Carbon taxes are not a costless way to boost the economy

Economists recognise that any choice we make comes with an opportunity cost - for every thing that we choose to do, we are giving up the opportunity of doing something else. This is memorably captured in the acronym TANSTAAFL - There Ain't No Such Thing As A Free Lunch. So, I was interested to read  this article in The Conversation last week, by Mona Mashhadi Rajabi (University of Technology Sydney), about carbon taxes:

A new study has found that a carbon tax, accompanied by “revenue recycling”, can produce both environmental and economic benefits for Australia.

Revenue recycling means money reaped from a carbon tax would be redirected back into the economy. This means the money accumulated from the tax would be redistributed between different stakeholders in the economy without increasing the government’s revenue.

To be more specific, the tax income should be used to support consumption, invest in new research and development projects, and subsidise energy saving and pollution reducing programs. Using this approach makes the tax more politically appealing to companies and other opponents.

So far, so good. But this bit is more than a little surprising:

My study recommends that in the first year, all the tax revenue would be used to support consumption. However, the amount of money allotted to investment would rise from the second year as the carbon tax rate increases. It is estimated that about $57 billion would be available for new technologies over 13 years under this carbon tax.

Imposing a carbon tax would also provide a financial incentive for industry to reduce its fossil fuel use. It would motivate the sector to shift to low-carbon technologies as they would bear a smaller tax bill and reap larger profits.

My study concludes Australia could reduce carbon emissions by 35% while GDP would increase by 0.286% by 2035 and new jobs would be created in research and development. Following the recommended carbon tax design, Australia’s transition to a low-carbon economy would be accelerated, which would benefit both the economy and the environment.

This appears to describe a policy choice with no trade-off. That is, there is no opportunity cost. If the government can tax carbon, pump that money back into the economy to support consumption, and increase consumption and output (GDP), then someone ought to be shouting this from the rooftops. Rajabi is describing a route to infinite consumption. Because, having increased consumption and GDP, the government can then raise taxes again, increasing consumption and GDP by more, and then raise taxes again, increasing consumption and GDP by even more. Repeat this process over and over again, all the way to infinite GDP. Of course, that makes no sense.

To see why, let's consider what happens when you tax a product, and give all of the tax revenue back to consumers as additional income. We'll start with the basic consumer choice model (or the constrained optimisation model of the consumer), as shown in the diagram below. We are using some made up numbers, but the example works the same with other combinations of numbers. The diagram shows the budget constraint for a consumer with income of $1000, choosing between buying carbon goods (with a price of $1), or all other goods (AOG, also with a price of $1). The consumer can choose to consume anywhere on their budget constraint or below it (this is the feasible set). The budget constraint runs from a bundle of goods with no carbon goods at all, and the consumer spending all of their income to buy 1000 AOG, to a bundle of goods with no AOG at all, and the consumer spending all of their income to buy 1000 carbon goods. The slope of the budget constraint is equal to the relative price of the goods (the price of carbon goods, divided by the price of AOG), which is equal to 1 ($1/$1). The consumer is trying to get to the highest possible indifference curve, which is the indifference curve I0 (for more on indifference curves, read this post). They buy the bundle of goods E0, which contains 500 of AOG (costing $500) and 500 carbon goods (costing $500).

Now consider what happens when carbon goods are taxed. Let's assume that the tax is so high that it doubles the price of carbon goods [*]. The effect of this change is shown in the diagram below. The consumer's budget constraint pivots inwards to the red line, and becomes steeper. The slope of the budget constraint is now equal to 2, which is the new relative price of the goods (the price of carbon goods, divided by the price of AOG, which is now $2/$1). If the consumer were only buying AOG (and no carbon goods), they could still buy 1000 AOG. However, if they were only buying carbon goods (and no AOG), they could now only buy 500 AOG. The consumer can no longer afford the bundle E0 - it is outside the feasible set (outside the budget constraint). Instead, the consumer will consume the bundle of goods on the highest indifference curve that they can reach on the new budget constraint. That is the bundle E2, which is on the indifference curve I2, and contains 600 of AOG (costing $600), and 200 carbon goods (costing $400). Notice that the consumer is still spending all of their income, but they have been made much worse off (they are now on a lower indifference curve, meaning that they get less utility from their consumption).

Now let's see what happens if we recycle the tax revenue back to the consumer. The budget constraint remains steep (because the relative price of carbon goods and AOG is still equal to 2), but moves outwards parallel to the previous budget constraint. It doesn't move out all the way to E0 though. At E2, the consumer was paying $200 in carbon tax, so their income goes up by $200, to $1200. The new budget constraint, shown in blue, extends from the point where they spend all $1200 on AOG, buying 1200 AOG, to the point where they spend all $1200 on carbon goods, buying 600 carbon goods. The consumer can now do better than the bundle of goods E2, and reach a higher indifference curve I1, by buying the bundle of goods E1. That bundle contains 700 AOG (costing $700), and 250 carbon goods (costing $500). However, notice that even after the tax revenue has been recycled to them, the consumer is not as well off as they were before the tax was introduced. They may be spending more ($1200 instead of $1000), but their utility is lower.

This demonstrates that there is a cost to this policy. The consumer pays it in the form of lower utility. To be fair, in a sense Rajabi is correct. The consumer is now spending more than before ($1200 instead of $1000), so consumption has increased. But that is an increase in nominal terms. The price of carbon goods has gone up. If we think about the value of the goods that the consumer is buying, at the original (non-taxed) prices, they are only buying $950 worth of goods now (700 AOG worth $700 and 250 carbon goods worth $250), compared with $1000 before the tax was introduced. Or if we think about the value of the goods that the consumer was buying before the tax was introduced, but valued at the new prices, they were previously buying $1500 worth of goods (500 AOG worth $500 and 500 carbon goods worth $1000), but now they are buying $1200 worth. Either way, they are now buying a total bundle of goods that is worth less - the consumer's real income has decreased.

Of course, most people who advocate for 'revenue recycling' are not arguing that every taxpayer would receive back exactly what they paid in the tax. Many prefer that the 'carbon dividend' would be paid only to low income households. That would change the analysis somewhat. First, there would be high-income households for which the analysis looks much like the second diagram - a carbon tax with no offsetting dividend. These households would be unambiguously worse off with the tax. Second, there would be low-income households for which the analysis looks like the third diagram, but with the increase in income from the revenue recycling being much larger. In theory, these low-income households would be better off as a result of the carbon dividend. In other words, the tax would redistribute income from high-income taxpayers to low-income taxpayers. However, it still wouldn't increase the real value of consumption or GDP overall. It would simply redistribute who is doing the consumption spending.

Overall, we can conclude that it isn't possible to simply pump up the economy endlessly by taxing carbon goods and recycling the tax revenue to consumers as additional income. Any analysis that shows this is possible is clearly missing something important. There ain't no such thing as a free lunch.

*****

[*] In reality, this would require a tax of more than 100 percent, because a tax raises the price that consumers pay, but producers share the burden of the tax, so the whole tax amount is not passed onto consumers as a higher price. For more on this, see this post. However, for simplicity we will assume that the entire tax is passed onto the consumer in the form of a higher price. This assumption would affect the exact numbers from the example, but not the overall conclusion.