The trajectories illustrating the necessary changes in the production sphere, which are caused by the necessity or the wish of producers, who adjust their activities to the given requirements, are analyzed in the paper. The producers’ activities are modeled in the Debreu economy, while the requirements are given analytically, by using the linear functionals.
If the producers change their plans of action due to the considered trajectories, equilibrium in the economy will be kept, although the initial state of equilibrium can be replaced by the other one.
In the set of trajectories under study, the preference relation is defined. Under some assumptions, the maximal element of the above relation, so called the best producers’ adjustment trajectory, indicates the best path of changes in producers’ activities, under the criterion of losses minimization.
private ownership economy, equilibrium, linear sets, projections
Aliprantis C. D., (1996), Problems in Equilibrium Theory, Springer – Verlag Berlin, Heidelberg, German.
Cheney E. W., (1966), Introduction to Approximation Theory, Mc Grow Hill, New York.
Debreu G., (1959), Theory of Value, New York, Viley.
Lewicki G., Odyniec W., (1990), Minimal Projections in Banach Spaces, Lecture Notes in Mathematics, 1449, Springer-Verlag, Berlin/New York.
Lipieta A., (1999), Cominimal Projections in . Journal of Approximation Theory, 98, 86–100.
Lipieta A., (2010), The Debreu Private Ownership Economy with Complementary Commodities and Prices, Economic Modelling, 27, 22–27.
Lipieta A., (2012), The Economy with Production and Consumption Systems Changing in Time, Przegląd Statystyczny, 59 (3), 233–245.
Lipieta A., (2013), Mechanisms of Schumpeterian Evolution, in: Malawski A., (ed.), Innovative Economy as the Object Investigation in Theoretical Economics, Cracow University of Economics Press, 94–119.
Magill M., Quinzii M., (2002), Theory of Incomplete Markets, MIT Press, Cambridge.
Mas-Colell A., Whinston M. D., Green J. R., (1959), Microeconomic Theory, Oxford University Press, New York.
Moore J., (2007), General Equilibrium and Welfare Economics, Springer Berlin-Heidelberg-New Jork.
Radner R., (1972), Existence of Equilibrium of Plans, Prices and Price Expectations in a Sequence of Markets, Econometrica, 40 (2), 289–303.
Sibirskij K. S., Szube A. S., (1987), Semidynamical Systems (Topological Theory). Russian, Sztinica, Kiszyniów, Belknap Press of Harvard University Press.
Schumpeter J. A., (1912), Die Theorie der Wirtschaftlichen Entwicklung, Leipzig, Duncker & Humblot; English translations, The Theory of Economic Development, Cambridge, MA, Harvard University Press 1934 and A Galaxy Book, New York, Oxford University Press 1961.
Varian H. R., (1999), Intermediate Microeconomics, A Modern Approach. W. W. Norton & Company, New York, London.