Blog-Normal Distribution - Analytic lessons and random observations by John Sall, JMP creator and SAS co-founder

In my Earth Day blog post last week, I introduced some claims that actions on price were better than actions on quantity in the carbon market. Now it is time to back up those claims.

The main tool of economic thinking is supply and demand curves. Let's draw hypothetical supply and demand curves for carbon in carbon fuels. Economists reverse the usual X and Y and put price on the Y axis and quantity on the X axis. At low prices, people are willing to buy more carbon; and at high prices, people will buy less, substituting other goods (alternative energy) or withdrawing (energy conservation).

Thus, we have the red demand curve. Supply has the reverse slope, with low prices reducing supply and high prices increasing supply (the blue line). Where the curves cross, we have where the price and quantity are determined, at point A, with quantity 50 and price 50.





Now consider a charge on carbon sourcing. OK, it is a carbon tax, but please don't let the word tax scare you.

The carbon tax just shifts the supply curve upward by the amount of the tax, 20, resulting in a new supply curve, the orange line. The new supply curve crosses the demand curve at point B now, resulting in a smaller quantity (40) and higher price (60).

The alternative to a carbon tax is a carbon cap, restricting quantity to not exceed a cap of 40, the green line. Actually, the supply curve is the gray-shadow that begins with the blue line, but then turns straight up at the green line. The new capped supply also crosses the demand curve at quantity 40 and price 60. We have constructed the lines to show that you can set the tax at an amount that would be equivalent to some cap.





Suppose that we have fluctuations in the economy, business cycles, booms and recessions. These things do happen, you know. In recession, the demand curve shifts down, with less quantity demanded at a given price. In a boom, the demand curve shifts up, with more quantity demanded at a given price. This variation is represented by the three red demand curves below.

Now see how the different supply curves change the solution. With a carbon tax (orange supply curve), we have the price quantity solution varying from B up to D1 in a boom, and down to D2 in a recession -- resulting in prices varying between 55 and 65.

If we have a cap (the green line) instead of a tax, then the three demand curves change the solution from B down to C2 and up to C1 -- resulting in prices varying between 50 and 70.





I don't know the true locations of carbon supply and demand, but we don't have to know to make some conclusions. A vertical supply curve (the cap) will always produce more-variable prices than any positively sloped supply curve. The cap produces the maximum price variation possible for any non-negatively sloped supply curve.

What about total carbon consumed between a cap and a tax? The cap's quantity will be fixed, assuming the economy is not so bad that demand is less than the cap. The tax's quantity will be variable, but it can be designed so that the average quantity produced is the same as the carbon cap. Just imagine the variations between the three red lines, and the quantity solves between 35 and 45, with a long-run mean of 40, the same as the cap. Carbon goals are long term. We need to limit the average carbon emitted; we don't care whether carbon emissions vary some from year to year.

So the mean carbon emitted is the same between cap and tax, but the price variation is much higher for the cap. The goal is to limit carbon emissions. But the way you get to the goal is through alternative energy and energy conservation. There is no other mechanism. And the economic driver for alternative energy and energy conservation is price. We have to have higher energy prices to solve demand to lower quantity, whether through a cap or a tax.

Energy conservation and alternative energy are structural changes driven by investments. For example, when gasoline prices are high, like a year ago, we tend to buy high-mileage cars. And when gasoline prices are low, like now, we tend to buy bigger cars. When prices are high, we make long-term investments in solar and wind energy. When prices are low, we don't. It's not good business. But investments are decided on variability as well as price. Why invest in a solar farm if prices are so variable as to make that investment risky? We need stable prices, as well as high prices to make the structural change happen.

Carbon taxes produce more stable prices than carbon caps do. History on previous caps back that up. The CBO study, "Policy Options for Reducing CO2 Emissions," which I referred to in my previous post, notes that sulfur-dioxide emission permits had prices that varied much more than the economy. And EU carbon credits collapsed to half the price that prevailed six months earlier, as reported in the issue of the journal Nature that I also mentioned last week.

The Waxman climate-change bill only specifies a cap of 3% below 2005 levels by 2012. Will that make prices high enough to stimulate investments in energy conservation and alternative energy? 2005 was a huge boom year, and we are unlikely to demand that much energy unless we have another huge boom economy. Therefore, I would expect almost no price support by then for alternative energy or energy conservation.

Of course, support for alternative energy and energy conservation can be in the form of subsidies. Subsidies are an inefficient manipulation of the market. The economy adjusts far more efficiently to real prices than it does to subsidies. We want people and businesses to invest in energy conservation and alternative energy because energy prices are high enough for that to make solid business sense. Let the market do what it will. Let taxes that account for externalities (commons costs) make the adjustments we need to supply.

What happens later when the economy booms again? Then we have a huge price impact from a cap, and this is so worrisome that the Waxman bill has a strategic carbon reserve ready to unload more emissions credits to auction when needed. This makes for an unpredictable wiggle to the right of the cap. It is better than not having it, but a smooth supply curve would be much better.

You still might not want a carbon tax because it is new tax burden. Well, a cap is even more of a burden; you either have ineffective limits or even higher energy prices. Carbon taxes can be returned to taxpayers, per capita, to make them revenue-neutral. Caps could also, if the emissions credits were auctioned and the proceeds distributed, but that is not the current plan. The current plan needs to be changed.

There is much more to say in future blog posts about the reserve, market manipulation, time-banking, operational considerations and international issues.