# American Institute of Mathematical Sciences

July  2016, 3(3): 279-301. doi: 10.3934/jdg.2016015

## Evolution and jump in a Walrasian framework

 1 Facultad de Economa de la UASLP, Aveninda Pintores S/N, San Luis Potosi, 78280, Mexico, Mexico

Received  May 2016 Revised  September 2016 Published  October 2016

Lower profit rates play an importan role in the evolution of an ownership private economy. We argue that if managers look to maximize profits rates, then the decision to change, to those branches, or technologies, that offer higher rates of profits, plays an important role in the characterization of economies. If managers choose to produce according to those technologies that promise higher profit rates, then along the time, the distribution of the firms over the set of available technologies change, and therefore the economic fundamentals change. Under conditions of imperfect information, the imitation of the most successful firms plays can a decisive role in deciding how to produce. Along a path of Walrasian equilibria, regular economies can become singular and if this occurs, big changes must be expected after decisions of the firms for the next period.
Citation: Elvio Accinelli, Enrique Covarrubias. Evolution and jump in a Walrasian framework. Journal of Dynamics and Games, 2016, 3 (3) : 279-301. doi: 10.3934/jdg.2016015
##### References:
 [1] E. Accinelli and M. Puchet, A Classification of infinite dimensional Walrasian economies and the economic crisis, In Dynamic, Game and Science (in Honour of Maurício Peixoto and David Rand) Series, Springer-Veralg, 2 (2011), 55-77. doi: 10.1007/978-3-642-14788-3_4. [2] C. D. Aliprantis, D. J. Brown and O. Burkinshaw, Existence and Optimaility of Competitive Equilibria, Springer Verlag, 1990. doi: 10.1007/978-3-642-61521-4. [3] Y. Balasko, The Equilibrium Manifold Postmodern Developments in the Theory of General Economic Equilibrium, The Mit Press, 2009. doi: 10.7551/mitpress/9780262026543.001.0001. [4] A. Ben-Shohama, R. Serrano and O. Volijc, The evolution of exchange, Journal of Economic Theory, 114 (2004), 310-328. doi: 10.1016/S0022-0531(03)00112-1. [5] G. Gigerenzer and D.G. Goldstein, Reasoning the fast and frugal way: Models of bounded rationality psychological review by the american psychological association, Inc, 103 (1996), 650-669. doi: 10.1016/S0022-0531(03)00112-1. [6] M. W. Hirsch, S. Smale and R. L. Devaney, Differential Equations, Dynamical Systems, and an Introduction to Chaos, Academic Press, 2004. [7] M. Kandori, R. Serrano and O. Volij, Decentralized Trade, Random Utility and the Evolution of Social Welfare, Working Paper, Department of Economics, University of Tokyo ,2004. doi: 10.1016/S0022-0531(03)00112-1. [8] A. Mas-Colell, The Theory of General Equilibrium: A Differentiable Approach, Cambrdige University Press, 1989. [9] J. Perla, Equilibrium Imitation and Growth, Journal of Political Economy, 2014. doi: 10.1016/S0022-0531(03)00112-1. [10] A. Sard, The measure of the critical values of differentiable maps, Bulletin of the American Mathematical Society, 48 (1942), 883-890. doi: 10.1090/S0002-9904-1942-07811-6. [11] K. H. Schlag, Why imitate, and if so, how? A boundedly rational approach to multi-armed bandits, Journal of Economic Theory, 78 (1998), 130-156. doi: 10.1006/jeth.1997.2347. [12] F. Vega Redondo, The evolution of walrasian behavior, Econometrica, 65 (1997), 375-384. doi: 10.1016/S0022-0531(03)00112-1. [13] J. W. Weibull, Evolutionary Game Thery, The Mit Press, 1985.

show all references

##### References:
 [1] E. Accinelli and M. Puchet, A Classification of infinite dimensional Walrasian economies and the economic crisis, In Dynamic, Game and Science (in Honour of Maurício Peixoto and David Rand) Series, Springer-Veralg, 2 (2011), 55-77. doi: 10.1007/978-3-642-14788-3_4. [2] C. D. Aliprantis, D. J. Brown and O. Burkinshaw, Existence and Optimaility of Competitive Equilibria, Springer Verlag, 1990. doi: 10.1007/978-3-642-61521-4. [3] Y. Balasko, The Equilibrium Manifold Postmodern Developments in the Theory of General Economic Equilibrium, The Mit Press, 2009. doi: 10.7551/mitpress/9780262026543.001.0001. [4] A. Ben-Shohama, R. Serrano and O. Volijc, The evolution of exchange, Journal of Economic Theory, 114 (2004), 310-328. doi: 10.1016/S0022-0531(03)00112-1. [5] G. Gigerenzer and D.G. Goldstein, Reasoning the fast and frugal way: Models of bounded rationality psychological review by the american psychological association, Inc, 103 (1996), 650-669. doi: 10.1016/S0022-0531(03)00112-1. [6] M. W. Hirsch, S. Smale and R. L. Devaney, Differential Equations, Dynamical Systems, and an Introduction to Chaos, Academic Press, 2004. [7] M. Kandori, R. Serrano and O. Volij, Decentralized Trade, Random Utility and the Evolution of Social Welfare, Working Paper, Department of Economics, University of Tokyo ,2004. doi: 10.1016/S0022-0531(03)00112-1. [8] A. Mas-Colell, The Theory of General Equilibrium: A Differentiable Approach, Cambrdige University Press, 1989. [9] J. Perla, Equilibrium Imitation and Growth, Journal of Political Economy, 2014. doi: 10.1016/S0022-0531(03)00112-1. [10] A. Sard, The measure of the critical values of differentiable maps, Bulletin of the American Mathematical Society, 48 (1942), 883-890. doi: 10.1090/S0002-9904-1942-07811-6. [11] K. H. Schlag, Why imitate, and if so, how? A boundedly rational approach to multi-armed bandits, Journal of Economic Theory, 78 (1998), 130-156. doi: 10.1006/jeth.1997.2347. [12] F. Vega Redondo, The evolution of walrasian behavior, Econometrica, 65 (1997), 375-384. doi: 10.1016/S0022-0531(03)00112-1. [13] J. W. Weibull, Evolutionary Game Thery, The Mit Press, 1985.
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