The Economic Problem: Market Failure

Switching to energy alternatives is not a terribly difficult issue if the alternative allows direct savings of money for the energy producer. High oil costs make wind-generated electricity directly competitive; even though there may be a high up-front capital cost and uncertainty about future oil pricing, the financing problem is reasonably straightforward. If this were the case across the board for replacement of fossil fuels, we could just go home and let the market take care of everything. But in most cases the costs do not accrue so directly; in fact market incentives continue to favor fossil fuels and particularly coal, for many applications. Nevertheless these threaten huge long-run costs for the world economy as the Stern Review makes clear. Even individual nations may see little benefit from tackling their own CO2 emissions if the big players (China and the US particularly) don't do their part. This turns out to be a clear case of prisoners' dilemma-style market failure. 

A simplified model of the situation is a "game" with N players, of which m players continue polluting and N-m players "quit", so that the costs are:

where 'x' is the cost to each player of ceasing to emit CO2, while 'z' is the cost to each player of full-scale global warming (if everybody continues polluting), and we assume that the global warming costs scale linearly with emissions - for m polluters then m*z/N.

Note that total costs for a given value of m are then:

so as long as x < z, the optimal solution in terms of total costs has m = 0.

However, for a given player, no matter how many 'm' other players are polluting, if that player quits their costs change from

i.e. a difference of (x - z/N).

Therefore, if x < z/N it is in that player's natural interests to quit. But if x > z/N, but still < z, the market incentives push each player to continue polluting, even though the benefits if *everybody quits* are clear.

I.e. if everybody quits, additional costs for each player are x. If nobody quits, additional costs to each player are z which is more than x.

So, the boundary conditions for market failure in the N-player game are:

This is *far* more likely to be the case, if N is large. That's why global warming is one of the clearest examples of market failure you could have. As long as the costs of solution are not tiny, but also not so large as to make solving the problem a bad idea, CO2 mitigation is always going to be an example of market failure requiring government (cooperative) action.
Created: 2007-02-21 23:42:40 by Arthur Smith
Modified: 2007-02-21 23:46:08 by Arthur Smith