Existence of equilibria in a basic tax-competition model

While the properties of equilibria in games of interjurisdictional tax competition have been heavily scrutinized, no hard evidence is available that these equilibria exist. Even for the fundamental tax competition game introduced by Zodrow and Mieszkowski [J. Urban Econ. 19 (1986) 356] and Wildasin [J. Public Econ. 35 (1988) 229], only few positive, but arguably restrictive, results have been derived. Applying a weaker concept than the standard Nash equilibrium-the concept of a second-order locally consistent equilibrium (2-LCE)-we are able to show both the existence and uniqueness of a symmetric equilibrium in tax rates, when regions are homogeneous and either (i) there are only two regions, (ii) capital demand curves are concave, (iii) the inverse of the elasticity of the marginal product of capital is not increasing, or firms apply (iv) CES, (v) Cobb-Douglas, or (vi) logistic production functions.