A Semigroups Approach to the Study of a Second Order Partial Diferential Equation Applied in Economics
AbstractIn this paper we will study the well-known problem of production functions in an operator semigroup approach. In general, semigroups can be used to solve a large class of problems com-monly known as evolution equations. They are usually described by an initial value problem for a differential equation, also known as a Cauchy problem. After summarizing some of the major properties of semigroups theory, we will provide an application to the theory of production functions. In order to arrive to our main result, we consider that the production function F (L(t), K (t), t) is assumed to be homogenous of degree one. To simplify the computation procedure, we denote by x(t) = K (t)/ L(t), y = f ( x(t), t ), and we suppose that x(t) is the solution for a stochastic differential equation. Finally we present some concluding remarks.
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Bibliographic InfoArticle provided by West University of Timisoara, Romania, Faculty of Economics and Business Administration in its journal Timisoara Journal of Economics.
Volume (Year): 4 (2011)
Issue (Month): 4(16) ()
Postal: 16 J. H. Pestalozzi Street, 300115, Timisoara, Romania
Other versions of this item:
- Chilarescu, Constantin & Viasu, Ioana Luciana, 2011. "A Semigroups Approach to the Study of a Second Order Partial Differential Equation Applied in Economics," MPRA Paper 33908, University Library of Munich, Germany.
- C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models &bull Diffusion Processes
- C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
- D24 - Microeconomics - - Production and Organizations - - - Production; Cost; Capital; Capital, Total Factor, and Multifactor Productivity; Capacity
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- repec:ebl:ecbull:v:3:y:2007:i:9:p:1-8 is not listed on IDEAS
- Constantin Chilarescu & Nicolas Vaneecloo, 2007. "A Stochastic Approach to the Cobb-Douglas Production Function," Economics Bulletin, AccessEcon, vol. 3(9), pages 1-8.
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