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Climate Change: Department of "Huh?"

Greg Mankiw hopes Obama vetoes a cap-and-trade bill. His column, with emphasis added:

A Missed Opportunity on Climate Change: The danger in a cap-and-trade system is that the permits to emit greenhouse gases are given away for free.... How much does it matter? For the purpose of efficiently allocating the carbon rights, it doesn’t. Even if these rights are handed out on political rather than economic grounds, the “trade” part of “cap and trade” will take care of the rest. Those companies with the most need to emit carbon will buy carbon allowances on newly formed exchanges. Those without such pressing needs will sell whatever allowances they are given and enjoy the profits that resulted from Congress’s largess.

The problem arises in how the climate policy interacts with the overall tax system. As the president pointed out, a cap-and-trade system is like a carbon tax. The price of carbon allowances will eventually be passed on to consumers in the form of higher prices for carbon-intensive products. But if most of those allowances are handed out rather than auctioned, the government won’t have the resources to cut other taxes and offset that price increase. The result is an increase in the effective tax rates facing most Americans, leading to lower real take-home wages, reduced work incentives and depressed economic activity....

As for me, I hope the president refuses to sign a bill that fails to auction most of the allowances. Some might say a veto would make the best the enemy of the good. But sometimes good is not good enough.

I have been trying to think of a model of the economy in which Mankiw's claim is true. I am not having an easy time doing so.

The simplest model has two tax rates, a tax rate on labor income tl and a tax rate on carbon tc which is correcting for a pollution externality of v per unit of carbon emitted. And let λl and λc be the slopes of the supply curves for labor and carbon, respectively.

Then the Harberger triangles associated with the tax on labor and the tax on carbon are:

Hl = λltl2

and:

Hc = λc(v-tc)2

We currently have a tax on carbon of zero. We don't think that a zero tax on carbon is where we should be right now, do we? It is good to raise the tax on carbon whether you use the revenues to reduce the tax rate on labor or whether you distribute them in some other way. Only if our tax on carbon were already equal to the pollution externality v, and we were thinking of raising it even higher, would it be a bad bet unless we used the revenues to reduce the tax on labor income--or if our tax on carbon was inescapably also a tax on labor income via joint production.

There are, I think, some very strong assumptions about the form of the production function and the demand for and supply of labor underlying Mankiw's claim: for his claim to be true, production has to be joint or nearly joing. Nearly every way of employing labor from playing Peruvian shepherd pipes in the public square to making aluminum via a Hall process powered by low-pressure steam generated by the combustion of lignite must involve nearly the same carbon footprint. And I can't figure out why he thinks that the production function takes that form...

My Varian micro book has to be around here somewhere... And there also should be a Stiglitz-and-Dasgupta that answers all these questions in one of these filing cabinets...

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