Which economic states are sustainable under a slightly constrained tax-rate adjustment policy

Viability theory is the study of dynamical systems that asks what set of initial conditions will generate evolutions which obey the laws of motion of a system and some state constraints, for the length of the evo- lution. We apply viability theory to Judd’s (JPE, 1987) dynamic tax model to identify which economic states today are sustainable under only slightly constrained tax-rate adjustments in the future, when the dynamic budget constraint and consumers’ transversality condition at infinity are satisfied. We call the set of such states the economic viability kernel. In broad terms, knowledge of the viability kernel can tell the planner what economic ob- jectives are achievable and assist in the choice of suitable controls to realise them. We observe, unsurprisingly, that a very high consumption economy lies outside such kernels, at least for annual tax-adjustment levels limited by 20%; higher consumption levels can only be sustained when capital is abundant. Furthermore, we notice that the sizes of the kernel slices for a given taxation level do not diminish as the tax 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 neces- sary to keep many consumption choices viable, especially when capital approaches the constraint-set boundaries.