Existence of Stationary Equilibrium in an Incomplete-Market Model With Endogenous Labor Supply

In this article, I first study an income fluctuation problem with endogenous labor supply. Let beta be the agent's time discount factor and R > 0 be the constant gross rate of return on assets. For beta R = 1, I show that the agent's wealth either approaches infinity almost surely or converges to a finite level almost surely. For beta R < 1, I prove the existence, uniqueness, and stability of the stationary distribution of state variables. I then show the existence of the stationary general equilibrium in an incomplete-market model with endogenous labor supply.