Median-voter equilibria in the neoclassical growth model under aggregation

We study a dynamic version of Meltzer and Richard's median-voter model where agents differ in wealth. Taxes are proportional to income and are redistributed as equal lump-sum transfers. Voting occurs every period and each consumer votes for the tax that maximizes his welfare. We characterize time-consistent Markov-perfect equilibria twofold. First, restricting utility classes, we show that the economy's aggregate state is mean and median wealth. Second, we derive the median-voter's first-order condition interpreting it as a tradeoff between distortions and net wealth transfers. Our method for solving the steady state relies on a polynomial expansion around the steady state.