competitive equilibrium,
core,
incomplete markets,
infinite dimensional economy,
infinite dimensional commodity space,
the overlapping generations of economic agents,
contract,
equilibrium with nonstandard prices.
Subject:
Main research activities are in mathematical economics, substantially it is the area of general equilibrium applied to the modern neoclassical models, non-perfect markets and infinite dimensional models, as well as various applications of functional and nonstandard analysis to economics. Some of major results: a) the creation of an equilibrium theory with nonstandard prices (by means of nonstandard analysis), in which framework an equilibrium exists without restrictive survival assumption; there were stated very general existence theorems for an abstract model, which may be applied to study a number of classical models mdash; pure exchange economies as well as Arrowndash;Debreu, economies with public goods etc., where a kind of "Slater's condition" can appear in consumer problem; the structure of (standard) budget sets with nonstandard prices was investigated in details &Mdash; this is the key concept of theory; the finiteness of the number of "nonstandard equilibria"' was also studied; b) a variety of existence equilibrium results were stated for the models with infinite dimensional commodity space, which is described as linear vector lattice (lattice operations may be discontinues). The difficulties are appeared due to the "uncomfortable"' properties of commodity space in which positive cone can have empty interior, that precludes to find a continuous price functional. To overcome the case a series of (weakest in literature) properness assumptions for preferences and production sets is considered. Overlapping generations economies with the same structure assumptions for commodity space also were studied. A concept of generalized equilibrium was introduced applying nonstandard methods and its existence theorem was proved. The main specific of our concept, which generalizes known compensated equilibrium, is that values, which are added to the right hand side of budget constrains are linear relative to initial endowments; c) a theory of (exchange) contracts was created (it develops some forgotten results of other authors from early 80's) in which some of economic theory primitives are reconsidered and which complements the classical approach to domination via coalitions. The focus of theory is transmitted from final resource allocation directly on "the webs of contacts" (the finite set of the elementary exchange bargains of commodities), realizing allocations. The agents are allowed to break contracts and to sign new ones. A series of stability properties for webs are introduced and studied, applying them one can describe and clarified some of classical concepts (equilibrium, core, Pareto boundary etc.). The language of contracts is more convenient than classical one. The inadmissibility of some exchange contracts is the specific feature many of modern non-classical models and reflects the essence of approach which, being complementing classical one, can help to clarify and to solve many of difficult problems of economic theory. In particular an concept of core for incomplete (financial) markets was introduced and investigated. There are other possible applications.
Biography
Graduated from Faculty of Mathematics and Mechanics of Novosibirsk State University in 1978 (M.Sc. in mathematics). The candidate of physical and mathematical sciences, (Ph. D. in mathematics) — Institute of Mathematics, Siberian Branch of the Soviet Academy of Sciences, 1985. Doctoral Degree in mathematics (habilitation) in 2004 for the thesis "On existence equilibrium theorems in modern economic theory" (defended in Central Economic-Mathematical Institute, Moscow, 2003). The Leading researcher of Optimization Methods Laboratory, Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences. More than 70 publications (mainly in English). The former member of Econometric Society, participated in 6-th and 7-th World Congresses (Barcelona-90, Tokyo-95 and Seatl-2000-in absetia) and European Meetings of the Econometric Society (Cambridge-91, Brussels-92, Uppsala-93, Maastriht-94) and in other scientific conferences; Teaching experience in Novosibirsk State University (Departments of Mathematics and Economics faculty), Professor. The lecturer of course "Game Theory with applications to mathematical economics".
Main publications:
Florenzano, M., Marakulin, V. M. Production Equilibria in Vector Lattices // Economic Theory 17, 3, pp.
577–598, 2001.
Marakulin, V. M. Equilibria in Infinite Dimensional Commodity Spaces Revisited // Economic Theory 18, 3, pp. 621–633, 2001.
Marakulin, V. M. Equilibria with Nonstandard Prices in Vector Lattice Overlapping Generations Economies// Journal of
Mathematical Analysis and Applications 282, 2, pp. 648–667, 2003.
Marakulin, V. M. An abstract equilibrium analysis of economic-mathematical models, Novosibirsk: SB Russian Academy of Science Publisher, 2012. – 348 p. (in Russian) ISBN 978-5-7692-1242-0
Konovalov, A. V., Marakulin, V. M. Equilibria Without the Survival Assumption// Journal of Mathematical Economics, 42 pp. 198–215, 2006.
V. M. Marakulin, “A theory of spatial equilibrium: the existence of migration proof country partition in a uni-dimensional world”, Sib. J. Pure and Appl. Math., 17:4 (2017), 64–78
2004
2.
V. M. Marakulin, “Equilibrium analysis in Kantorovich spaces”, Zap. Nauchn. Sem. POMI, 312 (2004), 188–214; J. Math. Sci. (N. Y.), 133:4 (2006), 1477–1490