Dynamic Politico-economic Equilibrium: Aggregation, First-order Conditions, and Computation

We study a dynamic version of Meltzer and Richard's median-voter model where agents differ in initial wealth. Taxes are proportional to total income, and they are redistributed as equal lump-sum transfers. Voting takes place every period and each consumer votes for the tax rate that maximizes his or her welfare. We define and characterize time-consistent Markov-perfect equilibria in three ways. First, by restricting the class of utility functions, we show that independently of the number of wealth types, the economy's aggregate state can be summarized by two statistics: mean and median wealth. Second, we derive the median-voter's first-order condition and interpret it in terms of a tradeoff between distortions and net wealth transfers. Finally, we discuss methods for computing steady-state equilibria that are easy to implement because they do not require global solutions for equilibrium laws of motions/policy functions, whose shape are key in pinning down any steady state