Clean economic models

Tyler Cowen strangely argues that alternative clean options make the world dirtier. To which my reaction is what?????? Here is what he says:

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.

How about we actually use a formal model? We have a monopolist selling costly transportation with a demand function p(Q; ALT) for quantity sold, Q, and depending upon the availability of an alternative option, ALT. Marginal costs of c so the monopolist’s profit is (p(Q; ALT) – c)Q. Cowen argues that by building an alternative option, price will fall and quantity will rise. Not true.

Take the derivative of the profit function with respect to Q. You get:

(dp/dQ)*Q + (p(Q; ALT) – c) = 0

Now if you increase ALT this has two effects. First, the second term falls (by definition, consumers are less willing to pay for the dirty option) and so quantity is reduced. Second, the first term is related to the price elasticity of demand for the dirty option. If the alternative option makes demand less price elastic that term also goes down. Once again, quantity falls. Even if it had made it a little more price elastic the same thing would have occurred.

So price AND quantity are lower. What do you know consumers are unambiguously better off because of the competition.

The point is that it is the same marginal customer that would drive the quantity choice just as if you took out that customer and shot them! And that is why we have economic models. They make the world cleaner.

3 thoughts on “Clean economic models”

  1. You’ve made a sign error.

    If the alternative makes demand more inelastic, quantity will unambiguously decrease. If it makes demand more elastic (and this effect is sufficiently large), then quantity may increase.

    This is exactly what Tyler is arguing — his sidewalk example is a case where the alternative makes demand for dirty power much more elastic.

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  2. Steve,

    You are right in my haste I interpreted the elasticity condition incorrectly. Nonetheless, the basic result is that when demand curves shift down, price and quantity fall.

    Indeed, what would have to happen for the ALT option to make demand so price elastic that quantity rises? It would seem to me that it couldn’t cause an everywhere fall in demand to even have a chance of getting the effect that Cowen was asserting as a general one.

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