Lindahl Equilibrium Versus Voluntary Contribution to a Public Good: The Role of the Income Distribution

Lindahl equilibria are often seen as an ideal outcome of cooperation in a public-goods economy. But it has also been observed that, if no transfer payments are possible, the Lindahl equilibrium may not be Pareto-superior to the Nash outcome of the voluntary-contribution game. We derive conditions under which agents (or countries in the case of an international public good) will prefer the Lindahl over the Nash solution. In particular we show that rich agents in general are better off in the Lindahl equilibrium than in the voluntary-contribution equilibrium. When the exogenously given income distribution is not skewed too much or the original economy is replicated sufficiently often, all agents will gain by the move from the Nash to the Lindahl outcome. The underlying effects are related to the famous exploitation of the rich by the poor countries occurring in Nash equilibrium (which follows from Warr neutrality) and the fact that the underprovision of the public good in Nash equilibrium is particularly serious in large economies. Finally, we tentatively discuss some potential applications concerning international cooperation on global public-good provision.