A Justification for Government Interference in Pollution

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Although not a recent phenomenon, the particular flavor of the times (temporarily pushed under the rug over concern for the economy) is what should be done about global warming. Topics have included carbon cap and trade agreements, green energy grants and requirements, etc. One thing I think that is important to discuss is whether government regulation could effectively create a positive solution for the climate change problem.

To begin, I'll have to posit some assumptions, for which if one were to disagree with would inherently prevent the same conclusions I am about to draw from being reached:

(1) Pollution has a negative impact on everyone's health, yet remains unpriced because of a tragedy of the commons scenario and an incapability of observing its true cost

(2) Ceteris paribus, a firm earning a profit has positive externalities for society in so much that either through direct distribution or wealth trickle down effects, people are better off (i.e. profit seeking is positive for society, all other things staying equal)

(3) Earning a profit is not a zero sum game, in that if someone is making money someone else does not have to be losing money.

To start off, I think it's important to think of a basic scenario of two polluting companies, G and E. These two companies produce the exact same product for the same market, and the only two choices available to them are whether they're going to implement capital intensive pollution control devices, or not. This breaks out in to a game theory problem.

The picture above represents the payoff matrix for firms G and E in the market described earlier

We'll say that the market is fixed in terms of demand and whichever company can produce the product the cheapest is going to capture the entire market. In the case where the cost of producing the good is the same for the two firms, they will split the market. In splitting the market in the 'Not Pollute' scenario, both firms' payoffs are less than in the 'Pollute' scenario because of the cost of the pollution limiting capital expenditures, let's presume.

The payoff matrix is quite simplistic, but the goal is to convey that in a situation where the winner is the company that can produce the product the cheapest, the Nash equilibrium is going to be that the firms will pollute (in this case, [4,4]).

Now this might not be the most beneficial situation for society, based on the cost we place on pollution (or value on clean air). Let's say cost of pollution to society is 10, such that even though the firms in aggregate would be making a profit of 8 in any combination involving pollute, society as a whole would be incurring a negative payoff even with the addition of this 8 of profit.

In this scenario, it might be in the best interest of the society (of course not for the companies individually) for the government to require a certain level of pollution control, thus forcing the [2,2] payoff to be the Nash equilibrium by preventing the choice of pollution. Presuming this 10 cost is eliminated in this scenario, there's a positive 4 aggregate payoff where before there would have previously been a negative 2.

This can generally be summarized such that the government should intervene when the aggregate payoff from not-polluting is greater than polluting, or:

Er(Diminished G and E earnings, bureaucracy costs, no pollution payoff) ≥ Er(Heightened G and E earnings, pollution cost)

Conclusion

While this is a fun way to look at the problem, it doesn't address the fact that we still don't have a price for pollution. Some have tried in this department, but you will still have difficulty valuing some of the side effects not directly related to human health (i.e. how do you value things like biodiversity?).

In addition, although the bureaucracy cost of implementing said regulation should be a considered cost, it is very likely that the group determining if and how we should regulate (the bureaucracy) might not consider this cost or might dramatically undervalue it.

In light of this, while it is theoretically easy to determine whether to regulate, the inputs of the equation are still unknown. To an investor involved with the G or E firms of the world, a big chunk of the valuation of your investment is determining what the likelihood is that those making decisions will determine that the left side of the equation is greater than the ride side i.e. the value they and their constituents place on clean air. Perhaps this is why in a Democratic regime coal burning utilities and other environmentally questionable investments have gotten crushed.