Abstract
This chapter considers different modelling approaches to study nonlinear monopolies with a downward and concave demand function based on the model by Naimzada and Ricchiuti (Appl Math Comput 203:921–925, 2008). In particular, the article characterises the dynamics of continuous time models with delays related to several assumptions regarding the bounded rationality of the monopolist. Some results about global dynamics are also obtained through simulations.
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Notes
- 1.
In order to guarantee the nonnegativity of prices, we assume that \(q<\root 3 \of {a/b}\) holds from now on.
- 2.
The transversality condition can easily be verified.
References
Al-Hdaibat B, Govaerts W, Neirynck N (2015) On periodic and chaotic behavior in a two-dimensional monopoly model. Chaos Solitons Fractals 70:27–37
Baumol WJ, Quandt RE (1964) Rules of thumb and optimally imperfect decisions. Am Econ Rev 54:23–46
Berezowski M (2001) Effect of delay time on the generation of chaos in continuous systems. One-dimensional model. Two-dimensional model - tubular chemical reactor with recycle. Chaos Solitons Fractals 12:83–89
Cavalli F, Naimzada AK (2015) Effect of price elasticity of demand in monopolies with gradient adjustment. Chaos Solitons Fractals 76:47–55
Cooke K, van den Driessche P, Zou X (1999) Interaction of maturation delay and nonlinear birth in population and epidemic models. J Math Biol 39:332–352
Györi I (1990) Interaction between oscillations and global asymptotic stability in delay differential equations. Differ Integral Equ 3:181–200
Kuang Y (1993) Delay differential equations with applications in population dynamics. Academic Press, New York
Matsumoto A, Szidarovszky F (2012) Nonlinear delay monopoly with bounded rationality. Chaos Solitons Fractals 45:507–519
Matsumoto A, Szidarovszky F (2014a) Complex dynamics of monopolies with gradient adjustment. Econ Model 42:220–229
Matsumoto A, Szidarovszky F (2014b) Discrete and continuous dynamics in nonlinear monopolies. Appl Math Comput 232:632–642
Matsumoto A, Szidarovszky F (2015a) Dynamic monopoly with multiple continuously distributed time delays. Math Comput Simul 108:99–118
Matsumoto A, Szidarovszky F (2015b) Learning monopolies with delayed feedback on price expectations. Commun Nonlinear Sci Numer Simul 28:151–165
Matsumoto A, Chiarella C, Szidarovszky F (2013) Dynamic monopoly with bounded continuously distributed delay. Chaos Solitons Fractals 47:66–72
Naimzada AK, Ricchiuti G (2008) Complex dynamics in a monopoly with a rule of thumb. Appl Math Comput 203:921–925
Naimzada AK, Ricchiuti G (2011) Monopoly with local knowledge of demand function. Econ Model 28:299–307
Piotrowska MJ (2007) A remark on the ODE with two discrete delays. J Math Anal Appl 329:664–676
Puu T (1995) The chaotic monopolist. Chaos Solitons Fractals 5:35–44
Schotter A (2008) Microeconomics: a modern approach. South-Western College, California
Acknowledgments
The authors are grateful to an anonymous reviewer for valuable comments on an earlier draft. The usual disclaimer applies.
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© 2016 Springer Science+Business Media Singapore
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Gori, L., Guerrini, L., Sodini, M. (2016). Different Modelling Approaches for Time Lags in a Monopoly. In: Matsumoto, A., Szidarovszky, F., Asada, T. (eds) Essays in Economic Dynamics. Springer, Singapore. https://doi.org/10.1007/978-981-10-1521-2_5
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DOI: https://doi.org/10.1007/978-981-10-1521-2_5
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