Internal Seminar: Francesco Lippi (Visiting Luiss)

Title: "Price Setting with Strategic Complementarities as a Mean Field Game"

  • Data: 15 dicembre 2021 dalle 13:00 alle 14:00

  • Luogo: Seminar Room - Piazza Scaravilli, 2 & Microsoft Teams


We analyze the impulse response of output after a monetary shock in a general equilibrium setup where firms set prices subject to adjustment costs and feature strategic complementarities with the decision of other firms. The firm's decision problem and the aggregate outcomes are cast as a Mean Field Game (MFG) and several analytical results are established. First, in a canonical menu cost setup featuring an Ss rule the MFG framework allows us to study the effect of strategic complementarity/substitutability on the  firm's optimal Ss rules after the shock. We establish existence and uniqueness of the perturbed equilibrium (as long as the strategic complementarity is not too large) and analytically characterize the impulse response function (IRF) of output. We show that the presence of the strategic complementarity makes the IRF larger at each horizon. On the one hand, as the complementarity becomes large enough, the IRF diverges and at a critical point there is no equilibrium. On the other hand, as substitutability becomes arbitrarily large, the IRF converges to zero. Second, we extend the results to the Calvo model, where we show that the cumulative impulse response is approximately proportional to the one without strategic complementarity.