Sticky Prices and Constraints to Produce

We study whether firms in medium-scale New Keynesian models would voluntarily satisfy demand at their posted prices, or whether nominal rigidities may push prices below marginal costs. In the Altig et al (2011) framework, which features full indexation of non-adjusting prices and wages to steady-state inflation and near constant returns to scale at the firm level, we find that violations of firms’ willingness-to-supply condition are negligible: fewer than one percent of firms are ever constrained, and the associated output losses are tiny. Two features of the model drive this result: marginal costs that are nearly unresponsive to output, and prices that adjust more frequently than wages. When the short-run marginal-cost schedule is sufficiently steep, willingness-to-supply violations become quantitatively relevant. Our findings thus characterize the conditions under which the standard demand-determination assumption is a reliable approximation and those under which it may not be.