1.2 Definition of Stationary Equilibrium

We focus on a stationary equilibrium concept in which factor prices and age-wealth distri-bution are constant over time. The collection of all of the agents ’ possible states is denoted by x. An equilibrium is described as follows. Definition 1 A stationary equilibrium is given by government tax rates, transfers, and spending (τl, τs, τa, τb, xb, P (ey), G); an interest rate r and a wage rate w; value functions 1 V (x), allocations c(x), a′(x); and a constant distribution of people m∗(x), such that the following conditions hold: (i) Given government tax rates and transfers, the interest rate, the wage rate, and dened bene t policies, the functions V (x), c(x) and a′(x) solve the described maximization problem for a household in state x. (ii) m ∗ is the invariant distribution of households over the state variables for this econ-omy.1 (iii) All markets clear. C = cm∗(dx), K = am∗(dx), L = ϵy m∗(dx), C + (1 + n)K (1 δ)K +G = F (K;L). (iv) The price of each factor is equal to its marginal product. r = F1(K,L) δ, w = F2(K,L). (vi) The government budget constraints are balanced at each period. G = τar am∗(dx)+ τlwL+ τb(1 pt)It>9max(a′ xb, 0)m∗(dx)+ τl It>9P (ey)m∗(dx),∫ It>9P (ey)m∗(dx) = τswL