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Using Game Theory to Optimize the Pace of New Technology Adoption
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Proportional Reduction Scenario

Equal Reduction Scenario

Minimum Cost Reduction Scenario

Discussion of Alternative Reduction Scenarios

 

 

Alternative Emissions Reduction Scenarios

My previous blog entry, Understanding Cap and Trade through Example, Part 1, described how CO2 emissions associated with the generation of electricity from different types of inputs (coal, natural gas, renewable resources) are calculated, how utilities achieve reductions in emissions, and how under the requirement that utilities must reduce emissions, they are better off if they can buy and sell rights to pollute, as opposed to being forced to retool operations so as to achieve reduced emissions on their own.  Now that we have a better understanding of the basics of emissions reductions, let’s consider some alternative scenarios.

Proportional Reduction Scenario

Return to the example from Part 1.  From Figure 4, we have total emissions for the 3 utilities of 2.37 million MT.  We want to reduce their total emissions by 300,000 MT, or 13%.  The current consensus is to initially grant (or sell) permissions to pollute in proportion to current levels of pollution.  As this applies in our example, to achieve a 13% overall reduction in emissions, the 3 utilities would each initially be granted rights to pollute for 1 – 13% = 87% of their original emissions (see column [E] in Figure 5A).  That is, Utility 1 would be granted the right to emit 960,000 tons of CO2, Utility 2 would be granted the right to emit 746,000 tons, and Utility 3 would be granted the right to emit 267,000 tons.

As for the remaining 13% of emissions (see column [D] in Figure 5A), the utilities would then be forced either to retool their systems so as to reduce their emissions by this amount, or to purchase emissions permits from other utilities.  (Utilities will be willing to sell their permits to others if the costs of reducing their emissions are less than the costs other utilities would be willing to pay for those rights to pollute.)

 fig_5A

Utility 1 must now either retool his operations and/or buy some of the rights to pollute given to the other utilities, so that in the end he has reduced his own emissions and/or he has purchased the right to pollute from the other utilities for/by a total of 146,000 tons (see column [D] in Figure 5A).  The same goes for Utility 2, which must reduce its emissions and/or buy permits to pollute for/by a total of 114,000 tons and Utility 3, which must reduce its emissions and/or buy permits to pollute for/by a total of 41,000 tons.  If each of the utilities were to pay to retool their operations so as to reduce emissions by the required amounts, it would cost them a combined total of $5.953M (see column [F] in Figure 5A).

Since Utility 1 emits the most CO2, under the proportional reduction scenario, it will face the highest reduction in CO2.  And since Utility 1 also faces the highest costs of reducing emissions, it will end up spending much more than the other utilities to meet the reductions requirements (see columns [F], [G], and [H] in Figure 5A.  Assuming the utilities pass their cost increases onto their customers in the form of price increases, then under this proportional scenario, Utility 1’s customers face the highest price increases.

On the other hand, electricity generated from coal is less expensive than electricity generated from gas, which in turn, is less expensive than electricity generated from renewable (excluding nuclear) sources.  Bloomberg New Energy Finance  produced the following very cool comparison of the pre-subsidies cost of producing energy using alternative inputs (the chart was taken from an article in the WSJ: “Clean Energy Sources: Sun, Wind and Subsidies” by Jeffrey Ball ):

 

cost_altv_power

So if all else is the same, Utility 1’s customers will originally have been paying lower prices for electricity than were Utility 2’s customers, which, in turn, will have been paying lower prices than were Utility 3’s customers.  In this case, the forced reduction in emissions will end up making all customers pay more for electricity, though they will now be paying more similar amounts.

A complication is the fact that supply and demand conditions, as well as subsidies and tax breaks, vary across markets and energy input types.  This means that coal plant customers don’t necessarily end up paying less than gas plant customers, and gas plant customers don’t necessarily end up paying less than customers using energy generated from renewable sources.

Equal Reduction Scenario

Now suppose that instead of the proportional allocation just described, a reduction in emissions is achieved by requiring each Utility to reduce its emissions by equal amounts.  In the case of a 300,000 ton reduction, this “equal reduction” scenario would force each utility to reduce emissions by 100,000 tons (see column [D] in Figure 5B). Under this scenario, as seen in column [E] in Figure 5B, Utility 1 would be granted rights for 1,005,000 tons of emissions, Utility 2 would be granted rights for 760,000 tons of emissions and Utility 3 would be granted rights for 207,000 tons. If each of the utilities were to pay to retool their operations so as to reduce emissions by the 100,000 tons each, it would cost them a combined total of $3.750M (see column [F] in Figure 5B).

fig_5B

Under this equal reduction scenario, since Utilities 1 and 2 will end up reducing their emissions by less than their proportional share, their total costs of reduction under this second scenario will be less than that under the previous scenario.  The reverse holds true for Utility 3.

Minimum Cost Reduction Scenario

Given that it is decided that CO2 emissions must be reduced by 300,000 tons, the minimum cost way of achieving this result is presented in Figure 5C.

 fig_5C

Under this scenario, most of the reduction in emissions is borne by Utility 3, the utility with the lowest cost of reducing emissions.

Discussion of Alternative Reduction Scenarios

A summary of the three alternative reduction scenarios is illustrated in Figure 6.

fig_6

To clarify, Figure 6 compares the amount of emissions that the utilities would be required to cut from their operations (bars, left axis), together with the costs associated with retooling their operations to achieve these cuts (line, right axis) when utilities are not permitted to buy and sell rights to emit CO2.

Under a cap and trade system, however, the same total amount of emissions can be eliminated, but at a lower cost to utilities and consumers than those shown in the figure for the proportional and equal allocation scenarios.

In Figure 6, the minimum cost scenario shows the amount by which utilities will actually end up reducing their emissions under a cap and trade system by retooling their operations, together with the costs associated with the retooling.  Understand, though, that under a cap and trade system, Utilities 1 and 2 will end up paying more than just the cost of retooling indicated in Figure 6.  They will also spend additional funds to buy rights to pollute from Utility 3.  Likewise, Utility 3 will end up paying less than the costs of retooling, because it will be able to offset some of the retooling costs with funds it receives from selling rights to emit CO2 that it did not use to Utility 1 and 2.

In effect, then, the actual realized total costs associated with reducing emissions under a cap and trade system will fall somewhere between the costs of retooling under the minimum cost scenario and the costs of retooling under the initial allocation scheme (e.g., proportional or equal allocation).

In sum, then, according to the Coase Theorem, regardless of the initial allocation of permits, under a perfect information and low transactions costs scenario, the utilities should end up actually retooling their operations to reduce their emissions by the amounts shown in the minimum cost scenario in Figure 6.  The utilities will then buy, in the case of Utilities 1 and 2, or sell, in the case of Utility 3, rights to pollute for the difference between the actual reduction achieved by retooling and the reduction required by the initial allocation scheme.  In other words, who ends up polluting how much will be the same under all initial allocation scenarios.  What will be different will be the amount of money that utilities lose or gain from buying or selling permits.

Applying these concepts to the example, Utility 1 is initially allocated fewer rights to pollute under the proportional allocation scenario (960,000 tons – see Figure 5A, column [E]) as compared with under the equal allocation scenario (1,005,000 tons – see Figure 5B, column [E]).  As per the minimum cost scenario, we know that Utility 1 will end up reducing its emissions by 45,000 tons (see Figure 5C, column [D]), regardless of the initial allocation scheme.  As such, Utility 1 will end up paying more to buy rights to pollute under the proportional allocation scenario (under which Utility 1 will buy rights to emit 100,000 tons – see Figure 5D, column [E] – at a price ranging from $11.12 per ton to $38.28 per ton – see Figure 5D, column [F]), than it will under the equal allocation scenario (under which Utility 1 will buy rights to emit 55,000 tons – see Figure 5D, column [H]  – at a price ranging from $14.09 per ton to $29.09 per ton – see Figure 5D, column [I]).  The exact amount that permits will end up being bought and sold for will depend on how liquid the market is and/or the amount of leverage the buyer or seller has (where leverage depends on the alternatives available to the buyer and seller, together with the amount of information on retooling costs and other permit buy/sell options available to the buyer and seller).

fig_5D

Continue on to Part 3.

Return to Part 1.

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