Vortex Stabilization of Market Equilibrium in Theory and in Practice of Economics |
| A. Jakimowicza and J. Juzwiszynb
a Institute of Economics, Polish Academy of Sciences,, Palace of Culture and Science, 1 Defilad Sq., PL-00-901 Warsaw, Poland b Department of Mathematics and Cybernetics, Wroclaw University of Economics, Komandorska 118/120, PL-53-345 Wrocław, Poland |
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| 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. |
| DOI: 10.12693/APhysPolA.121.B-54 PACS numbers: 89.65.Gh, 45.40.-f, 47.32.C- |