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A Semigroups Approach to the Study of a Second Order Partial Diferential Equation Applied in Economics

Author

Listed:
  • Ioana VIASU

    (Faculty of Economics and Business Administration, West University of Timisoara, Romania)

  • Constantin CHILARESCU

    (Laboratory CLERSE, University of Lille1, France)

Abstract

In 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.

Suggested Citation

  • Ioana VIASU & Constantin CHILARESCU, 2011. "A Semigroups Approach to the Study of a Second Order Partial Diferential Equation Applied in Economics," Timisoara Journal of Economics, West University of Timisoara, Romania, Faculty of Economics and Business Administration, vol. 4(4(16)), pages 239-244.
    • Handle: RePEc:wun:journl:tje:v04:y2011:i4(16):a06
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    References listed on IDEAS

    as
    1. Constantin Chilarescu & Nicolas Vaneecloo, 2007. "A Stochastic Approach to the Cobb-Douglas Production Function," Economics Bulletin, AccessEcon, vol. 3(9), pages 1-8.
    2. repec:ebl:ecbull:v:3:y:2007:i:9:p:1-8 is not listed on IDEAS
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    More about this item

    Keywords

    production functions; partial differential equations; semigroups;
    All these keywords.

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; 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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