Abstract
In this paper, we analyze the dynamics of a monopoly model with constant elasticity in which the monopolist faces a form of bounded rationality due to limited accessibility to information. We assume the firm adopts a gradient mechanism to adjust the output level, and we investigate how the introduction of fixed and continuously distributed delays within the resulting continuous-time system may affect the long-run dynamics. We find that the stability of the equilibrium depends on the weighting function adopted to model continuously distributed delays, and the convergence of the realized output toward the steady state is crucially affected by the choice of the delay type which, in turn, reflects the availability and the weight assigned to information. Indeed, depending on the assumptions on modeling delays, the equilibrium point may undergo a Hopf bifurcation after which a limit cycle arises.
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Notes
We recall that in the latter case, for \(m\rightarrow +\infty \), the weight is assigned to a unique value, that is a fixed delay.
References
Askar, S.S.: On complex dynamics of monopoly market. Econ. Model. 31, 586–589 (2013)
Baumol, W.J., Quandt, R.E.: Rules of thumb and optimally imperfect decisions. Am. Econ. Rev. 54(2), 23–46 (1964)
Bischi, G.I., Chiarella, C., Kopel, M., Szidarovszky, F.: Nonlinear Oligopolies: Stability and Bifurcations. Springer, New York (2009)
Bischi, G.I., Panchuk, A., Radi, D. (eds.): Qualitative Theory of Dynamical Systems, Tools and Applications for Economic Modelling: Lectures Given at the Cost Training School on New Economic Complex Geography at Urbino, Italy. Springer, New York (2016)
Cavalli, F., Naimzada, A.: Effect of price elasticity of demand in monopolies with gradient adjustment. Chaos Solitons Fractals 76, 47–55 (2015)
Cavalli, F., Naimzada, A.: A multiscale time model with piecewise constant argument for a boundedly rational monopolist. J. Differ. Equ. Appl. 22(10), 1480–1489 (2016)
Clower, R.W.: Some theory of an ignorant monopolist. Econ. J. 69(276), 705–716 (1959)
den Boer, A.V., Zwart, B.: Simultaneously learning and optimizing using controlled variance pricing. Manage. sci. 60(3), 770–783 (2013)
den Boer, A.V.: Dynamic pricing and learning: historical origins, current research, and new directions. Surveys Oper. Res. Manage. Sci. 20(1), 1–18 (2015)
Eren, S.S., Maglaras, C.: Monopoly pricing with limited demand information. J. Revenue Pricing manag. 9(1–2), 23–48 (2010)
Felis, A., Garrido, A.: Market power dynamics and price volatility in markets of fresh fruits and vegetables. In: Working Paper 7. Research Centre for the Management of Agricultural and Environmental Risks (CEIGRAM), Technical University of Madrid, Spain (2015)
Gori, L., Guerrini, L., Sodini, M.: Different Modelling Approaches for Time Lags in a Monopoly. Essays in Economic Dynamics, pp. 81–98. Springer, Singapore (2016)
Gouel, C.: Agricultural price instability: a survey of competing explanations and remedies. J. Econ. Surv. 26(1), 129–156 (2012)
MacDonald, N.: Time Lags in Biological Systems. Springer, New York (1978)
Matsumoto, A.: Let it be: chaotic price instability can be beneficial. Chaos Solitons Fractals 18(4), 745–758 (2003)
Matsumoto, A., Szidarovszky, F.: Nonlinear delay monopoly with bounded rationality. Chaos Solitons Fractals 45(4), 507–519 (2012)
Matsumoto, A., Szidarovszky, F.: Discrete and continuous dynamics in nonlinear monopolies. Appl. Math. Comput. 232, 632–642 (2014a)
Matsumoto, A., Szidarovszky, F.: Discrete-time delay dynamics of boundedly rational monopoly. Decis. Econ. Finance 37(1), 53–79 (2014b)
Matsumoto, A., Szidarovszky, F.: Complex dynamics of monopolies with gradient adjustment. Econ. Model. 42, 220–229 (2014c)
Matsumoto, A., Szidarovszky, F.: Dynamic monopoly with multiple continuously distributed time delays. Math. Comput. Simul. 108, 99–118 (2015)
Matsumoto, A., Chiarella, C., Szidarovszky, F.: Dynamic monopoly with bounded continuously distributed delay. Chaos Solitons Fractals 47, 66–72 (2013)
Naimzada, A.K., Ricchiuti, G.: Complex dynamics in a monopoly with a rule of thumb. Appl. Math. Comput. 203(2), 921–925 (2008)
Puu, T.: The chaotic monopolist. Chaos Solitons Fractals 5(1), 35–44 (1995)
Tintner, G.: Monopoly over time. Econom. J. Econom. Soc, 160–170 (1937)
Tomek, W.G., Kaiser, H.M.: Agricultural Product Prices. Cornell University Press, Ithaca (2014)
Tversky, A., Kahneman, D.: Judgment under uncertainty: heuristics and biases. Science 185(4157), 1124–1131 (1974)
Weron, R., Simonsen, I., Wilman, P.: Modeling highly volatile and seasonal markets: evidence from the Nord Pool electricity market. In: Takayasu, H. (ed.) The Application of Econophysics, pp. 182–191. Springer, Tokyo (2004)
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We wish to thank two anonymous reviewers for useful comments and suggestions. The usual caveats apply.
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Guerrini, L., Pecora, N. & Sodini, M. Effects of fixed and continuously distributed delays in a monopoly model with constant price elasticity. Decisions Econ Finan 41, 239–257 (2018). https://doi.org/10.1007/s10203-018-0222-3
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DOI: https://doi.org/10.1007/s10203-018-0222-3