Strategic Complementarities Due to Monetary Shock Under Sticky Price

Abstract

In this paper, we determine the optimal complementarity strategy of a firm under a Cox-Ingersoll-Ross (CIR) stochastic framework with a non-zero drift. The firm’s objective function is maximized using percent deviations from symmetric equilibrium of its own and aggregate consumer price index (CPI) as state variables, while the complementarity strategy due to random monetary shock serves as the control variable. Extending the driftless Calvo model, we employ a mean field approach to derive a closed-form solution for the optimal strategy. Our findings indicate that higher volatility leads to a reduction in the firm’s optimal complementarity strategy. To validate our theoretical results, we apply the model to four major consumer goods firms such as Nestle, Westrock, Dover, and Palmolive. Empirical observations reveal that, in practice, the decline in complementarity strategy is significantly more pronounced than predicted by the theoretical model, highlighting the impact of market uncertainty.