More fun than chess

Let’s consider a power supplier with market power and zero marginal cost.  Capacity suffices for ten units but five units are sold at p = 10; selling more would lower profits.  Now, using carbon offsets, bribe the fifth buyer to stay out of the market, say by walking to work rather than flying his jetpack.  Even better, just shoot him. 

The company has two options.  It can stick with selling four units and raise price.  Or it could drop price a bit and pick up a fifth buyer again.  Hard to say what will happen.  Alternatively, if buyers stand along a continuum, is there a general proof one way or the other? 

Rather than bribing the fifth buyer to walk, invest the "carbon offsets" money in building a nice comfy sidewalk.  In principle all buyers could walk on this new path.

It is then easy to see how the power company might lower price and expand to six units or more.  Otherwise they might lose all their customers.

A key question is the cost structure of the alternative clean technology.  Non-scalable technologies, with little potential for expansion, are the least likely to backfire and least likely to lead to more dirty power.  Scalable technologies, such as the sidewalk, are most likely to backfire and make the world dirtier.  They require a bigger competitive response on the part of the dirty power supplier.  (At least in the short run this is true, in the longer run the scalable technology might eliminate dirty power altogether.)

This counterintuitive conclusion is one reason why we have economic models.


Counter-intuitive perhaps, but useless. Marginal cost for a coal fired plant is not zero. The is a substantial cost for pulling coal out of the ground.

You really need to write down the model (I just did here That argument is wrong. The alternative clean technology shifts the demand curve facing the dirty monopolist in. Both price and quantity fall. The end result is a cleaner world.

OK, I've read the two posts (plus a lot of the other stuff on the other websites about Al Gore's offset payments), and, IMHO, the offsets work much like the two MR posts describe (i.e. they don't really move the needle and may be counterproductive to boot).

HOWEVER...there is another economic prism to view this through, the corporate economic model. A "rational" corporation will not pursue a project if the net return on investment is less than the cost of capital to finance the project. Right now, projects that directly remove CO2 from the atmosphere (i.e. sequestration in salt mines, planting trees, etc.) does not produce an economic profit, because no one is paying the company to remove said CO2 (at least in the U.S., with the exception of CO2 injection to improve oil well yields). Many of these carbon offset programs fund these "non-economic" projects, which does directly remove CO2, without affecting the supply-demand balance for power.

A cap-and-trade program would make offset programs moot in this respect, because CO2 will become a commodity with VALUE, rather than a "free" waste product. (I imagine that the best uses for carbon offsets in this environment would be to buy CO2 allowances in the open market, thereby driving up their price and making more CO2 removal projects economical under the cap-and-trade program)

Of course, verification and auditing are the key factor in offset programs' success, since the potential for abuse is high.

To ramble on some more, cap-and-trade is notoriously difficult to pull off worldwide, since there are sovereignity issues on top of "leakage" issues on top of political gamesmanship issues (which is killing the EU program right now - nobody wants to drop the hammer for non-compliance). A fuels-based program might be more feasible.

"Rather than bribing the fifth buyer to walk, invest the "carbon offsets" money in building a nice comfy sidewalk. In principle all buyers could walk on this new path."

I'm sorry Professor Cowen, but i'm having trouble understanding this part of the example. What exactly is the incentive for the 5th buyer to choose not to buy? I realize that it's necessary to have a more practical solution than bribing(or shooting, haha) the 5th buyer, but im failing to understand what that may be in regards to the Carbon offsets which would finance public projects--something in which everyone would enjoy the benefit. If this at all seems like common knowledge for the typical reader here please excuse me, I'm still merely an undergrad economics student.

On a side note, if you're not careful you may evolve into a public commentator with all these posts discussing reader questions. It's really a great idea connecting with the viewers of your site, and giving them a small stake in the community here. Kudos.

Joshua Gans,

I don't think it requires contorting the demand curve at all. I'm simply saying that the marginal revenue curve's slope necessarily decreases in absolute value terms (flattens) when market power decreases. The increasing competition means that the incumbent firm becomes less of a price setter and so has more of an incentive to produce additional units.

I have difficulties visualizing the model. Here is what I've got
- Carbon offset, "an" alternative technology to carbon, leads to a shift-in of the carbon demand curve, i.e., everyone is tempted by a lovely walk or a nice metro ride in some way
- The marginal revenue curve for the carbon monopolist also shifts in because of the shift of the demand curve
- The profit-maximizing monopolist will cut price AND produce less according to the shift of its marginal revenue curve
- The market will end up in 4 carbon consumers and a p<10


Is there a real world example of this sort of thing?

I'm thinking maybe paper production may fall under this model.

How has the market for regular paper moved with the addition of recycled paper and electronic mail as viable alternatives?

1) The original post could be clearer ... but

2) I think the problem with Josh Gans' model is that it assumes that the monopolist stays a monopolist. My impression is that Tyler is driving at the possibility that buying carbon offsets might, in the limit, drive the incremental mark-up to zero, as in perfect competition. This is important because firms with market power operate at a lower production level than is technically efficient. This leads into the point of the argument that has been ignored in the comments:

3) There is more latitude for unusual outcomes if the technology is scalable. Most power suppliers have some market power, and some unused capacity. Carbon offsetting is competition, an increase of which will generally push them to start producing more with that capacity. This is similar to Don's Bertrand suggestion. The cute thing is, this is all a non-issue if production isn't scalable at the carbon producer you go after.

4) Lastly, is this posted in the "Sport" category because the sport aspect is Tyler sending us off on a scavenger hunt for results?

It's a nice example. For anyone still puzzling over the sidewalk, consider the similar case making a new technology available to everyone that produces electricity at small marginal cost. The monopolistic maximizes profit by undercutting this, and producing 10 units.

This is different from bribing/shooting the fifth buyer, which shifts the demand and/or marginal revenue curves left by one unit. With continuous quantities and typical assumptions the profit-maximizing quantity of dirty power is reduced (but not necessarily -- e.g. if marginal revenue is upward-sloping it could be increased). toshiba portege m300 battery,

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