An Equilibrium Model with Computationally Constrained Agents

Abstract: We study a large economy in which firms cannot compute exact solutions to the non-linear equations that characterize the equilibrium price at which they can sell future output. Instead, firms use polynomial expansions to approximate prices. The precision with which they can compute prices is endogenous and depends on the overall level of supply. At the same time, firms' individual supplies, and thus aggregate supply, depend on the precision with which they approximate prices. This interrelation between supply and price forecast induces multiple equilibria, with inefficiently low output, in economies that otherwise have a unique, efficient equilibrium. Moreover, exogenous parameter changes, which would increase output were there no computational frictions, can diminish agents' ability to approximate future prices, and reduce output. Our model therefore accommodates the intuition that interventions, such as unprecedented quantitative easing, can put agents into "uncharted territory".