On the existence and uniqueness of stationary equilibrium in Bewley economies with production

I prove existence of stationary recursive competitive equilibrium in Bewley economies with production under specifications in which (i) the utility function is allowed to be unbounded, and (ii) the underlying discrete idiosyncratic productivity process can take any form, aside from mild restrictions. Some of the intermediate results provide theoretical basis for assumptions often made in the quantitative macroeconomics literature. By providing an example, I illustrate that the equilibrium is not necessarily unique, even under typical specifications of the model, and discuss the underlying reasons for multiplicity.