
- Previous Article
- JDG Home
- This Issue
-
Next Article
A note on the lattice structure for matching markets via linear programming
A dynamic for production economies with multiple equilibria
1. | Universidad Autónoma de San Luis Potosí, Facultad de Economía, San Luis Potosí, 78213, México |
2. | Instituto Potosino de Investigación Científica y Tecnológica, División de Control y Sistemas Dinámicos, San Luis Potosí, 78216, México |
In this article, we extend to private ownership production economies, the results presented by Bergstrom, Shimomura, and Yamato (2009) on the multiplicity of equilibria for the special kind of pure-exchanges economies called Shapley-Shubik economies. Furthermore, a dynamic system that represents the changes in the distribution of the firms on the production branches is introduced. For the first purpose, we introduce a particular, but large enough, production sector to the Shapley-Shubik economies, for which a simple technique to build private-ownership economies with a multiplicity of equilibria is developed. In this context, we analyze the repercussions on the behavior of the economy when the number of possible equilibria changes due to rational decisions on the production side. For the second purpose, we assume that the rational decisions on the production side provoke a change in the distribution of the firms over the set of branches of production.
References:
[1] |
E. Accinelli and E. Covarrubias,
Evolution and jump in a Walrasian framework, J. Dyn. Games, 3 (2016), 279-301.
doi: 10.3934/jdg.2016015. |
[2] |
T. C. Bergstrom, K.-I. Shimomura and T. Yamato, Simple economies with multiple equilibria, B. E. J. Theor. Econ., 9 (2009), 31pp.
doi: 10.2202/1935-1704.1609. |
[3] |
E. Dierker,
Two remarks on the number of equilibria of an economy, Econometrica, 40 (1972), 951-953.
doi: 10.2307/1912091. |
[4] |
T. Hens and B. Pilgrim, The index-theorem, in General Equilibrium Foundations of Finance, Theory and Decision Library, 33, Springer, Boston, MA, 2002.
doi: 10.1007/978-1-4757-5317-2_4. |
[5] |
T. J. Kehoe,
An index theorem for general equilibrium models with production, Econometrica, 48 (1980), 1211-1232.
doi: 10.2307/1912179. |
[6] |
T. J. Kehoe,
Multiplicty of equilbria and compartive statics, Quart. J. Econom., 100 (1985), 119-147.
doi: 10.2307/1885738. |
[7] |
A. Mas-Colell, The Theory of General Economic Equilbrium. A Differential Approach, Econometric Society Monographs, 9, Cambridge University Press, Cambridge, 1989.
![]() |
[8] |
P. A. Samuelson, Foundations of Economic Analysis, Harvard University Press, Cambridge, Mass., 1947.
![]() |
[9] |
L. Shapley and M. Shubik,
An example of a trading economy with three competitive equilibria, J. Political Economy, 85 (1997), 873-875.
doi: 10.1086/260607. |
show all references
References:
[1] |
E. Accinelli and E. Covarrubias,
Evolution and jump in a Walrasian framework, J. Dyn. Games, 3 (2016), 279-301.
doi: 10.3934/jdg.2016015. |
[2] |
T. C. Bergstrom, K.-I. Shimomura and T. Yamato, Simple economies with multiple equilibria, B. E. J. Theor. Econ., 9 (2009), 31pp.
doi: 10.2202/1935-1704.1609. |
[3] |
E. Dierker,
Two remarks on the number of equilibria of an economy, Econometrica, 40 (1972), 951-953.
doi: 10.2307/1912091. |
[4] |
T. Hens and B. Pilgrim, The index-theorem, in General Equilibrium Foundations of Finance, Theory and Decision Library, 33, Springer, Boston, MA, 2002.
doi: 10.1007/978-1-4757-5317-2_4. |
[5] |
T. J. Kehoe,
An index theorem for general equilibrium models with production, Econometrica, 48 (1980), 1211-1232.
doi: 10.2307/1912179. |
[6] |
T. J. Kehoe,
Multiplicty of equilbria and compartive statics, Quart. J. Econom., 100 (1985), 119-147.
doi: 10.2307/1885738. |
[7] |
A. Mas-Colell, The Theory of General Economic Equilbrium. A Differential Approach, Econometric Society Monographs, 9, Cambridge University Press, Cambridge, 1989.
![]() |
[8] |
P. A. Samuelson, Foundations of Economic Analysis, Harvard University Press, Cambridge, Mass., 1947.
![]() |
[9] |
L. Shapley and M. Shubik,
An example of a trading economy with three competitive equilibria, J. Political Economy, 85 (1997), 873-875.
doi: 10.1086/260607. |









[1] |
Jingzhen Liu, Ka-Fai Cedric Yiu, Tak Kuen Siu, Wai-Ki Ching. Optimal insurance in a changing economy. Mathematical Control & Related Fields, 2014, 4 (2) : 187-202. doi: 10.3934/mcrf.2014.4.187 |
[2] |
M. D. Troutt, S. H. Hou, W. K. Pang. Multiple workshift options in aggregrate production Multiple workshift options in aggregrate production. Journal of Industrial & Management Optimization, 2006, 2 (4) : 387-398. doi: 10.3934/jimo.2006.2.387 |
[3] |
Bo Wang, Jiguang Bao. Mirror symmetry for a Hessian over-determined problem and its generalization. Communications on Pure & Applied Analysis, 2014, 13 (6) : 2305-2316. doi: 10.3934/cpaa.2014.13.2305 |
[4] |
Marzia Bisi, Giampiero Spiga. A Boltzmann-type model for market economy and its continuous trading limit. Kinetic & Related Models, 2010, 3 (2) : 223-239. doi: 10.3934/krm.2010.3.223 |
[5] |
Nicola Bellomo, Sarah De Nigris, Damián Knopoff, Matteo Morini, Pietro Terna. Swarms dynamics approach to behavioral economy: Theoretical tools and price sequences. Networks & Heterogeneous Media, 2020, 15 (3) : 353-368. doi: 10.3934/nhm.2020022 |
[6] |
Lou Caccetta, Elham Mardaneh. Joint pricing and production planning for fixed priced multiple products with backorders. Journal of Industrial & Management Optimization, 2010, 6 (1) : 123-147. doi: 10.3934/jimo.2010.6.123 |
[7] |
Silvia Caprino, Guido Cavallaro, Carlo Marchioro. A Vlasov-Poisson plasma with unbounded mass and velocities confined in a cylinder by a magnetic mirror. Kinetic & Related Models, 2016, 9 (4) : 657-686. doi: 10.3934/krm.2016011 |
[8] |
Katherine A. Kime. Palindromic control and mirror symmetries in finite difference discretizations of 1-D Schrödinger equations. Discrete & Continuous Dynamical Systems - B, 2018, 23 (4) : 1601-1621. doi: 10.3934/dcdsb.2018063 |
[9] |
Ruofeng Rao, Shouming Zhong. Input-to-state stability and no-inputs stabilization of delayed feedback chaotic financial system involved in open and closed economy. Discrete & Continuous Dynamical Systems - S, 2021, 14 (4) : 1375-1393. doi: 10.3934/dcdss.2020280 |
[10] |
Chongyang Liu, Meijia Han. Time-delay optimal control of a fed-batch production involving multiple feeds. Discrete & Continuous Dynamical Systems - S, 2020, 13 (6) : 1697-1709. doi: 10.3934/dcdss.2020099 |
[11] |
Timothy Chumley, Renato Feres. Entropy production in random billiards. Discrete & Continuous Dynamical Systems, 2021, 41 (3) : 1319-1346. doi: 10.3934/dcds.2020319 |
[12] |
Biswajit Sarkar, Bimal Kumar Sett, Sumon Sarkar. Optimal production run time and inspection errors in an imperfect production system with warranty. Journal of Industrial & Management Optimization, 2018, 14 (1) : 267-282. doi: 10.3934/jimo.2017046 |
[13] |
Jian-Xin Guo, Xing-Long Qu. Robust control in green production management. Journal of Industrial & Management Optimization, 2020 doi: 10.3934/jimo.2021011 |
[14] |
Eric A. Carlen, Maria C. Carvalho, Amit Einav. Entropy production inequalities for the Kac Walk. Kinetic & Related Models, 2018, 11 (2) : 219-238. doi: 10.3934/krm.2018012 |
[15] |
Eduardo Liz, Cristina Lois-Prados. A note on the Lasota discrete model for blood cell production. Discrete & Continuous Dynamical Systems - B, 2020, 25 (2) : 701-713. doi: 10.3934/dcdsb.2019262 |
[16] |
P. Bai, H.T. Banks, S. Dediu, A.Y. Govan, M. Last, A.L. Lloyd, H.K. Nguyen, M.S. Olufsen, G. Rempala, B.D. Slenning. Stochastic and deterministic models for agricultural production networks. Mathematical Biosciences & Engineering, 2007, 4 (3) : 373-402. doi: 10.3934/mbe.2007.4.373 |
[17] |
Dieter Armbruster, Michael Herty, Xinping Wang, Lindu Zhao. Integrating release and dispatch policies in production models. Networks & Heterogeneous Media, 2015, 10 (3) : 511-526. doi: 10.3934/nhm.2015.10.511 |
[18] |
Simone Göttlich, Stephan Knapp. Semi-Markovian capacities in production network models. Discrete & Continuous Dynamical Systems - B, 2017, 22 (9) : 3235-3258. doi: 10.3934/dcdsb.2017090 |
[19] |
Simone Göttlich, Patrick Schindler. Optimal inflow control of production systems with finite buffers. Discrete & Continuous Dynamical Systems - B, 2015, 20 (1) : 107-127. doi: 10.3934/dcdsb.2015.20.107 |
[20] |
Juan Gabriel Brida, Gaston Cayssials, Oscar Córdoba Rodríguez, Martín Puchet Anyul. A dynamic extension of the classical model of production prices determination. Journal of Dynamics & Games, 2020, 7 (3) : 185-196. doi: 10.3934/jdg.2020013 |
Impact Factor:
Tools
Metrics
Other articles
by authors
[Back to Top]