Stationary Heterogeneous-Agent Models in Continuous Time

We study a classical Bewley-Huggett-Aiyagari model in continuous time in which ex-post heterogeneity arises due to idiosyncratic, uninsurable income shocks. Our framework is rooted in the Fiscal Theory of the Price Level (FTPL), and we investigate the existence and multiplicity of stationary equilibria in models with and without capital. We establish the existence of an arbitrary even number of equilibria in which the government runs small constant deficits, which in turn implies the multiplicity of price levels.