Preferences help
enabled [disable] Abstract
Number of results
2012 | 121 | 2B | B-54-B-60
Article title

Vortex Stabilization of Market Equilibrium in Theory and in Practice of Economics

Title variants
Languages of publication
Rotary movements of the object around the position of equilibrium is the most common type of dynamics in nature. The way of plotting trajectory resembles winding a line onto a cone of revolution or some other solid of revolution. The state of equilibrium, which is usually not reached by the system, is marked with the cone axis. The trajectory can move away from the state of equilibrium, or get closer to it. A similar behavior is observed in many two-dimensional economic models, both linear, and nonlinear. The simplest example is a linear cobweb model, where - depending on slopes of linear demand function and linear function of supply - price and quantity make a broken line with a growing, constant or decreasing amplitude around the equilibrium point. In nonlinear models, trajectories are more realistic. A natural space for exploring spiral trajectories is a three-dimensional space. Usually, it requires magnifying the model's dimension by one. Economic vortices are made up by economic vectors of three constituents. It may be price, quantity, and time. Apparently, flat zigzags that can be seen on two-dimensional graphs of cobweb models are orthogonal projections of spinning trajectories. Vortexes created by nonlinear models are much smoother than the vortices created by linear models. The real economic vectors create smooth spiral trajectories, which indicates necessity to employ nonlinear dynamics in economic modeling. The basis for rotary movements are surface areas of solids of revolution of the second degree. The kinematics of solids indicated by market shows that they also rotate in three-dimensional space. It resembles precession movements. In economic dynamics we have at least a double rotation. What rotates are both economic vectors as well as the solids created by them.
  • Institute of Economics, Polish Academy of Sciences,, Palace of Culture and Science, 1 Defilad Sq., PL-00-901 Warsaw, Poland
  • Department of Mathematics and Cybernetics, Wroclaw University of Economics, Komandorska 118/120, PL-53-345 Wrocław, Poland
  • [1] R.G.D. Allen, Ekonomia matematyczna, PWN, Warszawa 1961
  • [2] G. Gandolfo, Mathematical Methods and Models in Economic Dynamics, North-Holland, Amsterdam 1971
  • [3] R.M. Goodwin, in: Ed. C.H. Feinstein, Socialism, Capitalism and Economic Growth. Essays Presented to Maurice Dobb, Cambridge University Press, Cambridge, 54 (1967)
  • [4] R. Veneziani, S. Mohun, Structural Change and Economic Dynamics 17, 437 (2006)
  • [5] G. Colacchio, M. Sparro, C. Tebaldi, International Journal of Bifurcation and Chaos 17, 1911 (2007)
  • [6] A.J. Lotka, Proc. Natl. Acad. Sci. USA 6, 410 (1920)
  • [7] A.J. Lotka, Proc. Natl. Acad. Sci. USA 7, 168 (1921)
  • [8] V. Volterra, Leçons sur la théorie mathématique de la lutte pour la vie, Gauthier-Villars, Paris 1931
  • [9] V. Pareto, Manual of Political Economy, Macmillan, London 1971
  • [10] P.A. Samuelson, Foundations of Economic Analysis (Enlarged edition), Harvard University Press, Cambridge, Mass. 1983
  • [11] J. Juzwiszyn, Wiry ekonomiczne i fale R.N. Elliotta, Katedra Matematyki i Cybernetyki, Wydział Zarządzania i Informatyki, Akademia Ekonomiczna im. Oskara Langego, Wrocław 2006
  • [12] A. Jakimowicz, Źródła niestabilności struktur rynkowych, Wydawnictwo Naukowe PWN, seria: Współczesna Ekonomia, Warszawa 2010
  • [13] U. Ricci, Zeitschrift für Nationalökonomie, Band I, Heft 5, 649 (1930)
  • [14] H. Schultz, Der Sinn der statistischen Nachfragekurven, in: Ed. E. Altschul, Veröffentlichungen der Frankfurter Gesellschaft für Konjunkturforschung, Heft 10, Kurt Schroeder Verlag, Bonn 1930
  • [15] J. Tinbergen, Zeitschrift für Nationalökonomie, Band I, Heft 5, 669 (1930)
  • [16] N. Kaldor, The Review of Economic Studies 1, 122 (1934)
  • [17] M. Ezekiel, The Quarterly Journal of Economics 52, 255 (1938)
  • [18] R. Manning, The Economic Record 46, 588 (1970)
  • [19] G. Gandolfo, Economic Dynamics: Methods and Models, North-Holland, Amsterdam 1980
  • [20] W.D. Dechert, Ed., Chaos Theory in Economics: Methods, Models and Evidence, Edward Elgar Publishing, Cheltenham 1996
  • [21] A. C. Chiang, Podstawy ekonomii matematycznej, PWE, Warszawa 1994
  • [22] G. Åkerman, The Quarterly Journal of Economics 71, 151 (1957)
  • [23] C.H. Hommes, Chaotic Dynamics in Economic Models. Some Simple Case-Studies, Wolters-Noordhoff, Groningen 1991
  • [24] C.H. Hommes, Journal of Economic Behavior and Organization 24, 315 (1994)
  • [25] P.E. Smith, International Economic Review 8, 1 (1967)
  • [26] M.G. Allingham, Economica 43, 169 (1976)
  • [27] J. Juzwiszyn, Ekonomia Matematyczna 5, 133 (2001)
  • [28] J. Juzwiszyn, W. Rybicki, Niektóre modele matematyki ubezpieczeniowej i finansowej. Statystyka i ryzyko. Praktyka statystyki, Wydawnictwo Akademii Ekonomicznej im. Oskara Langego we Wrocławiu, Wrocław 2006
  • [29] T. Żylicz, Wykłady z równań różniczkowych i różnicowych, Wydawnictwo Uniwersytetu Warszawskiego, Warszawa 1986
  • [30] J. Tadion, Rozszyfrować rynek, WIG Press, Warszawa 1999
  • [31] S. Banach, Mechanika, Spółdzielnia Wydawnicza Czytelnik, Warszawa 1947
  • [32] N.H. Barbosa-Filho, L. Taylor, Metroeconomica 57, 389 (2006)
  • [33] N.J. Moura, M.B. Ribeiro, Eur. Phys. J. B 67, 101 (2009)
  • [34] M.M. García, M.E. Herrera, Cuadernos de Economía 29, 1 (2010)
  • [35] H. Poincaré, Sur le problème des trois corps et les équations de la dynamique, in: Oeuvres de Henri Poincaré, Vol. VII: Masses fluides en rotation. Principes de mécanique analytique. Problème des trois corps, Gauthier-Villars, Paris 262 (1952)
Document Type
Publication order reference
YADDA identifier
JavaScript is turned off in your web browser. Turn it on to take full advantage of this site, then refresh the page.