A Carbon Tax vs. the Personal Income Tax

According to my back of the envelope calculations, at current government spending and fossil fuel consumption levels a $.67/kg tax on the carbon content of fossil fuels could replace the income tax. This should be a conservative dream come true: in return for a doubling of residential electric bills and an extra $2 for a gallon of gasoline, we get to do away with the personal income tax! Not only that, we also get to cut the trade deficit and bankrupt those pesky Arabs. It seems too good to be true.

And it might be. My calculations did not take into account the effect of conservation and increased use of renewable energy – which is the whole point of a carbon tax from an environmental standpoint.

The Laffer Curve and a Carbon Tax

Suppose people reduce their usage by 25% at the tax rate proposed. Then, we would need to adjust the tax rate upward to make up the shortfall. But when we do that, people will conserve more. So we need a higher rate yet. There may be a rate high enough that allows us to replace the income tax, or there may not. Welcome to the world of the Laffer Curve.

The answer to this question cannot be found without doing the experiment. But we can make an educated guess. In the chart below I estimate what energy price increases are needed to replace the income tax. First, I raise the carbon tax rate so that the new rate times the reduced amount of carbon burned equals the desired revenue target. I then multiply this rate by 3 kg/gallon to get the estimated impact on the price of a gallon of gasoline. Finally, I estimate the additional cost per kilowatt hour of electricity.

Estimating the impact of a carbon tax with conservation on the price of electricity is tricky because a significant amount of electricity is currently generated by non fossil fuels sources, roughly 1200 out of 4000 terawatt hours according to the EIA. In the chart below, I assume that conservation is proportional for all uses. So if f is the fraction of carbon still consumed after conservation, then:

price = carbon tax rate * 640 * f / (1200 + 2800 * f)

That is, I assume all carbon reduction for electricity is accomplished through conservation or home generation. This is a decent short term assumption. For a longer term projection, we would need to figure in the cost of new alternative energy power plants. Since we already have significant "alternative" energy for electricity, conservation can keep electricity prices in check even as conservation requires us to up the carbon tax rate.

(Oh, and a note to economists: I used average costs vs. marginal costs for estimating electricity retail price increases. In an open market, this would be a questionable assumption. Instead, we would likely get higher energy costs reflecting the increase marginal rates due to a carbon tax, with alternative energy produces getting a windfall. But since utilities are regulated, such windfalls would be kept in check.)

Tax rate required to raise $1.000 trillion given various conservation rates
Given a Conservation Rate ofRequired Carbon Tax RateAdditional Cost per Gallon GasolineAddition Cost per kw-hr Electricity
0%$0.67/kg
=$606.06/ton
$2.00/gallon$0.11/kw-hr
10%$0.74/kg
=$673.40/ton
$2.22/gallon$0.11/kw-hr
20%$0.83/kg
=$757.58/ton
$2.50/gallon$0.12/kw-hr
33%$1.00/kg
=$904.57/ton
$2.99/gallon$0.14/kw-hr
40%$1.11/kg
=$1010.10/ton
$3.33/gallon$0.15/kw-hr
50%$1.33/kg
=$1212.12/ton
$4.00/gallon$0.16/kw-hr
60%$1.67/kg
=$1515.15/ton
$5.00/gallon$0.18/kw-hr

To determine if replacing the income tax is feasible, read the chart in reverse. Look at the tax rates for a line on the chart. Estimate how much people would conserve if energy prices are at that level. If this is less than the conservation rate in the left column, then the carbon tax will work at that level as a replacement for the income tax.

For example, if people are determined to avoid the tax, they can quickly cut their energy use by car pooling, driving less, wearing long underwear in the winter, etc. Suppose these result in a quick 33% drop in carbon burning. Then we'd need roughly a dollar per kg carbon tax to fully displace the income tax. The question is: will the dollar rate cause people push harder yet to conserve? Will this rate cause solar to be competitive?

In the long term the answer is yes. But it will take a while for people to make the switch. So a carbon tax might work as a temporary replacement for the income tax. Further down the road, other taxes would be needed to supplement the carbon tax, or the federal government would need to cut spending.

Spending cuts are an option. The U.S. government currently spends huge amounts of money keeping the sea lanes open to oil tankers. The current war in Iraq is largely over oil. If we truly commit to burning less oil, we could take our soldiers home and save big bucks. Also, the income tax itself causes a huge number of social harms, which require government programs to mitigate. The income tax hurts small business, increases unemployment, and drives healthcare costs through the roof. These problems increase the need for welfare spending and other social programs.

On the other hand, a carbon tax might be regressive. It is a consumption tax, and consumption taxes hit hardest those who spend all their income as they receive it. If so, a carbon tax could increase the demand for welfare programs, which brings us to our second problem: liberals might object to a carbon tax.

A Progressive Carbon Tax

Is a carbon tax regressive? How does carbon use scale up with income?

Big houses do use more energy than small houses. But big houses tend to be more energy efficient per square foot than small houses. Surface area of a solid object goes up as the square of its linear dimension. Volume goes up as the cube (third power). Thus big objects retain heat better. This is why polar animals tend to be big. Small animals freeze to death. The same goes with houses. Therefore McMansions tend to be cheaper to heat and cool per volume of home space than a mobile home. Furthermore, such houses are better insulated. On the other hand, apartment buildings are bigger yet, and many of the poor live in apartments. On the third hand, many poor people live in old housing, which is not well insulated, or in trailers which can be terrible. Balanced on the big toe, McMansions are currently the subject of a big income tax break, which would go away if there were no income tax...

Similar uncertainties arise with transportation. Hummers and other gargantuan SUVs are playthings of the upper classes. Then again, so are hybrid cars. Many poor people are driving old full sized cars. On the other hand, many poor people ride the bus. On the third hand, motor yachts and private jets are very carbon intensive playthings of the rich.

A carbon tax would hit industry pretty hard, but elimination of the income tax would be a boon. Construction jobs should go up, as people add solar collectors and insulation.

Farms use a great deal of energy, but farms also have plenty of sunlight for solar and biomass for burning. Diesel engines can be made to run off of plant oils.

All in all, I cannot say whether a carbon tax would be progressive or regressive. Here is a good project for those who like to do in depth economic studies. This is a job for a think tank or government agency. Neither will get it exactly right, but either could do a much better estimate than I could.

In the meantime let us explore a possible fix: a rebate. This is the same idea used by the Fair Tax folks to make their national sales tax idea less regressive. Take a fraction of the tax proceeds and give out a citizen dividend. This performs the same function as the personal exemption and the standard deduction, except that the proceeds go to all citizens, not just identified taxpayers. Under our current systems non-workers get government money as well, but through different channels.

For example, for 2007, a single person had a $5,350 standard deduction and a $3,400 personal exemption, making the first $8,750 tax free. At a 10% tax rate this was the equivalent of a $875 rebate. For a couple, the standard deduction is $10,700 and two exemptions come out to $6,800, which makes the first $17,500 tax free. At 10% tax rate this is the same as a $1,750 rebate or $875 each. Each child is worth another $3,400 exemption plus a $1,000 tax credit. At 10% tax rate this is equivalent to a $1,340 rebate.

If a carbon tax is flat or even regressive, however, we need use a figure greater than 10% to compute the required rebate needed to make a carbon tax equivalent to the income tax for the poor.

Once again, we need a think tank or government agency to do a better job of crunching the numbers. I'll just give some round number example. Suppose we were to offer every citizen a $100/month rebate on their carbon tax—this includes children and non-working adults. With a 300 million population this comes out to $360 billion extra we would need to collect before rebate.

$1.36 trillion / 1.5 trillion kg = $.91/kg of carbon marginal cost

Our table now looks like:

Tax rate required to raise $1.000 trillion with a $100.00/month rebate given various conservation rates
Given a Conservation Rate ofRequired Carbon Tax RateAdditional Cost per Gallon GasolineAddition Cost per kw-hr Electricity
0%$0.91/kg
=$824.24/ton
$2.72/gallon$0.15/kw-hr
10%$1.01/kg
=$915.82/ton
$3.02/gallon$0.16/kw-hr
20%$1.13/kg
=$1030.30/ton
$3.40/gallon$0.17/kw-hr
33%$1.35/kg
=$1230.21/ton
$4.06/gallon$0.19/kw-hr
40%$1.51/kg
=$1373.74/ton
$4.53/gallon$0.20/kw-hr
50%$1.81/kg
=$1648.48/ton
$5.44/gallon$0.22/kw-hr
60%$2.27/kg
=$2060.61/ton
$6.80/gallon$0.25/kw-hr

But maybe we need to go higher on the rebate. Let's run the numbers with a $150/month rebate:

Tax rate required to raise $1.000 trillion with a $150.00/month rebate given various conservation rates
Given a Conservation Rate ofRequired Carbon Tax RateAdditional Cost per Gallon GasolineAddition Cost per kw-hr Electricity
0%$1.03/kg
=$933.33/ton
$3.08/gallon$0.16/kw-hr
10%$1.14/kg
=$1037.04/ton
$3.42/gallon$0.18/kw-hr
20%$1.28/kg
=$1166.67/ton
$3.85/gallon$0.19/kw-hr
33%$1.53/kg
=$1393.03/ton
$4.60/gallon$0.21/kw-hr
40%$1.71/kg
=$1555.56/ton
$5.13/gallon$0.23/kw-hr
50%$2.05/kg
=$1866.67/ton
$6.16/gallon$0.25/kw-hr
60%$2.57/kg
=$2333.33/ton
$7.70/gallon$0.28/kw-hr

And a $200/month = $2400/year rebate:

Tax rate required to raise $1.000 trillion with a $200.00/month rebate given various conservation rates
Given a Conservation Rate ofRequired Carbon Tax RateAdditional Cost per Gallon GasolineAddition Cost per kw-hr Electricity
0%$1.15/kg
=$1042.42/ton
$3.44/gallon$0.18/kw-hr
10%$1.27/kg
=$1158.25/ton
$3.82/gallon$0.20/kw-hr
20%$1.43/kg
=$1303.03/ton
$4.30/gallon$0.21/kw-hr
33%$1.71/kg
=$1555.86/ton
$5.13/gallon$0.24/kw-hr
40%$1.91/kg
=$1737.37/ton
$5.73/gallon$0.25/kw-hr
50%$2.29/kg
=$2084.85/ton
$6.88/gallon$0.28/kw-hr
60%$2.87/kg
=$2606.06/ton
$8.60/gallon$0.32/kw-hr

The higher we go with the rebate the more we help the and the happier we make environmentalists happy as we have boost up the marginal cost of fossil fuels. If we really jack up the rebate, we could get rid of some of the welfare programs to the able-bodied. An unconditional citizen's dividend is worth more to the poor than an equivalent welfare check since it doesn't penalize work, marriage, or saving.

But the higher we go with the rebate, the harder we run up against the Laffer Curve. We would have to be even more aggressive with government spending cuts and/or other sources of tax revenue to supplement the carbon tax. This could make liberals unhappy. And a carbon tax might still be regressive at the top end.

Too Good to be True?

All in all, I think using a carbon tax to replace the income tax is a bit too good to be true. The potential benefits are indeed very good, nay wonderful. These benefits far outweigh the costs of conservation and alternative energy, even if the global warming is a false alarm. The U.S. could stop being a nation of accountants and lawyers and go back to being a can do nation of tinkerers and entrepreneurs. But alas, I fear that we would run up against the Laffer Curve limits faster than Congress could cut spending. And then there is the issue of a carbon tax being regressive at the top end.

Fortunately, a carbon tax could replace another tax, one that is smaller and already regressive. A carbon tax can play a vital portion of the tax reform puzzle.