Part V: Impact of 2020 limits

The previous posts showed the calculations for the revenue collected in the short-run (up to 2012), where the time frame is too short for the producers to change the means of production (no changes in the supply curve) and the consumers respond only to the price, but cannot alter their demand habits (i.e., no shift in the demand curve, just going up and down) . Over the longer time-frame, the consumer habits can certainly change, and the long-run elasticity has been estimated to be 0.7 for electricity. The emissions reduction is expected to be 17%. If we assumed that the producers are unable to change their production mix at all (not a realistic assumption, but this will provide the worst case, highest cost answer), then once again, the price of carbon can be estimated using the relationships described in part IV.

Interestingly, even though the limits for 2020 are ~6X the limit for 2012, the price increases from $24.5 to only $39.5, ~60%. The reason for this significantly lower increase is the higher value of elasticity of demand for electricity over the long run.

Part IV: Elasticity of Demand and the Price for CO2

In this section, the carbon price is evaluated using the elasticity of demand of electricity*. The elasticity of demand for electricity has been estimated to be ~0.2 in the short run, and ~0.7 in the long run. In subsequent calculations, the short-run value of 0.2 is assumed for calculations, providing a conservative estimate of the reduction in the emissions. In the short-run (2009-2012), it is unlikely that there will be significant deployment of any new technology for electricity generation, and therefore, the entire reduction in emissions has to occur through a reduction in consumption. The WM targets are a 3% reduction in the emissions, and therefore, we have:

DQ/Q (for electricity) = 0.03

Elasticity =0.2

--> DP/P (for electricity) =0.03/.2=0.15

Therefore, electricity is 15% more expensive due to WM. Since this 15% increase in electricity price is entirely due to the carbon price, the price of carbon may be estimated as:

DP/P=0.15 ==> DP = 0.15*P = 0.15*0.1 ($/KWhr)= $0.015 /KWhr

1KWhr = 1.35 pounds of CO2 = $0.015

1 Ton = 2204 pounds of CO2 = 2204*0.015/1.35 = $24.5/Tonne of CO2.

This value is clearly higher than the floor price used in earlier calculations ($10), indicating that the "fundamental value" of a CO2 permit is ~$25 in the period up to 2012. The estimates for periods beyond 2012 are fraught with uncertainty, because of the following reasons:

(1). Higher (and uncertain) elasticity of demand

(2). Possible role for deployment of new technologies (though 10 years seems relatively small from a utility context. However, other possibilities, such as plug-in hybrids could indeed be deployed faster, resulting in faster changes in demand).

Since the actual CO2 price is $25 per tonne, the price increase per household is now 24.5/10*73.5 ~ $180 per household per year.

*Elasticity of demand refers to the % change in demand of a good due to a specific % change in price. For details, see here.

Part III: Revenues from Cap and Trade (Floor Price = $10)

The revenues from cap and trade can be estimated in a straightforward manner by estimating the area of the shaded rectangle in the figure below.

The price increase per household is $73.5 per year, and there are 110M households in the country, leading to $8.5B/year. This calculation is for carbon emissions from electricity only. The total size of the carbon markets can be estimated as ~6B Tons of CO2 at $10 being ~$60B in the early stages.

Part II: Limits to CO2 Emission

Carbon dioxide emissions may be reduced by two means: (1). Limits (2). Taxes. The difference between the two approaches is whether we choose a vertical control or the horizontal control in the supply-demand diagram, and they both have their pros and cons.

Limits on CO2: Caps

Let us first consider limits (or "caps") on carbon emission. Intuition tells us that if the limit is higher than the amount currently emitted, then the CO2 price is zero, and there is no change in the amount of CO2. So, the first requirement is that the limit set should be less than the amount emitted. This might seem obvious, but could pose problems during early stages of implementation if the emitted amounts are not known with a high degree of confidence. In fact, this uncertainty wreaked havoc in the European Emissions Trading Scheme (EU ETS) , where prices collapsed after it was discovered that the caps were set too high.


Fig. 2. Price of energy vs. the quantity of CO2 emitted in the presence of a limit (Cap). In this case, the price of electricity = marginal cost + cost of CO2.

When the limits are set lower than the current levels of emission, then equilibrium requirements dictate that the price of electricity has to rise sufficiently such that the intersection of the demand curve with the limit is now the price of electricity. Since the cost of the electricity by itself (production cost) has not changed, the difference between the two horizontal lines is therefore the cost of CO2.

Now, cost estimation can be done given the limits and the demand curve. Since limits are not set yet, and the obtaining the demand curve is non-trivial, we have to resort to other means for estimation. We can use the range of prices observed in the European market as a guide to estimate. (Note that the CO2 price is completely determined by the limits being set and the demand curve, and therefore, the regulator can choose any value such that the price falls in a desired band.)

The calculations are given below, along with the assumptions and the sources of the data.


Therefore, under the simple assumptions that we listed above, the average house-hold is likely to spend $6.13 per month higher once the legislation is introduced. If the carbon price increases, the amount will also increase. The plot below shows the linear relationship (Additional amount spent = 0.613*Price per Ton of CO2) between the carbon price and the additional amount to be spent by the household.

Micro-economic Analysis of Waxman-Markey bill: Part 1: No Limits

I haven't seen an analysis of the provisions in the Waxman-Markey bill in terms of basic supply and demand. This post is also an attempt to make back-of-the-envelope calculations on how much the individual household has to pay additionally if Waxman-Markey is implemented. This post is a bit wonky, but should be accessible to a lay person. Any comments and suggestions are welcome.

Let us first consider the relatively simpler case of power generation. We first start with the assumption that the producers of electricity have a constant (marginal) cost (The implications of relaxing this assumption will be addressed in subsequent posts). For example, the (marginal) cost of electricity is ~$0.12/KWHr.

Fig. 1. Price vs. Quantity, assuming a constant marginal price for energy. The intersection of the two lines is the equilibrium price (same as the marginal price) and the equilibrium quantity, which is the quantity that will be consumed.

The demand curve (which is the curve representing the quantity demanded Q at any price P) is downward sloping, as the demand is likely to be high if energy is cheap. For example, people drive more (resulting in more demand for energy) when gas is cheap and less when it is more expensive.

Note: One could argue that nobody demands CO2, and therefore this whole argument is flawed. However, even though CO2 is a pollutant, which is a "bad" rather than a "good" that we actually want, supply-demand arguments are still applicable. This is because the CO2 is actually a byproduct of the good that we seek, which is energy.

In the absence of any limits the quantity of CO2 emitted is the equilibrium quantity, which happens to be 5.6 GigaTons in the US (~44,000 lbs of CO2/per person). In the next post, we will focus on limits and the basis for determination, taxation vs. cap and trade etc.

Preventing Windfalls to the Polluters

Here is a piece that argues that, even the Waxman-Markey bill has allocations to regulated utilities, it is able to preserve the carbon price, and therefore, the bill is appropriate. The key distinction appears to be that the permits are given to the distribution company rather than the generator.

Carbon Pricing and Avoided Deforestation

It is rare that there is positive news on the environment, but this economist article points out an actual case where the"financial innovation"may have actually helped save the rainforest. The carbon sequestration capability of the rainforest is pegged at 1Tonne per hectare, and the world wide acreage of the rainforest is quoted as being 1B Hectares. Therefore, the monetary value of the Carbon permits sold amounts to $10B worldwide. Now, the US timber industry alone has $30B in revenue, so, the question is: Is carbon pricing sufficient to ensure that forests are not destroyed? It appears that additional externalities due to forests (benefits such as habitats for animals and plants, and prevented losses, such as soil erosion) may need to be factored into calculations to ensure that the forests are not destroyed.

Krugman Part II: Taxes vs. Cap and Trade

Krugman argues that cap and trade is better than taxes, particularly from a verification perspective. He points out that it is going to be difficult for anyone to check whether a specific firm in China was taxed for its carbon emissions or not, but it will be easier to verify that the total emissions have been reduced by China if they relied on the cap and trade mechanism. It is not clear to me how the verification of whether a given firm has actually paid carbon taxes (which should be in the company's financial statements, presumably) is more difficult to verify than whether the same company did actually do the activity that enabled it to get the carbon credits to trade (This would likely need a full scale carbon audit). While I am in favor of cap and trade over carbon taxes, verification does not appear to be a factor that favors cap and trade over carbon taxes.

Krugman on China and Climate Change

Krugman proposes a "Carbon Tariff" on imports from China, and presumably any other country that does not accept a cap on its emissions. This could be a good bargaining chip to encourage developing nations to join in climate change reduction initiatives, but as Lord Stern noted, it may amount to only 1-2% of the overall cost of any imported good, and may not achieve meaningful reduction in emissions or a difference in the sourcing strategies of companies. If that is the case, then it may marginally reduce consumer demand for goods without any additional impact on GHG emissions.

The Energy and Climate Change Bill Progresses (slooowly...)

It appears that the Waxman-Markey bill is coming out of committee finally. The lobbying efforts appear to have been quite successful, with the breakup as follows:

(1). Utilities : 35%
(2). Energy Intensive Industries (Steel, Aluminum, and Cement): 15%
(3). Refineries: ??
(4). Auto: 3%

So, in all, more than 50% is of the credits are already spoken for. This is almost exactly along expected lines. The key is the sunset provisions for these credits, whether they expire automatically, or not, a point that Felix Salmon addressed earlier.

Good Old Fashioned Rent Seeking

WSJ reports that industries are pushing for free pollution credits. This is a huge giveaway from the government to the industry if it happens, with the consumer paying the difference in costs anyway. Since the motivation is clearly political, one option is to have the give away a small portion, say 20% of the credits for free, and have them phased out on an annual basis in the next 5-10 years. This could result in securing the votes necessary to pass the deal, and have the expectations set for the rent-seekers in the industry that their rent is going away in the near future. Of course, Congress has a checkered record in dealing with sunset provisions, so perhaps it is not viable.

Alternatively, the government could auction 100% of the credits, and give the producers cash (from the proceeds) which would clearly be unpopular in the long run, and politically indefensible (or at least less defensible, considering farm subsidies are not that different, and they have been around for a while).

Either way, the cap and trade legislation is an excellent Economics 101 primer. A somewhat technical analysis of this legislation is provided here.

Lord Stern's Approach

The influential Lord Stern believes that use of carbon tariffs on imported goods is just "covert protectionism". He seems to be more in favor of cap and trade, and part of the reasoning seems to be that it will lower cost of compliance.

However, I think this is not universal. Let us consider a case where offsets are freely tradeable across international boundaries, and where each country has a specific target to meet. If a major carbon producer finds itself short, then the demand for carbon in that market rises, increasing the price of the offsets. This would lead to migration of the offsets from other countries into this country. Since offsets play a significant role in meeting emissions targets in most markets, this would lead to an increase in compliance costs for all the other producers as well.

So, while the overall cost of compliance may come down, all the different entities may not see a reduction in the price. In fact, if USA came online and started demanding CDM credits similar to Europe, the likely scenario is that the cost of compliance will go up for the Europeans. So, this might be a good time to buy the guaranteed CERs or the CER futures.

Price Floor for Carbon

Michael Grubb of Carbon Trust and a member of the UK Committee talks about the price floors built into the EU carbon markets through the use of auctions with a minimum set price. However, since the EU Emissions Trading System (ETS) allows trading of validated credits from the developing world through Kyoto's Clean Development Mechanism (CDM), and the overall demand for carbon has dropped substantially, the floor may not have the intended effect. In order for the price floor to be effective, the supply of the CDM credits should also be substantially reduced. This does not seem to be an appropriate time for reduction of CDM credits, as the these credits could potentially help the developing world mitigate the negative impact of the global financial crisis.

Carbon Tax vs. Cap and Trade

The carbon tax center, not surprisingly, is in favor of a carbon tax, rather than cap and trade. The cap-and-trade proposals are being discussed in Australia currently, and the mood is clearly against cap-and-trade as well. Even Tom Friedman seems to be against cap-and trade, though for different reasons. However, as MicroEconomics 101 tells us, you go for limits if you are (a) clear as to what the limit should be rather than the price (b) The limit is enforceable. I think both of these factors point to a well-designed cap-and-trade scheme rather than a carbon tax.

An additional factor that has not got much attention is the fact that, in the presence of offsets, (assuming they are allowed after Copenhagen), one could see the emergence of a global carbon price. If the offsets are cheaper than carbon permits in the domestic market, then the demand for carbon offsets would rise, increasing their price, and achieving an equilibrium with the different carbon markets around the world. This could lead to a lower cost of compliance, although this lower cost of compliance will likely benefit the producers rather than the consumers). I haven't seen an analysis of this effect, so I will be scouring the literature to see the effects.

Over the counter vs. Exchange Traded

It appears that the bankers would like carbon trading to be over the counter in addition to being exchange traded. Over-the-counter refers to the trading done through market makers where the buyer and seller are trading directly without an intermediary such as an exchange. The argument is as follows:

"Granville Martin, vice-president for environmental affairs at JP Morgan, said access to OTC contracts was critical for bank financing. “You can’t scale up carbon finance without OTC markets,” he said.

For example, a utility wanting to build a power plant would only get a loan if it could hedge its long-term carbon and fuel risks. In many cases, he said, an appropriate contract is not available and, moreover, the utility would have to tie up a huge chunk of capital with the exchange as collateral.

For such contracts, investment banks would often be the only counterparty, and they could manage the risk by, for instance, taking a second lien in the power plant rather than upfront cash.

Forcing such trades through exchanges would add a significant hurdle to low-carbon development, and would be pointless if the reason was just to ensure transparency, Martin said.

“If the concern is ‘dark corners’ you can come up with solutions. You can have disclosure and preserve OTC,” he said."

I agree that financial innovation is likely to foster the rapid growth of the carbon markets. Unfortunately, the rapid growth of CDS and CDOs, and the pain they brought, as well as the financial innovations of Enron are too fresh in memory to believe that the different players will opt for transparency and full-disclosure. Setting up appropriate regulatory structure is going to be critical in determining not only the growth of the carbon finance industry, but also its ability to withstand systemic shocks.

The Problem with multiple goals

Greenpeace is apparently against inclusion of forest conservation in a market-based mechanism for reducing greenhouse gases (GHGs) on the grounds that industry will continue spewing carbon offset by avoided deforestation carbon credits. I think that if your goal is to reduce overall carbon emitted, you should actually be pleased that industry can find a source that is both cheap and helps preserve the natural habitat. Greenpeace is caught between its twin goals of reducing overall carbon emissions *and* reducing industrial emissions in particular, and it is clear that the two goals are not always aligned.

Becker, Murphy and Topel on economics of climate change

Becker, Murphy and Topel have an interesting take on the economics of climate change. They state here that "the expected benefit from climate change policies is actually more sensitive to a very small probability that global warming results in a catastrophe than to a change in the discount rate". They appear to be in favor of limited action through small broad-based carbon tax that could be ramped up over time.

However, if there is a very small probability of a catastrophic event (essentially tail risk) and if global warming has some positive feedback (in the non-judgemental engineering sense of the word), then there is no way to know this probability*the expected loss, and therefore, the expected value calculations could be off significantly. If the recent financial crisis has highlighted one thing, it is that people are terrible at tail risk assessment. Given that people are unable to appropriately assess tail risk, it seems to me that Pascal's wager arguments would suggest that we should be more actively pursuing climate change mitigation. Taleb makes a similar point here.

Welcome Post

I am interested in learning about the economics and finance of carbon trading. I expect this area is going to attract significant attention in the near future, given the interest in Congress to pass climate change legislation, as well as the Copenhagen conference later this year to discuss the successor to the Kyoto Protocol. Stay tuned for future posts on this topic.