Cross-border shopping and commodity tax competition in imperfectly competitive markets

This paper studies price competition between two firms and tax competition between two governments by using a spatial model under the assumption of imperfect competition. With considering firms' fixed location and cross-border shopping, consumers try to take advantage of price or tax differentials and each government which maximizes the tax revenue on the basis of Leviathan model may attempt to induce cross-border shoppers into its own country by lowering its own tax rate than the competitors. This corresponds to the idea of tax competition which is the process of lowering tax rates to induce cross-border shoppers. This is a two-stage noncooperative game in which two firms compete independently in prices in the second stage and then two governments compete noncooperatively in taxes in the first stage. In this Nash noncooperative game, there exists symmetric or asymmetric Nash equilibrium which depends on cost structures. In particular, tax differential between governments implies 'asymmetric Nash equilibrium' in a noncooperative game. In our model, assuming imperfect competition and in particular, considering the case of different production costs, it is shown that tax differential stems from the difference in costs between two firms. This difference in tax rates induced by cost differential provides a major incentive not only for consumers to engage in cross-border shopping but also for governments to compete in taxes noncooperatively.