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Memory, market stability and the nonlinear cobweb theorem

Published online by Cambridge University Press:  17 February 2009

J. M. Gaffney  and
C. E. M. Pearce
J. M. Gaffney
Affiliation:
School of Applied Mathematics, The University of Adelaide, SA 5005, Australia; e-mail: jgaffney@maths.adelaide.edu.au and cpearce@maths.adelaide.edu.au.
C. E. M. Pearce
Affiliation:
School of Applied Mathematics, The University of Adelaide, SA 5005, Australia; e-mail: jgaffney@maths.adelaide.edu.au and cpearce@maths.adelaide.edu.au.
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Abstract

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Carlson has shown that if the predicted price in the linear cobweb model is taken as the average of all previous actual prices, then stability results independently of parameter values provided only that the demand–curve gradient is less than that of the supply curve. This result has subsequently been generalised by Manning and by Holmes and Manning. We investigate the robustness of their results.

Type
Research Article
Information
The ANZIAM Journal , Volume 45 , Issue 4 , April 2004 , pp. 547 - 555
Copyright
Copyright © Australian Mathematical Society 2004

References

[1]Artstein, Z., “Irregular cobweb dynamics”, Econ. Lett. 11 (1983) 15–17.CrossRefGoogle Scholar
[2]Bull, C., “Expectations of others' expectations”, in Individual forecasting and aggregate outcomes. ‘Rational expectations’ examined (eds. Frydman, R. and Phelps, E. S.), (Cambridge University Press, Cambridge, 1983) 66–68.Google Scholar
[3]Carlson, J. A., “An invariably stable cobweb model”, Rev. Econ. Stud. 35 (1968) 360–362.CrossRefGoogle Scholar
[4]Chiarella, C., “The cobweb model. Its instability and the onset of chaos”, Econ. Model. 5 (1988) 377–384.CrossRefGoogle Scholar
[5]Ezekiel, M., “The cobweb theorem”, Q. J. Econ. 52 (1938) 255–280.CrossRefGoogle Scholar
[6]Finkenstädt, B. and Kuhbier, P., “Chaotic dynamics in agricultural markets”, in Nonlinear methods in economic dynamics and optimal control, International Conference on Operations Research, Vienna(1990) (eds. Feichtinger, G. and Hartl, R. F.), Ann. Oper. Res. 37 (1992) 73–96.CrossRefGoogle Scholar
[7]Friedman, B. M., “Optimal expectations and the extreme information assumptions of ‘rational expectations’ macromodels”, J. Monetary Econ. 5 (1979) 27–41.CrossRefGoogle Scholar
[8]Holmes, J. M. and Manning, R., “Memory and market stability: the case of the cobweb”, Econ. Lett. 28 (1988) 1–7.CrossRefGoogle Scholar
[9]Jensen, R. V. and Urban, R., “Chaotic price behaviour in a non-linear cobweb model”, Econ. Lett. 15 (1984) 235–240.CrossRefGoogle Scholar
[10]Manning, R., “A generalization of a cobweb theorem”, Rev. Econ. Stud. 36 (1971) 123–125.CrossRefGoogle Scholar
[11]Muth, W., “Rational expectations and the theory of price movements”, Econometrica 29 (1961) 315–335.CrossRefGoogle Scholar
[12]Nerlove, M., “Adaptive expectations and cobweb phenomena”, Q. J. Econ. 22 (1958) 227–240.CrossRefGoogle Scholar