Search

The study of the minimality of (hyper)surfaces is a fundamental problem in mathematics with major applications in both fundamental and applied sciences. Recently, the minimality of production models in microeconomics has been investigated by several authors who obtained important classification results for quasi‐sum and quasi‐product production functions with two and three inputs. In the present work, we deal with the minimality of isoquants of production functions with arbitrary number of inputs, this being a key concept used in making the best decision for optimizing the production costs. In the main result of the article, we give the complete classification of quasi‐product production functions whose isoquants are minimal, showing that there are exactly nine production models with such a property. Among them, we can identify a particular classic model already widely used in economic analysis (viz., a Cobb–Douglas model with unit output elasticities with respect to some production factors) and various production models completely unknown until now and which will open new opportunities for applied research in the field of mathematical economics. [ABSTRACT FROM AUTHOR]

In Appl. Econ. Lett. 18 (2011), 1777–1784, as a natural generalization of some famous production models with two inputs, C.A. Ioan and G. Ioan introduced a new class of production functions with constant return to scale, calledsum production function, and proved three theorems of characterization for such production models. In this article, we give new and more simple proofs of these theorems, extending also the results to the case of increased/decreased return to scale. The generalization to the case of an arbitrary number of inputs is also discussed. [ABSTRACT FROM PUBLISHER]

Abstract: In this paper, we completely classify homogeneous production functions with an arbitrary number of inputs whose production hypersurfaces are flat. As an immediate consequence, we obtain a complete classification of homogeneous production functions with two inputs whose production surfaces are developable. [Copyright &y& Elsevier]

Abstract: In this paper we prove that the generalized CES production function has constant return to scale if and only if the corresponding hypersurface is developable. Moreover, we establish that this production function has decreasing/increasing return to scale if and only if the corresponding hypersurface has positive/negative Gaussian curvature. These results are a generalization of some recent results concerning the generalized Cobb–Douglas production functions [G.E. Vîlcu, A geometric perspective on the generalized Cobb–Douglas production functions, Appl. Math. Lett. 24 (2011) 777–783]. [Copyright &y& Elsevier]

Abstract: In this work we obtain an interesting link between some fundamental notions in the theory of production functions and the differential geometry of hypersurfaces in Euclidean spaces. In fact we establish that a generalized Cobb–Douglas production function has decreasing/increasing return to scale if and only if the corresponding hypersurface has positive/negative Gaussian curvature. Moreover, this production function has constant return to scale if and only if the corresponding hypersurface is developable. [Copyright &y& Elsevier]

In this paper, we investigate the class of quasi-homogeneous production models, obtaining the classification of such models with constant elasticity with respect to an input as well as with respect to all inputs. Moreover, we prove that a quasi-homogeneous production function f satisfies the proportional marginal rate of substitution property if and only f reduces to some symmetric production functions. [ABSTRACT FROM AUTHOR]