Some Examples Of Production Functions
Abstract
The aim of this paper is to give some basic geometrical
characteristics of generalized Cobb-Douglas surfaces and
some examples of these surfaces. In case of growing re-
turns to scale Cobb-Douglas surfaces have the form
(x; y) = (x; y; Ax
y
); where x > 0; y > 0; + > 1:
In case of decrease returns to scale Cobb-Douglas surfaces
have the form
(x; y) = (x; y; Ax
y
); where x > 0; y > 0;
0 < + < 1:
Analogically in case of constant returns to scale CobbDouglas
surfaces have the form
(x; y) = (x; y; Ax
y
); where x > 0; y > 0; + = 1:
In connection with this surfaces we are interested in Gaus-
sian curvature, mean curvature and principal curvatures.
References
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Kanka, M., 1995, “An example of basic structure equations for Riemannian Manifolds” Mundus Symbolicus 1995, 57–62
Kobayashi, S., Nomizu, K., 1963, “Foundations of differential geometry” New York
Nomizu, K., 1956, “Lie groups and differential geometry” The mathematical society of Japan Sternberg, S., 1964, “Lectures on Differential Geometry” Prentice
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