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A model of monopoly with lags in the planning and production activity

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  • Fausto, Cavalli

Abstract

In this note, departing from the traditional static and fully rational economic agent setting, I study a dynamic model of a boundedly rational monopolist who, in a partially known environment, follows a rule of thumb learning process. Instead of considering the classical differential model with smooth argument, the proposed dynamic model consists of a piecewise constant argument differential equation, in order to take into account the more realistic assumption of a lag between the learning activity and the output production activity. It is shown how this simple first order differential equation can be rephrased into a nonlinear difference equation which, differently from the classical model with smooth argument, can exhibit complex behaviors. The aim of the paper is to illustrate, from a methodological point of view, the potential applications and the dynamical effects of piecewise constant argument differential equations in economics.

Suggested Citation

  • Fausto, Cavalli, 2016. "A model of monopoly with lags in the planning and production activity," Working Papers 326, University of Milano-Bicocca, Department of Economics, revised 07 Feb 2016.
  • Handle: RePEc:mib:wpaper:326
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    Keywords

    Monopoly; lags; bounded rationality; pie ewise onstant argument differential equation; complex dynamics.;

    JEL classification:

    • D42 - Microeconomics - - Market Structure, Pricing, and Design - - - Monopoly
    • L12 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance - - - Monopoly; Monopolization Strategies
    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • C65 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Miscellaneous Mathematical Tools

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