Summary
In dealing with dynamic economic policy models one encounters optimization problems whose objective function is an integral of a linear function of a finite number of continuous variables and whose constraints are linear integral inequalities. A set of intertemporal efficiency conditions (equilibrium conditions) yielding the optimal policy are given. By approximating the continuous problem by a set of discrete problems and appealing to a well known convergence theorem in functional analysis a continuous analog of the duality theorem is proved.
Zusammenfassung
Bei der Beschäftigung mit dynamischen Modellen der ökonomischen Politik stößt man auf Optimierungsprobleme, deren Zielfunktion ein Integral einer linearen Funktion von einer endlichen Anzahl stetiger Variablen ist und deren Beschränkungen lineare Integral-Ungleichungen sind. Eine Menge intertemporaler Effizienz-Bedingungen (Gleichgewichtsbedingungen), die zur optimalen Politik führen, sind gegeben. Durch Approximation des kontinuierlichen Problems mittels einer Menge von diskreten Problemen und Berufung auf einen wohlbekannten Konvergenzsatz aus der Funktionalanalysis wird ein stetiges Analogon des Dualitätstheorems bewiesen.
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References
Bellman, R. E.: Dynamic Programming. Princeton University Press (1957), pp. 197–199.
Gale, D.: The Theory of Linear Economic Models. McGraw-Hill, New York, 1960.
Taylor, A. E.: General Theory of Functions and Integration. Blaisdell Publishing Company, 1965.
Kumar, T. K.: “On the Existence of an Optimal Economic Policy.” (Sent for publication.)
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The author is indebted to Mr.Arnold Faden for helpful suggestions and to ProfessorKarl A. Fox andGerhard Tintner for encouragement during the preparation of the paper. This research has been partially supported by a grant from the Ford Foundation to the School of Business Administration administered by the Center for Research in Management Science, University of California, Berkeley.
Vorgel. v.:G. Tintner.
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Kumar, T.K. A duality theorem for continuous-time linear programming problems. Operations Research 10, 224–236 (1966). https://doi.org/10.1007/BF01967463
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DOI: https://doi.org/10.1007/BF01967463