An inquiry into the existence and uniqueness of equilibrium with state-dependent pricing

State-dependent pricing models are now an operational framework for quantitative business cycle analysis. The analysis in Ball and Romer [1991], however, suggests that such models may be rife with multiple equilibria: in their static model price adjustment is always characterized by complementarity, a necessary condition for multiplicity. We study existence and uniqueness of equilibrium in a discrete-time state-dependent pricing model. In steady states of our model, we find only weak complementarity and no evidence of multiplicity. We likewise find no evidence of multiplicity in the presence of monetary shocks. However, nonexistence of symmetric steady-state equilibrium with pure strategies arises in a small region of the parameter space.