Dynamic Monopolistic Competition

Simon Hoof ()
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Simon Hoof: Paderborn University

Journal of Optimization Theory and Applications, 2021, vol. 189, issue 2, No 9, 560-577

Abstract: Abstract I study a dynamic variant of the Dixit–Stiglitz (Am Econ Rev 67(3), 1977) model of monopolistic competition by introducing price stickiness à la Fershtman and Kamien (Econometrica 55(5), 1987). The analysis is restricted to bounded quantity and price paths that fulfill the necessary conditions for an open-loop Nash equilibrium. I show that there exists a symmetric steady state and that its stability depends on the degree of product differentiation. When moving from complements to perfect substitutes, the steady state is either a locally asymptotically unstable (spiral) source, a stable (spiral) sink or a saddle point. I further apply the Hopf bifurcation theorem and prove the existence of limit cycles, when passing from a stable to an unstable steady state. Lastly, I provide a numerical example and show that there exists a stable limit cycle.

Keywords: Monopolistic competition; Differential games; Hopf Bifurcation; Limit cycles; 91A10; 91A23; 37G15 (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s10957-021-01843-w

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