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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.
Posted by Tyler Cowen on February 28, 2007 at 06:38 PM in Sports | Permalink
Comments
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.
Posted by: sd at Feb 28, 2007 7:13:36 PM
You don't need it to be zero, that is just a normalization.
Posted by: Tyler Cowen at Feb 28, 2007 7:23:29 PM
You really need to write down the model (I just did here http://www.economics.com.au/?p=678) 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.
Posted by: Joshua Gans at Feb 28, 2007 7:37:09 PM
"This counterintuitive conclusion is one reason why we have economic models."
Or maybe its the reason why the model is most likely wrong? Less profit => fewer coal plants. The marginal costs of new plants is large. The cost of maintaining old ones isnt tiny either.
And what about other externalities - even if we dont actually succeed in reducing the use of dirty fuels, reducing the profits of the bad guys (eg. Russia, Saudi) is an end in itself.
Posted by: Vish Subramanian at Feb 28, 2007 7:57:48 PM
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.
Posted by: Doug at Feb 28, 2007 9:01:16 PM
Joshua Gans,
Correct me if I'm wrong, but I think your model isn't accounting for the changed shape of the marginal revenue curve. It should approach the demand curve along the x-axis, and so might push quantity outwards. Competition reduces the polluter's market power, which has the result of lowering price and increasing quantity. This is intuitive, in fact: the reason why monopolies are bad is because they produce too little, so it would be an odd result if increased competition decreased the output of a firm with market power.
Posted by: ryan at Feb 28, 2007 9:02:36 PM
"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.
Posted by: Ryan Szabo at Feb 28, 2007 9:12:45 PM
Ryan,
You have to think about what competition means. If you move say from monopoly to oligopoly, the monopolist's output invariably falls but total output rises. Here though it is the previous incumbent that is producing the dirty stuff and so we care about them.
To get a monopolist to increase output when their demand curve shifts downward requires contorting that demand curve into funny and less plausible shapes. I just don't see how that would happen in this example.
The argument presented is that that demand becomes perfectly elastic when the sidewalk is built. However, that also means that some customers who were previously willing to pay less for a jetpack are now willing to pay more. That strikes me as implausible.
Posted by: Joshua Gans at Feb 28, 2007 9:27:17 PM
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.
Posted by: ryan at Feb 28, 2007 9:47:45 PM
I dunno, what I would like to do here is:
1) Devise a reasonable equation for the coal demand curve.
2) Devise a reasonable equation for coal supply curve.
3) Assume that everyone gets SOME extra utility (utils/kWH) from renewable energy. Assume this is a gaussian centered at some mean.
4) Just see what happens as the supply curve for renewable energy shifts towards a lower price/higher quantity.
That shift, mentioned in (4), might be a subsidy (as Tyler discusses) or it might just be e.g. technological improvements. I can understand it is theoretically possible that a "good" shift for renewable energy supply curve actually leads to more consumed dirty energy, but it is difficult for me to believe that this is the most plausible state of affairs.
As Tyler says, that's why we have models. (But what I want is a more fleshed out model). I'm not an economist but maybe I will try to do this myself.
Does anyone know whether demand curves are typically exponential, linear, etc.? I'm sure it depends...
Posted by: mk at Feb 28, 2007 10:16:41 PM
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
Posted by: Yan Li at Mar 1, 2007 4:44:15 AM
Like Joshua, I wasn't sure about this, so I wrote down a model. Consider a monopolist facing a linear demand curve and zero marginal cost. Standard maximization. Now introduce a Cournot competitor (the clean energy producer) with a positive marginal cost. It is fairly easy to show that total consumption in the market will rise, but production by the (former) monopolist will decline. The size of the incumbent's supply response is a function of his cost advantage, but it's never so large that the amount of dirty power produced actually increases.
Now, if the interaction is Bertrand...
Interesting topic, good problem.
Posted by: Don at Mar 1, 2007 6:41:06 AM
Tyler,
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?
Posted by: Xmas at Mar 1, 2007 11:18:47 AM
A perfectly valid model, but perfectly beside the point when discussing carbon offsets. Offsets subsidizing clean power may have the counter-intuitive effect of increasing net carbon output, but it will only do so if accompanied by an increase in net energy output. That means more stuff being made and done that people want to have and do. The marginal unit of output will have lower marginal net carbon emissions.
That's a good thing.
Posted by: eddie at Mar 1, 2007 2:11:58 PM
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?
Posted by: Dave Tufte at Mar 1, 2007 4:02:39 PM
Isn't it likely that the monopolist will lose the customers with the greatest price elasticity of demand? In other words, the demand curve doesn't just shift, it changes shape. Intuitively, that suggests that the 4-unit higher price strategy will be best. I'm very far from sure of this, but it does seem that the change in elasticity is important.
Posted by: Bernard Yomtov at Mar 1, 2007 5:39:54 PM
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).
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