The determination of the main indicators of a production function

• Author: Catalin Angelo Ioan
• Position: Associate Professor, PhD, Danubius University of Galati, Faculty of Economic Sciences, Romania
• Pages: 626-635

European Integration - Realities and Perspectives 2012

626

The Determination of the Main Indicators of a Production Function

Using the Bernoulli Equations

Catalin Angelo Ioan

1

Abstract: Production functions are an essential tool for analysis of production processes. The indicators of

marginal production, marginal rates of substitution, elasticities of production and the marginal elasticity of

technical s ubstitution characterized, fr om different p oint of view, the behavior of the production under the

action of factors of labor or capital. This paper presents a new way of determining using the first-or der

differential equation of Bernoulli type, giving also a useful tool for the creation of new production functions.

Keywords: production function; marginal rate of substitution; elasticity

JEL Classification: D01

1Introduction

In the analysis of production processes, fundamentally important are the production functions, which

are accompanied by a series of indicators that provide useful information i n t he economic analysis.

The production functions approach can be based on practical needs ([10]) or on the conditions of their

indicators ([1], [3], [9], [11], [12], [13]). Another approach can be done in terms of purely geometric

properties ([4], [5]), but also through the generalization of existing functions and then putting in

obviousness their common characteristics ([6], [8]).

In this paper, we will broach the problem of determining the main indicators from a different point of

view. Even if they come from different economical considerations, we will construct a first-order

differential equation of Bernoulli type, whose coefficients will allow the immediate determination of

those indicators.

At first glance, the question arises: how to use such an approach? The problem has an immediate

response, although not very visible. The differential equation, by assigning different expressions to the

composing functions, can be a true generator of production functions!

Let therefore a production function Q:(0,∞)

2

→R

+

, (K,L)→Q(K,L) homogeneous of first degree.

Let note, also χ=

L

K

- the technical endowment of labor. We have:

Q(K,L)=













=











1,

L

K

LQL,

L

K

LQ

=L⋅q(χ)

where q(χ)=Q(χ,1).

The partial first-order derivations of Q, are obtained easily:

1

Associate Professor, PhD, Danubius University of Galati, Faculty of Economic Sciences, Romania, Address: 3 Galati Blvd,

Galati, Romania, tel: +40372 361 102, fax: +40372 361 290, Corresponding author: catalin_angelo_ioan@univ-danubius.ro.