Integral equation of the Volterra type : an application to a firm-sponsored off-the-job training

• Autorzy: Ekhosuehi V. U.

Identyfikatory

DOI

10.14708/ma.v44i2.1217

Warianty tytułu

PL

Użycie całkowego równania Volterry do opisu procesu kształcenia wewnątrz przedsiębiorstwa

• Języki publikacji: EN

Abstrakty

EN

This paper is concerned with deriving, using the Volterra integral equation, a production function for a single product firm financing off-the-job training from its revenue from output. The short-run scenario where labour is the only variable factor of production is studied within the the condition for profit-maximisation. The study utilises the Cobb-Douglas production function wherein capital is fixed as a theoretical underpinning. The Volterra integral equation is solved using the differential transform method. The solution reveals that the production function of the firm is a transcendental function. Some propositions on the properties of the new production function are stated along with their proofs. The behaviour of the production function is demonstrated by way of simulation.

PL

W artykule poszukuje się funkcji produkcji pojedynczego produktu w przedsiębiorstwie finansującym szkolenia ze środków uzyskanych ze sprzedaży tego produktu. Funkcja produkcji ma założoną formę równania całkowego Volterry a kryterium optymalizacji jest krótkoterminowa maksymalizacja zysku, w którym praca jest jedynym czynnikiem produkcji. W badaniu wykorzystano funkcję Cobba-Douglasa z ustaloną ilością kapitału. Wyniki wskazują, że otrzymana funkcja produkcji firmy jest funkcją analityczną, a wymagana część zysku potrzebna do sfinansowania szkolenia leży w przedziale z określoną górną granicą.

Słowa kluczowe

EN

firm; differential transform method; production function; Volterra integral equation

PL

przedsiębiorstwo; metoda przekształceń różniczkowych; funkcja produkcji; całkowe równanie Volterry

• Wydawca: Polskie Towarzystwo Matematyczne
• Czasopismo: Mathematica Applicanda
• Rocznik: 2016
• Tom: Vol. 44, No. 2
• Strony: 295--307
• Opis fizyczny: Bibliogr. 35 poz., fot., wykr.

Twórcy

autor

Ekhosuehi V. U.

• University of Benin, Department of Mathematics, Benin City, Nigeria

Bibliografia

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Uwagi

Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę (zadania 2017).