The political economy of labor subsidies

We explore a political-economy model of labor subsidies, extending Meltzer and Richard's median-voter model to a dynamic setting. We explore only one source of heterogeneity: initial wealth. As a consequence, given an operative wealth effect, poorer agents work harder, and if the agent with median wealth is poorer than average, a politico-economic equilibrium will feature a subsidy to labor. The dynamic model does not have capital, but it has perfect markets for borrowing and lending. This means that another channel appears: tax rates influence interest rates, and this is another channel for redistribution, since a decrease in current interest rates favors agents with below-average wealth. By the same token---and as is typically the case in dynamic politico-economic models with rational agents---the setting features time-inconsistency: the median voter would like to commit not to manipulate interest rates in the future. We define a time-consistent politico-economic equilibrium without commitment as a Markov-perfect equilibrium of a dynamic game between consecutive median voters. We rely on utility functions consistent with aggregation, and we show that, for arbitrary wealth distributions, politico-economic equilibria deliver tax outcomes as a function of a single state variable: median wealth. We use the first-order condition of the median voter to characterize equilibrium. For a parametric example, we study in some detail, both in infinite- and short-horizon contexts, and using a combination of analytical and numerical results, how tax rates and inequality are determined over time