Viable economic states in a dynamic model of taxation

Viability theory is the study of dynamical systems that asks “what is the set of initial conditions that generate evolutions, which obey the laws of motion of a system plus other constraints, for the length of the evolution”. We apply viability theory to Judd’s (JPE, 1987) dynamic tax model to identify which economic states are viable, in that the application of annually constrained tax-rate adjustments result in non-explosive and non-implosive evolutions of capital, consumption and debt. The set of such states we call the economic viability kernel. We observe, unsurprisingly, that a very high consumption economy lies outside such kernels, at least for annual tax-adjustment levels limited by 20%, and that, generically, the higher the capital, the higher the consumption levels that can be sustained. Furthermore, we notice that the sizes of the kernel slices, for a given taxation level, do not diminish as the tax rate-rate rises, hence high taxation economies are not necessarily more prone to explode, or implode, than their low taxation counterparts. In fact, higher tax rates are necessary to keepmany consumption choices viable, when capital approaches the constraint-set boundary. We also see that raising the debt limit increases the viability kernel; however, for the economy to remain viable at the high debt levels, capital has to be maintained large. . 18th INTERNATIONAL CONFERENCE ON COMPUTING IN ECONOMICS AND FINANCE Prague, Czech Republic, June 2729, 2012