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Give All Permits to Polluters Plan

Auction All Permits to Polluters Plan

Other Emissions Allocation Plans and Conclusions


A Comparison of Proposed Initial Allocation Schemes

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.

My next blog entry, Understanding Cap and Trade through Example, Part 2, presented a couple of different initial allocation scenarios for rights to permit, discussed how the costs of achieving emissions reductions varied under the different scenarios, and established that the same pattern of pollution would result under all scenarios, equivalent to that in the minimum cost scenario, but payments for rights to pollute among the utilities will vary across scenarios, depending on the initial allocation of permits.

This blog entry will examine specific proposals for initially allocating emissions permits to polluters and see how their end results differ.  Various emissions reduction plans have been proposed:

  • Give all permits to polluters;
  • Give some permits to polluters and auction the remaining permits to polluters;
  • Auction all permits to polluters and have government keep the proceeds; or
  • Auction all permits to polluters, but return some of the proceeds to the public.

 I think it would help to provide a couple of points of clarification:

First, in the example I’ve been using in this series of examinations of cap and trade, I have assumed the decision has been made to reduce emissions by 13% or 300,000 tons, from a total of 2,972,000 tons of CO2 down to 1,972,000 tons.

The number of permits to pollute at issue in the proposals (“all permits”) corresponds to the tons of emissions utilities will end up emitting after the 13% reduction.  That is, the number of permits to be allocated corresponds to the 1,972,000 tons of emissions that will be left after the utilities have decreased their original levels by the 300,000 tons.

Second, common practice is to assign rights to emit based on historical levels of emissions, both at the regional level, as well as at the source emitter level.  In other words, for the proposed reduction plans listed above, I assume that the default is to assign emission rights to emitters as per the proportional reduction scenario described in Part 2.

Give All Permits to Polluters Plan

Under this scenario, the utilities are currently generating emissions at the original levels of 2.272 million tons (Figure 7, column [C]), and they are granted the right to emit the level of CO2 emissions corresponding to the proportionately reduced levels totaling 1.972 million tons (Figure 7, column [F]).

However, the lowest aggregate cost means of retooling the utilities’ operations to achieve the reduced total level of emissions, 1.972 million tons, is for the utilities to implement the minimum cost reduction scenario presented in Figure 7, columns [G], [H], and [I].

So under this “give all permits for free” scenario, the utilities will end up retooling operations to emit the levels corresponding to those in the minimum cost scenario.  Utilities 1 and 2 will end up emitting more CO2 (1.060 millions tons and 0.787 million tons respectively – see column [I]) than the amounts for which they own permits (0.960 millions tons and 0.746 million tons respectively – see column [F]).  In contrast, Utility 3 will end up emitting less CO2 (0.125 million tons – see column [I]) than the amount for which it owns permits (0.267 million tons – see column [F]).  Utilities 1 and 2 will then buy permits for their respective difference between allotments to emit and actual emissions from Utility 3.

Utility 3 will be willing to sell its extra permits for no less than the costs it incurred to retool operations to reduce emissions by the extra amount, $11.12 per ton ($1.571 million spent to reduce emissions by an extra 141,000 tons – see columns [J], [K], and [L]).  Utilities 1 and 2, on the other hand, will be willing to buy the permits for no more than the costs they saved by not retooling operations to reduce emissions by the difference between the proportional and minimum cost allocations, $38.28 and $23.28 respectively (see columns [J], [K], and [L]).  In other words, the transaction price for the exchange of permits between Utility 1 and Utility 3 will fall between $11.12 and $38.28, while the transaction price for the exchange of permits between Utility 2 and Utility 3 will fall between $11.12 and $23.28

In the end, the aggregate costs of achieving the reduction in emissions under this scenario will be $2.727 million, the retooling costs.  There will also be exchanges of payment for extra rights to pollute between Utility 1 and Utility 3, as well as between Utility 2 and Utility 3, but these “side payments” will be a wash in the aggregate.

More generally, the individual costs to each of the utilities of achieving the reduction in emissions will be highest for those utilities with the highest costs of reducing emissions.  The utilities with the lowest costs of reducing emissions might actually end up better off financially after the reductions, if their costs of reducing emissions are significantly lower than those of the other emitters that are forced to reduce.



Auction All Permits to Polluters Plan

If they had to purchase rights to pollute at an auction, how much would each of the utilities end up paying?

To answer this question, I returned to my earlier calculations.  I calculated the emissions each of the utilities create while generating electricity for their residential customers when they do not have to pay for CO2 emissions.  These calculations (from Part 1, Figure 1), yielded CO2 emissions of

  • Utility 1: 1.1 million MT
  • Utility 2: 0.86 million MT
  • Utility 3: 0.31 million MT

Next, I returned to the cost curves for each of the utilities of reducing emissions.  These costs curves (from Part 1, Figure 2) are provided again here for convenience.



Recall from the previous discussion in Part 1 that these cost curves embody two important concepts:

  1. Reduction in emissions from coal generators is more expensive than reduction in emissions from gas generators, which is more expensive than reduction in emissions from renewable resources generators, and
  2. The cost per unit of reduction in emissions is larger, the greater is the amount of reduction.

Now, let’s say the rights to pollute (i.e., the permits) are auctioned off in batches of 50,000 MT.  From the cost curves in Figure 2, I can calculate how much it would cost each of the utilities to reduce their emissions by successive batches of 50,000 MT from their current levels.  These costs are presented in Figure 9.


So, for example, if each of the utilities were required to reduce emissions from their initial levels (1.11 million MT, 0.86 million MT, and 0.31 million MT, respectively) by 50,000 MT (see row [1] in Figure 9),

  • it would cost Utility 1 $0.50M (column [C]), or $10.00 per MT (column [D]);
  • it would cost Utility 2 $0.31M (column [F]), or $6.25 per MT (column [G]); and
  • it would cost Utility 3 $0.13M (column [I]), or $2.50 per MT (column [J]).

If the utilities were required to reduce their emissions by an additional 50,000 MT (100,000 MT in total), then to reduce emissions by the second batch of 50,000 MT (see row [2] in Figure 9),

  • it would cost Utility 1 $1.50M (column [C]), or $30.00 per MT (column [D]) (for a total cost of $2M for the combined 100,000 MT reduction, see column [B]);
  • it would cost Utility 2 $0.94M (column [F]), or $18.75 per MT (column [G]); and
  • it would cost Utility 3 $0.38M (column [I]), or $7.50 per MT (column [J]).

Again, the idea here is that as the utilities reduce emissions, it cost them more per unit reduction in emissions – the second batch of 50,000 MT of emissions reductions costs more than the first batch of 50,000 MT of emissions, the third costs more than the second, and so on.

By moving down columns [D], [G], and [J], you can see how the costs per batch of reducing emissions by successive amounts is increasing as the number of batches of reductions increases.  You can also see that Utility 1’s costs per batch of reduction are higher than Utility 2’s costs, which are higher than Utility 3’s costs.

As indicated above, the original emissions for each of the utilities are, respectively, 1.1 million MT, 0.86 million MT, and 0.31 million MT.  As such, the relevant costs of reduction for Utility 1 include all 22 batches of reductions in Figure 9 (see blue highlights), while the relevant cost batches for Utility 2 extend through the 17th batch (see yellow highlights in Figure 9), and the relevant cost batches for Utility 3 extend through the 6th batch (see green highlights in Figure 9).

Since the scenario I’m considering here is that for purchasing permits to pollute in an auction setting, the utilities will not end up paying the full costs of reducing emissions for the right to pollute.  Rather, they will only pay what it takes to bid away the permits they need from the other utilities.  To figure out how much it would take to bid the permits away from the other utilities, I took each of the batch prices for each of the utilities (i.e., each of the rows in Figure 9), stacked them, then sorted in decreasing order of cost per permit per batch.  The result is presented in Figure 10, columns [A] – [D].


What Figure 10 says is that if Utility 1 were emitting a total of 50,000 MT, then it would cost $430 per MT for Utility 1 to reduce emissions from 50,000 MT to zero.  That means that Utility 1 would be willing to pay up to $430 per ton to avoid having to reduce emissions to zero, or in other words, Utility 1 would be willing to pay up to $430 per ton for the right to emit 50,000 MT of CO2.

Continuing on, if Utility 1 were emitting 100,000 MT, it would cost $410 per MT to reduce emissions from 100,000 MT to 50,000 MT, and it would cost $430 per MT to reduce emissions from 50,000 MT to zero.  So, Utility 1 would be willing to pay up to $430 per ton for the right to emit its first batch of 50,000 MT of CO2, and it would be willing to pay up to $410 per ton for the right to emit its second batch of 50,000 MT of CO2. And so on.

How much will Utility 1 have to bid (Figure 10, column [E]) to win the right to pollute its first 50,000 MT?  Moving down the rows of Figure 10, we see that the highest price one of Utility 1’s competitors would be willing to pay to emit its first batch of 50,000 MT of CO2 is $206 (see 13th batch in Figure 10).  That means that Utility 1 will outbid its next closest competitor with a bid of $207 per ton for the 1st batch of permits, for the 2nd batch of permits, and on down through the 12th batch of permits.  For its next batch of permits (Utility 1’s 13th batch = the auction’s 15th batch in Figure 10), though, Utility 1 would only be willing to pay up to $190 per ton.  However, Utility 2 would be willing to pay up to $206 per ton to buy Utility 2’s 1st batch of permits, which is the 13th batch in the auction.  So Utility 2 will outbid Utility 1 for the 13th batch in the auction with a bid of $191.

We can move on down each of the successive batches of 50,000 tons to see how much each Utility will have to bid to win the rights to permit from its competitors.

Throughout my examples, I have assumed that the total amount of emissions is capped at 1,972,000 MT, which rounds to 2 million MT.  In this case, the auction portrayed in Figure 10 will end after the 40th batch of emissions permits is sold.  The results of the auction are summarized in Figure 11.


By the end of the auction, Utility 1 will have purchased permits to emit a total of 1,050,000 MT of CO2 (see column [B] of Figure 11) for a total price of $172M (see column [D]), which works out to an average price of $164 per ton (see column [E]), or $429 per household (see column [F]).  Utility 1 would have been willing to pay up to $242M (see column [C]) for the right to emit the 1,050,000 MT, which is the cost Utility 1 would have had to incur to retool its operations to decrease emissions by the 1,050,000 MT.

Note, again, that through the Coase Theorem, after the auction we end up with the same pattern of emissions as that under the minimum cost scenario.  Recall that the minimum cost scenario yielded the pattern of emissions that ends up occurring under each of the alternative permit allocation scenarios examined in Part 2.

We are not yet done, however. As I described in the very beginning of this blog entry, the “all permits” case still involves a reduction in emissions of 300,000 tons relative to the case in which there are no restrictions on emissions.  Utility 1 has paid $172M for the right to emit 1,050,000 tons of CO2.  However, in the very first analysis, that in which there are no restrictions on emissions, we found that Utility 1 would emit 1,105,488 MT.  So now under this auction scenario, Utility 1 must still pay the cost of retooling operations so as to reduce emissions by 55,488 tons (= 1,105,488 – 1,050,000). As we saw in Figure 5C, column [F], these retooling costs amount to $0.413M.  Likewise, in addition to paying for the auctioned off rights to emit, Utilities 2 and 3 will have to pay retooling costs of $0.661M and $1.653M, respectively.  The total costs associated with reducing emissions by 300,000 MT and auctioning off the remaining rights to pollute 2 million MT are displayed in Figure 12.


So the auction will result in the utilities paying a total of $260.2M to emit 2 million tons of CO2, when they were previously emitting 2.3 million tons for free.  With these new operating costs, the utilities will increase their prices to their residential consumers by (at least) an average of $217 per household, though the households receiving power generated from coal will end up with substantially higher price increases than the others.

Other Emissions Allocation Plans and Conclusions

We have now examined the two extreme proposed emissions reduction plans, give “all permits” to polluters and auction “all permits” to polluters, where the “all permits” levels are lower than those that originated under the original unrestricted scenario.

The remaining proposals involve some combination of granting and auctioning permits to emit CO2, with total levels lower than those in the original, unrestricted scenario.  From all the analyses performed herein, we can deduce that the other emissions reduction plans will yield the same final allocation of emissions across the utilities (see, e.g., Figure 12, column [C]), with Utility 1 (the coal user) incurring the highest costs of compliance and Utility 3 (the natural gas and renewables user) incurring the lowest costs.  And since any increases in the costs of operations will be passed along to consumers, the residential users will end up with higher costs in the same patterns as their supplier utilities.

In the case in which government returns some of the auction proceeds to the public, the redistribution of proceeds will offset some of the price increases and tendency to reduce electricity usage, relative to the case in which the government keeps all the money.

It would be natural to assume that residential users bear the increased costs of operation for their respective electricity suppliers.  In other words, in the case of the “auction all permits scenario” represented in Figure 12, customers of Utility 1 will see their residential electricity costs increase by $430 per household per year, customers of Utility 2 will see their residential electricity costs increase by $210 per household per year, and customers of Utility 3 will see their residential electricity costs increase by $11 per household per year. Is this fair?

One could argue that the coal utility customers have been benefitting all along from the cheaper prices associated with coal generated electricity; so it’s fair that when emissions costs are accounted for, they have end up paying closer to what everybody else has been paying.  On the other hand, there’s the issue mentioned previously that other factors than just the resource costs, such as supply, demand, regulations, etc. also affect consumer prices, so that coal customers haven’t necessarily been paying less than gas or clean energy customers.  At the same time, one could argue that assuming local generators supply most of the power used by the local markets, then the coal customers will have been suffering the ill effects of greater local CO2 emissions than customers of other utilities that use cleaner resources.  In this case, charging for emissions it would be a double-whammy for coal customers – not only are they suffering the effects of pollution, but they are also now facing increased costs of doing so.

Finally, there’s the question of who should bear the costs associated with reducing emissions.  By putting a cost on the emissions that utilities generate and allowing them to pass on those costs to users, users of dirtier energy are forced to pay higher prices and encouraged to consume less energy, relative to users of cleaner energy.  So if we want to decrease the use of electricity generated from coal and encourage production of energy generated from renewables, this is the way to go (but probably at the expense of historic coal customers).

Alternatively, if the government reimburses consumers for their higher costs, then the impact of higher prices on decreasing demand for dirtier energy is attenuated.  In this case, the higher costs of electricity are spread across all customers of clean and dirty energy alike.  So coal and renewables customers will all end up reducing demand by “similar” amounts.  This is the way to go if you don’t want to penalize users of coal energy relative to users of renwable energy.

Phew!  What an analysis!  But I sure have learned a lot!  :)

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