Structure of distortion equilibria and welfare in a multiregional economy

Summary We consider a convex economy with multiregions, each region facing different specific tax-subsidies. The model reduces to a model of a closed economy with an aggregate production set when there is a single region. It can also represent a model of an international economy through a reinterpretation of variables. We show that there is a unique path of allocations from a distortion equilibrium to the optimum that can be followed by proportionate changes of price distortions. Welfare monotonically increases as one follows the path towards optimum. The information on the structure of equilibria reduces multidimensional comparative statics into a one dimensional problem. The global Newton method of Smale can be used to follow the path in the direction of increasing welfare, allowing us to do comparative statics computationally. Global considerations directly show that, under a sign condition of the Jacobian of a tax function, piecemeal proportional reductions of price distortions improve welfare. A variation of the condition unifies other such conditions in the literature.I would like to thank William Brock, Takashi Fukushima, Tatsuo Hatta, Michael Jerison, Taesung Kim and referees of this Journal who provided me with many constructive comments and references. Previous versions of this paper were presented at the Far Eastern Meeting of the Econometric Society, the Midwestern Mathematical Economics Conference, and the International Conference of Korean Economists. I wish to thank the participants of these conferences for many nice comments. I also wish to thank Bruce Dieffenbach, Thad Mirer and editors of this journal who helped to streamline exposition.