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Carbon taxes and the Marginalists’ difficult idea

Summary:
This Economists' Statements on Carbon Taxes has been signed by a host of prominent economists: Global climate change is a serious problem calling for immediate national action. Guided by sound economic principles, we are united in the following policy recommendations. I. A carbon tax offers the most cost-effective lever to reduce carbon emissions at the scale and speed that is necessary. By correcting a well-known market failure, a carbon tax will send a powerful price signal that harnesses the invisible hand of the marketplace to steer economic actors towards a low-carbon future. II. A carbon tax should increase every year until emissions reductions goals are met and be revenue neutral to avoid debates over the size of government. A consistently rising carbon price will encourage

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This Economists' Statements on Carbon Taxes has been signed by a host of prominent economists:

Global climate change is a serious problem calling for immediate national action. Guided by sound economic principles, we are united in the following policy recommendations.

I. A carbon tax offers the most cost-effective lever to reduce carbon emissions at the scale and speed that is necessary. By correcting a well-known market failure, a carbon tax will send a powerful price signal that harnesses the invisible hand of the marketplace to steer economic actors towards a low-carbon future.

II. A carbon tax should increase every year until emissions reductions goals are met and be revenue neutral to avoid debates over the size of government. A consistently rising carbon price will encourage technological innovation and large-scale infrastructure development. It will also accelerate the diffusion of carbon-efficient goods and services.

III. A sufficiently robust and gradually rising carbon tax will replace the need for various carbon regulations that are less efficient. Substituting a price signal for cumbersome regulations will promote economic growth and provide the regulatory certainty companies need for long- term investment in clean-energy alternatives.

IV. To prevent carbon leakage and to protect U.S. competitiveness, a border carbon adjustment system should be established. This system would enhance the competitiveness of American firms that are more energy-efficient than their global competitors. It would also create an incentive for other nations to adopt similar carbon pricing.

V. To maximize the fairness and political viability of a rising carbon tax, all the revenue should be returned directly to U.S. citizens through equal lump-sum rebates. The majority of American families, including the most vulnerable, will benefit financially by receiving more in “carbon dividends” than they pay in increased energy prices.

Although there are differences between their preferred model and the federal Liberals' backstop program (for example, the part about a carbon tax replacing regulations), the basic structure is the same: a carbon tax whose proceeds are remitted back in the form of cash transfers. This is one of those policy issues where economists are broadly in agreement.

To an economist, the mechanics are straightforward. The tax increases the relative price of greenhouse gas emitting activities, and the rebate serves to offset the income effect of the tax. The reduction in emissions is brought about by a substitution effect induced by the new price signal. But unless you're economist, those last two sentences probably read as impenetrable jargon.

This is a problem, not least because the federal Conservatives and their provincial allies are saying things like this:

Scheer

It may be good politics to describe the recipients of rebates as being exempt from the tax, but it's definitely subtracting from public understanding. And even though the federal Liberals like to congratulate themselves for their reputation of expertise in communications, they are - once again - unable to actually explain how their policy works. 

As I said, this is a problem. Kevin Milligan has been running this as his pinned tweet for a few months now: 

Kevin challenge

So far, my favourite example of this art form is from Blake Shaffer:

Shaffer

But I don't think these quick explanations are having much effect; the only people with whom they resonate seem to be people who already understand how the model works in the first place. It turns out that the underlying economics of the tax-and-rebate program are very hard to explain to non-economists.

The title is a reference to Paul Krugman's classic essay "Ricardo's Difficult Idea", on another economic idea that seems straightforward to economists but not to anyone else:

The idea of comparative advantage -- with its implication that trade between two nations normally raises the real incomes of both -- is, like evolution via natural selection, a concept that seems simple and compelling to those who understand it. Yet anyone who becomes involved in discussions of international trade beyond the narrow circle of academic economists quickly realizes that it must be, in some sense, a very difficult concept indeed.

Most economists are probably constructing a graph that looks like this in their heads to represent the tax-and-rebate model: 

Clip_image004_thumb212

I grabbed this image from the internet; I didn't even try to construct one on my own. This is second-year microeconomics textbook material, and I assumed - correctly - that someone, somewhere would have posted this diagram. 

Krugman again:

To a trained economist, the basic ... model seems almost trivial...

And yet if one tries to explain the basic model to a non-economist, it soon becomes clear that it really isn't that simple after all. Teaching the model, to docile students, is one thing: they get the model in the course of a broader study of economics, and in any case they are obliged to pay attention and learn it the way you teach it if they want to pass the exam. But try to explain the model to an adult, especially one who already has opinions about the subject, and you continually find yourself obliged to backtrack, realizing that yet another proposition you thought was obvious actually isn't.

Indeed.

A common criticism of the carbon tax backstop goes like this: "What is the point of taking tax revenues away and then giving it all back again? People will just carry on as before and nothing will happen to GHG emissions." It's not always clear if this question is asked in good faith or if it's an example of the argument from incredulity rhetorical fallacy. But even if you try to answer in good faith, you'd get bogged down very quickly.

Here is how a trained economist might explain how the carbon tax-and-rebate model affects households in terms of that graph:

Let X represent all GHG emitting activities, and Y represent all other activities that don't emit GHGs. The line PL is the original budget constraint, with optimal choice Q yielding utility associated with indifference curve IC1. The tax on X rotates the budget constraint in to PL", reflecting the increase in the price of X relative to Y, the rebate shifts the constraint out to GH, which is parallel to PL" and passes through Q. Although Q is still feasible, it is no longer optimal, because the indifference curve IC1 is no longer tangent to GH. The new optimum is S, which is strictly preferred to Q, and which provides an increase in welfare because the indifference curve through S - IC2 - lies above and to the right of the original indifference curve IC1. The reduction in X is equal to the distance KM. So we conclude that the tax-and-rebate model reduces greenhouse gas emissions while making people better off.

What could be simpler?

It is at this point one begins to appreciate the contributions of the people behind the Marginal Revolution of the mid- to late-nineteenth century. Our practice of talking about marginal benefits and marginal costs - that is, the extra costs or benefits incurred by making infinitesimal changes around a certain starting point - seems like the obvious thing to do for economists, because we've been trained to think that way. But this is clearly not an obvious approach for non-economists.

One criticism of the carbon tax - and again, it's not clear to what extent this point is raised in good faith - is that there's no point in trying to get people to substitute away from fossil fuels because there are as yet no feasible substitutes to take the place of fossil fuels in our society. From the marginalist perspective, this is a not a serious objection: there are any number of ways people can make marginal adjustments to their lifestyles in order to reduce emissions. You don't have to completely abandon fossil fuels, just reduce your consumption of them.

Two important concepts that come out the marginalist perspective are marginal costs and marginal benefits: the additional costs or benefits incurred from a marginal increase in its use. This is a powerful insight, but it's also one that throws up a significant barrier to public understanding - namely, calculus. If you understand differential calculus, then marginal analysis is fairly straightforward. But if you don't, then you can only get as far as graphs like the one above will take you, and that isn't very far.

Of course, you don't need calculus to understand the tax-and-rebate model; you don't even need that graph. All you need is to understand that for people and firms, the optimal choice is to set the ratio of the marginal benefits to the ratio of marginal costs:

Mbmc

It's actually a bit simpler here, because the marginal cost is just the price:

Mbp

If the carbon tax was only thing that was going on, households and firms would have to change their behaviour, simply because they couldn't afford to carry on as before. But if they received the appropriately-sized rebates, they could use use that extra income to pay the tax and carry on as before.

But here's the thing: they won't want to carry on as before.

A rebate might make it possible to carry on before, so that the ratio of marginal benefits doesn't change. But since the carbon tax will increase the ratio of prices, that old ratio of marginal benefits will now be less than new ratio of marginal costs. The new optimum will be one that aligns the ratio of marginal benefits to the ratio of marginal costs, either by increasing the marginal benefit of GHG emissions, by reducing the marginal benefit of everything else, or both.

Here's where declining marginal benefits comes in. If the marginal benefits of GHG emission are decreasing, then a higher level of emissions will reduce the marginal benefit. But that's just another way of saying that if you decrease GHG emissions, then their marginal benefit will increase. And if this reduction in emissions is accompanied by a substitution to something else, then the declining marginal benefits of other activities will decrease. This combination of a rising numerator and a falling denominator will increase the ratio of marginal benefits until they equal the ratio of prices.

I'm under few illusions about how many non-economists - especially non-economists who are heavily invested in denouncing carbon taxes - will be convinced by these arguments. After all, we've been trying to explain Ricardo's theory of comparative advantage - which is also based on a comparison of two ratios - for centuries now, and with very little to show for it.

But that doesn't mean we should stop trying, either.

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