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Dynamic Monopolistic Competition

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  • Simon Hoof

    (Paderborn University)

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.

Suggested Citation

  • Simon Hoof, 2021. "Dynamic Monopolistic Competition," Journal of Optimization Theory and Applications, Springer, vol. 189(2), pages 560-577, May.
    • Handle: RePEc:spr:joptap:v:189:y:2021:i:2:d:10.1007_s10957-021-01843-w
    DOI: 10.1007/s10957-021-01843-w
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    References listed on IDEAS

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    1. Agnieszka Wiszniewska-Matyszkiel & Marek Bodnar & Fryderyk Mirota, 2015. "Dynamic Oligopoly with Sticky Prices: Off-Steady-state Analysis," Dynamic Games and Applications, Springer, vol. 5(4), pages 568-598, December.
    2. Caputo,Michael R., 2005. "Foundations of Dynamic Economic Analysis," Cambridge Books, Cambridge University Press, number 9780521842723, January.
    3. Dixit, Avinash K & Stiglitz, Joseph E, 1977. "Monopolistic Competition and Optimum Product Diversity," American Economic Review, American Economic Association, vol. 67(3), pages 297-308, June.
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    7. C. Ling & M. R. Caputo, 2011. "A Qualitative Characterization of Symmetric Open-Loop Nash Equilibria in Discounted Infinite Horizon Differential Games," Journal of Optimization Theory and Applications, Springer, vol. 149(1), pages 151-174, April.
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