Ownership structure and efficiency in large economies. (English) Zbl 1248.91055
With Hart’s classical result [O. D. Hart, Econometrica 47, 1057–1083 (1979; Zbl 0418.90008)] in the background, the main point of this paper is, to give a frame (a suitable topology on the space of production economies) and conditions (esp. for ownership structures) such that the behavior of sequences of large economies and suitable limit economies can be considered. It is shown, that Hart’s assumption “all agents are typical” is very restrictive and a new proof of his result is given without the mentioned condition. From this some general convergence theorems are proved containing conditions, such that (e.g.) in the limit economy \(E\) there is a profit maximizing production plan \(y\) (at prices \(p\), where \(p\) is a unique equilibrium price associated with \(y\) in \(E\)).
Reviewer: Alfred Göpfert (Halle)
MSC:
| 91B54 | Special types of economic markets (including Cournot, Bertrand) |
| 91B52 | Special types of economic equilibria |
| 91B38 | Production theory, theory of the firm |
| 90B30 | Production models |
| 49J45 | Methods involving semicontinuity and convergence; relaxation |
| 90C33 | Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming) |
Keywords:
ownership structure; equilibrium; sequences of economies; firm’s objective; profit maximizing production planCitations:
Zbl 0418.90008References:
| [1] | Aliprantis C.D., Border K.C.: Infinite Dimensional Analysis. A Hitchhiker’s Guide, 3rd edn. Springer, Berlin (2006) · Zbl 1156.46001 |
| [2] | Aliprantis C.D., Brown D.J., Burkinshaw O.: Edgeworth equilibria in production economies. J Econ Theory 43, 252–291 (1987) · Zbl 0637.90017 · doi:10.1016/0022-0531(87)90060-3 |
| [3] | Allen B.: Randomization and the limit points of monopolistic competition. J Math Econ 23, 205–218 (1994) · Zbl 0821.90012 · doi:10.1016/0304-4068(94)90006-X |
| [4] | Bejan, C.: Market imperfections and the objective of a privately owned firm. PhD thesis, University of Minnesota (2005) |
| [5] | Bejan C.: The objective of a privately owned firm under imperfect competition. Econ Theory 37, 99–118 (2008) · Zbl 1148.91029 · doi:10.1007/s00199-007-0289-5 |
| [6] | Bejan, C., Bidian, F.: Ownership structure and efficiency in large economies. Mimeo, http://www.owlnet.rice.edu/\(\sim\)cmb3736/research/convergence.pdf (2010) · Zbl 1248.91055 |
| [7] | Debreu G., Scarf H.: A limit theorem on the core of an economy. Int Econ Rev 4, 235–246 (1963) · Zbl 0122.37702 · doi:10.2307/2525306 |
| [8] | Demichelis, S., Ritzberger, K.: A general equilibrium analysis of corporate control and the stock market. Econ Theory. doi: 10.1007/s00199-009-0511-8 (2009) · Zbl 1217.91108 |
| [9] | Dierker E., Grodal B.: Profit maximization mitigates competition. Econ Theory 7, 139–160 (1995) · Zbl 0840.90019 · doi:10.1007/s001990050046 |
| [10] | Dierker E., Grodal B.: The price normalization problem in imperfect competition and the objective of the firm. Econ Theory 14, 257–284 (1999) · Zbl 0942.91034 · doi:10.1007/s001990050293 |
| [11] | Dudley R.: Real Analysis and Probability. Cambridge University Press, Cambridge (2002) · Zbl 1023.60001 |
| [12] | Florenzano, M., Mercato, L.D.: Edgeworth and Lindahl-Foley equilibria of a general equilibrium model with private provision of public goods. Cahiers de la MSE, Universite Paris Pantheon-Sorbonne, B04082 (2004) |
| [13] | Gabszewicz J.J., Vial J.P.: Oligopoly ”a la Cournot” in a general equilibrium analysis. J Econ Theory 4, 381–400 (1972) · doi:10.1016/0022-0531(72)90129-9 |
| [14] | Hart O.D.: On shareholder unanimity in large stock market economies. Econometrica 47, 1057–1083 (1979) · Zbl 0418.90008 · doi:10.2307/1911950 |
| [15] | Hildenbrand W.: On economies with many agents. J Econ Theory 2, 161–188 (1970) · doi:10.1016/0022-0531(70)90003-7 |
| [16] | Hildenbrand W.: Distributions of agents’ characteristics. J Math Econ 2, 129–138 (1975) · Zbl 0323.90006 · doi:10.1016/0304-4068(75)90019-1 |
| [17] | Hildenbrand W., Mertens J.F.: Upper Hemi-Continuity of the equilibrium-set correspondence for pure exchange economies. Econometrica 40, 99–108 (1972) · Zbl 0244.90006 · doi:10.2307/1909724 |
| [18] | Kallenberg O.: Foundations of Modern Probability, 2nd edn. Springer, Berlin (2002) · Zbl 0996.60001 |
| [19] | Kelsey D., Milne F.: Externalities, monopoly and the objective function of the firm. Econ Theory 29, 565–589 (2006) · Zbl 1120.91021 · doi:10.1007/s00199-005-0036-8 |
| [20] | Kopp P.: Martingales and Stochastic Integration. Cambridge University Press, Cambridge (1984) · Zbl 0537.60047 |
| [21] | Mas-Colell A.: Noncooperative approaches to the theory of perfect competition: presentation. J Econ Theory 22, 121–135 (1980) · doi:10.1016/0022-0531(80)90036-8 |
| [22] | Mas-Colell, A.: The Cournotian foundations of Walrasian equilibrium theory: an exposition of recent theory. In: Advances in Economic Theory. Cambridge: Cambridge University Press (1982) · Zbl 0544.90008 |
| [23] | Mas-Colell A., Nachbar J.H.: On the finiteness of the number of critical equilibria, with an application to random selections. J Math Econ 20, 397–409 (1991) · Zbl 0735.90017 · doi:10.1016/0304-4068(91)90038-U |
| [24] | McKenzie L.W.: The classical theorem on existence of competitive equilibrium. Econometrica 49, 819–841 (1981) · Zbl 0461.90008 · doi:10.2307/1912505 |
| [25] | Roberts K.W.S.: The limit points of monopolistic competition. J Econ Theory 22, 256–278 (1980) · Zbl 0436.90019 · doi:10.1016/0022-0531(80)90043-5 |
| [26] | Stokey N., Lucas R.: Recursive Methods in Economic Dynamics. Harvard Press, Cambridge (1989) · Zbl 0774.90018 |
| [27] | Tvede M., Cres H.: Voting in assemblies of shareholders and incomplete markets. Econ Theory 26, 887–906 (2005) · Zbl 1116.91034 · doi:10.1007/s00199-004-0537-x |
| [28] | Xiong S., Zheng C.Z.: Core equivalence theorem with production. J Econ Theory 137, 246–270 (2007) · Zbl 1132.91535 · doi:10.1016/j.jet.2007.01.009 |
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