. Bob is frugal and is thus disinclined to tick the box. Prior to the carbon tax his bill is $50 and he gets all the power he needs. After the tax his bill is $70 dollars either way. Bob seems worse off, except that the government gives him $20 dollars to cover the expense of the carbon tax. Unless Bob is heartless he is going to tick the green energy box, because it now makes no difference to him regardless. The compensation has not driven down the cost of carbon, so now green energy is price competitive, and Bob will choose it. Bob is exactly where he was before in terms of utility, but the world has a little less carbon in it (and the government lost money).     

Some observant readers may have noticed that this hypothetical example (and graph) is not entirely accurate, because point C typically involves more carbon consumption than B. An uncompensated carbon tax would get the job done better than a compensated one, but it also leaves people worse off. Government compensation is expensive, as is a carbon tax in the first place, due to its adverse effects on economic activity. There is thus certainly an argument to be made that compensation mitigates the effectiveness of the anti-carbon policy, and an even better argument (though unconvincing in my opinion) to be made that it is prohibitively expensive. But to say that it makes the policy pointless is fallacious.

There are two counterarguments worth analysing. The first is that the above is all good and well at the level of consumers, but that Australia’s carbon tax compensates polluters. As I understand the carbon tax, this is incorrect. The government does not compensate polluters in a manner that allows them to continue ‘business as usual’. Firms can request funding to ‘clean-up’ or ‘green-up’ their operations. They don’t get money to just keep doing what they’ve been doing. That would indeed be a totally stupid policy.

The second counter argues that clean industry, particularly with regards to energy, does not have the capacity at present to handle all the new business generated by the tax. But this is a touch banal, because a key selling point of the tax is that it will encourage clean energy to build capacity. Under the new price regime clean industry is price competitive with dirty industry, which encourages consumers to purchase its goods. Firms respond to this demand by increasing supply. There may be some lag in the short run, but in a highly competitive and elastic economy like Australia that lag is minimal. This is especially the case given the long lead-in time for the carbon tax, wherein firms could position themselves to capitalise on the price regime as soon as it hit. I could explain this dynamic transition with the static model above, but it would be slow and clunky, so I won’t bother.

The line of reasoning pursued in this piece strikes me as reasonably easy to follow. I have left out the maths, but even that is not particularly difficult. Anyone who has done advanced maths in year 12 should be able to follow (there’s a bit of differentiation, that’s all). In this context it strikes me as bizarre that I have not come across such an explanation of the carbon tax outside of class. What is our media doing? The course I’m doing is the equivalent of microeconomics three for undergraduates. We expect our public intellectuals to be able to effectively explain third year political science concepts to us (like multiculturalism or feminism), so we should also expect them to be able to explain third year economics concepts to us. I recall Ross Garnaut expressing anger with the media’s analysis of the tax at the time of its implementation, but I had no idea it was this bad.

Our society is going to have a very hard time managing the increasingly complex policy issues of contemporary society if our media can’t (or won’t?) communicate an idea of this complexity to the public, at least to the educated public.