Theory of Production pp 41-82 | Cite as

# Various Methods of Describing a Continuous Production Law

## Abstract

We are now concerned with a momentary production where a single product is produced, of which the quantity can be measured in technical units (or at any rate in quantity indices). Each factor quantity can also be measured technically. Let *x* be the quantity of the product and *v* _{1}, *v* _{2}, ..., *v* _{ n } the factor quantities. We assume that the technique is constant during all the variations of factor quantities under consideration. In that case, corresponding to given magnitudes of *v* _{1}, *v* _{2}, ... *v* _{ n }, we have only one definite magnitude of *x*. We say that *x* is a function of the *n* variable *v* _{1}, ..., *v* _{ n }, and call this the *product function.*

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## References

- 1.The concept of continuity is discussed in R. Frisch,
*Tetthet og masse ved en Statistik fordeling.*Memorandum from the University Institute of Social Economics, Oslo, 8 February 1951, Section 21b.Google Scholar - 1.This name is an allusion to the inclination or slope, and is associated with a graphic representation of marginal productivity with the aid of arrows in the factor diagnose.Google Scholar
- 2.Cf. (7b.1).Google Scholar
- 1.These definitions apply to continuity factors. In dealing with
*limitational factors*in Part Three the definitions will have to be stated with greater precision.Google Scholar - 1.The figures in Table (5a.7) have been
*smoothed*in such a way that the factors are marginally*independent.*Google Scholar - 1.Erick Schneider uses the expression ‘Niveauelastizität eines Prozesses’ in his
*Einführung in die Wirtschaftstheorie*(Tübingen 1958), and the term ‘Ergiebigkeitsgrad der Produktion’ in his*Theorie der Produktion*(Vienna 1934). W. E. Johnson uses the term ‘elasticity of production’ in the*Economic Journal*, 1913, and Sune Carlson uses the term ‘function coefficient’ in*A Study on the Pure Theory of Production*(London 1939). R. G. D. Allen, in his*Mathematical Analysis for Economists*(1947), p. 263, speaks of ‘elasticity of productivity’.Google Scholar - 1.Equation (5g.16) can be derived by using any system of logarithms, provided we keep the same system throughout. Here, however, we use the natural system of logarithms as this will be the simplest.Google Scholar