The second best

When looking at many of the discussions of claims of some form of market failure and how governments can fix things, I wonder if this is one area where partial equilibrium modelling can leads us astray. While the use of taxes or subsidies may, in theory, correct a failure in a single market the question has to be asked, What effect does this have in general? It is here that the theory of second best can ruin the day of our would be market failure fixes.

It is well known that the attainment of a Paretian optimum requires the simultaneous fulfillment of all the optimum conditions. The general theorem for the second best optimum states that if there is introduced into a general equilibrium system a constraint which prevents the attainment of one of the Paretian conditions, the other Paretian conditions, although still attainable, are, in general, no longer desirable. In other words, given that one of the Paretian optimum conditions cannot be fulfilled, then an optimum situation can be achieved only by departing from all the other Paretian conditions. The optimum situation finally attained may be termed a second best optimum because it is achieved subject to a constraint which, by definition, prevents the attainment of a Paretian optimum.

From this theorem there follows the important negative corollary that there is no a priori way to judge as between various situations in which some of the Paretian optimum conditions are fulfilled while others are not. Specifically, it is not true that a situation in which more, but not all, of the optimum conditions are fulfilled is necessarily, or is even likely to be, superior to a situation in which fewer are fulfilled. It follows, therefore, that in a situation in which there exist many constraints which prevent the fulfillment of the Parteian optimum conditions, the removal of any one constraint may affect welfare or efficiency either by raising it, by lowering it, or by leaving it unchanged. (R. G. Lipsey and Kelvin Lancaster, The General Theory of Second Best, The Review of Economic Studies, Vol. 24, No. 1 (1956 - 1957): 11-2)

So even if the use of a tax or subsidy may appear to have removed some market failure in a single market it may cause more trouble that it is worth in a general equilibrium setting.