Abstract
An important feature of the mixed economic system under consideration, besides the presence of a mixed production sector, is that two different regulation mechanisms function jointly: central planning and flexible market prices. Thus, this model is characterized by the presence of dual markets. In the first market, prices are stable and the allocation of commodities is determined by rationing schemes and governmental orders. In the second market, prices are flexible and are formed by the standard mechanism of equating demand and supply. We assume that the excess of any commodity purchased in the first market may be resold by any economic agent at flexible market prices. Whereas a lot of papers are devoted to existence and efficiency of mixed market equilibria, this paper investigates extremal properties of equilibrium allocations in a mixed economy of Arrow-Debreu type. A notion of fuzzy domination in a mixed environment is given, and coincidence of the fuzzy core and equilibrium allocations in certain specifications of economy in question is shown to hold.
This research was supported by the program of fundamental scientific researches of the SB RAS I.5.1., project 0314-2016-0018, and by RFBR grant 16-06-00101.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
- 2.
As usual, \(x \cdot y\) stands for the scalar product \(\sum _{k = 1}^lx_ky_k\) of the vectors \(x = (x_1, \ldots , x_l)\) and \(y~=~(y_1, \ldots , y_l)\) from \(\mathbf {R}^l\).
References
Aubin, J.-P.: Mathematical Methods of Game and Economic Theory. North-Holland, Amsterdam, New York, Oxford (1979)
Ekeland, I.: \(\acute{E}\)l\(\acute{e}\)ments d’\(\acute{E}\)conomie Math\(\acute{e}\)matique. Hermann, Paris (1979)
van der Laan, G., Vasil’ev, V.A., Venniker, R.J.G.: On the transition from the mixed economy to the market. Sib. Adv. Math. 10, 1–33 (2000)
Makarov, V.L., Vasil’ev, V.A., et al.: On some problems and results of the modern mathematical economics. Optimizatsija 30, 5–87 (1982). (in Russian)
Makarov, V.L., Vasil’ev, V.A., et al.: Equilibrium, rationing and stability. Matekon 25, 4–95 (1989)
Nikaido, H.: Convex Structures and Economic Theory. Academic Press, New York (1968)
Rockafellar, R.T.: Convex Analysis. Princeton University Press, Princeton (1970)
Vasil’ev, V.A.: On Edgeworth equilibria for some types of nonclassic markets. Sib. Adv. Math. 6, 96–150 (1996)
Vasil’ev, V.A.: On the coincidence of the cores and coordinated allocations in mixed economic systems. Doklady Akademii Nauk 352, 446–450 (1997). (in Russian)
Vasil’ev, V.A.: Core equivalence in a mixed economy. In: Herings, J.J.P., van der Laan, G., Talman, A. (eds.) The Theory of Markets, pp. 59–82. North-Holland, Amsterdam, Oxford, New York, Tokyo (1999)
Vasil’ev, V.A., Wiesmeth, H.: Equilibrium in a mixed economy of Arrow-Debreu type. J. Math. Econ. 44(2), 132–147 (2008)
Acknowledgement
The author would like to thank the Program of Fundamental Scientific Researches of the SB RAS I.5.1. (project 0314-2016-0018), and Russian Foundation for Basic Research (grant No. 16-06-00101) for partial financial support.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2018 Springer International Publishing AG, part of Springer Nature
About this paper
Cite this paper
Vasil’ev, V.A. (2018). Fuzzy Core Allocations in a Mixed Economy of Arrow-Debreu Type. In: Eremeev, A., Khachay, M., Kochetov, Y., Pardalos, P. (eds) Optimization Problems and Their Applications. OPTA 2018. Communications in Computer and Information Science, vol 871. Springer, Cham. https://doi.org/10.1007/978-3-319-93800-4_19
Download citation
DOI: https://doi.org/10.1007/978-3-319-93800-4_19
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-93799-1
Online ISBN: 978-3-319-93800-4
eBook Packages: Computer ScienceComputer Science (R0)