Policy Competition, Factor Mobility and Multiple Policy Instruments: Existence and Non-Existence of Equilibrium

Most existing models of fiscal competition between states within federations or regional unions share at least two common features. First, they focus on inter-jurisdictional competition in but one policy instrument, for example, taxes, public goods or environmental quality. The second is that the models capture policy competition as a game and analyze the nature of the Nash equilibrium without considering existence. We recognize that jurisdictions wish to choose efficient policy packages (Non-malevolence Theorem) and this allows us to examine the existence of equilibrium when there are multiple policy instruments. Sufficient conditions for existence are established followed by three examples. In the first, the sufficient conditions are satisfied, guaranteeing existence. For the second example, the sufficient conditions are not met but an equilibrium exists, while in the third example there is no equilibrium. The analysis shows that existence is by no means assured in fiscal competition models and much depends on the particular specification of the model employed.