Saturday, December 16, 2006

Tax Competition and the Core of Justice

A blog reader, motivated by my previous post on French rocker Johnny Hallyday, wonders about the effects of tax competition:

There is a problem with tax competition, when people get away from high-tax regions and move to low-tax regions to maximize their own utility function....If there's no obstacle in politics and regional boundaries, and people could establish a new local governments freely, does there possibly exist an optimal government structure?
Let me put the question this way: If we built a model of pure tax competition, where any individual or group of individuals were free to opt out of a society to start their own, what would the equilibrium look like? And does that equilibrium have anything to commend it?

I don't know of work in this area (although that may reflect my ignorance rather than a hole in the literature). Here are some thoughts on the topic.

There is an old concept in cooperative game theory called the core, which wikipedia defines as follows:

The core of a game is a set of vectors allocating payoffs to players, which preserve the following conditions:

  • Efficiency: it is assumed that the players form the grand coalition (a coalition containing all players), and so the sum of individual payoffs should equal the value of the grand coalition.
  • Strategic stability or balance: no coalition can earn more by defecting from the grand coalition. E.g. no coalition has a value greater than the sum of its members' payoffs.
That seems to be the right concept for a pure theory of tax competition.

What do we know about the core as applied to economic situations? A classic paper by Herbert Scarf ("An Analysis of Markets with a Large Number of Participants", 1962, Recent Advances in Game Theory) showed that the core of economies with large numbers of people converges to the set of competitive equilibria. See also Debreu and Scarf. This core-convergence theorem, sometimes called the Edgeworth conjecture, is often interpreted as showing why competitive equilibria are the natural outcomes even if there is no Walrasian auctioneer calling out prices to balance supply and demand in all markets. In a sense, it gives a bargaining interpretation to the Walrasian equilibria.

Let me give this result an interpretation beyond what Scarf suggested: If we take it as an axiom of justice that people should be free to leave a society, either as individuals or in groups, then the competitive equilibrium is not only efficient but it is also just. In some sense, the core provides an axiomatic basis for the libertarian embrace of competitive market outcomes and rejection of income redistribution (but not completely--see below).

Scarf examined classical exchange economies without pure public goods. Maybe someone has extended this work to the provision and financing of public goods, but I have not seen it. Here is a guess: Under the core concept, taxes would have be set according to the benefits principles. That is, people would pay taxes to fund public goods based on the benefit they receive from those goods. Taxes can rise with income: You can get a rich person to pay more for, say, national defense because he gets greater benefit from it than a poor person does. Progressive taxation would arise if and only if the income elasticity of the demand for public goods were greater than one.

Now let's reconsider income redistribution. Must income redistribution disappear in this world where the core is the accepted concept of justice? Not necessarily. In this case, income redistribution would be possible if those funding the transfer system valued income distribution as a pure public good, as Lester Thurow has suggested. But the argument for redistribution is very different than the utilitarian calculus often used.

Utilitarians are comfortable taking from the rich to give to the poor simply because of diminishing marginal utility. They have problems with people like Mr Hallyday who choose to opt out. For a utilitarian to implement his plan, he has to restrict Mr Hallyday's freedom to exit the system. By contrast, if we grant the premise that no one should be compelled to remain in a society, then people pay taxes to the government only insofar as they get benefits from the government. The resulting theory of distributive justice looks more libertarian than utilitarian.