Notes on isotropic geometry of production models

Abstract

Abstract. The production function is one of the key concepts of mainstream neoclassical theories in economics. The study of the shape and properties of the production possibility frontier is a subject of great interest in economic analysis. In this respect, Cobb-Douglas and CES production functions with flat graph hypersurfaces in Euclidean spaces are first studied in [20,21]. Later, more general studies of production models were given in [5]- [9] and [11,13,22]. On the other hand, from visual-physical experiences [16,17,18], the second and third authors proposed in [15] to study production models via isotropic geometry as well. The purpose of this paper is thus to investigate important production models via isotropic geometry.

Classification Results on Surfaces in The Isotropic 3‐Space

“…For more details of , 1  n I see (Chen et al, 2014), (Sachs, 1978) and (Milin Sipus and Divjak, 1998). …”

Isotropic geometry of graph surfaces associated with product production functions in economics

“…B.-Y. Chen, et al [7,13] investigated the graph hypersurfaces of the production models via the isotropic geometry. In the present paper, we classify the graph surfaces of product production functions of 2 variables with constant curvature in the isotropic 3-space I 3 .…”

On Quasi-Homogeneous Production Functions

“…The characterization of the production models with constant elasticity of production, with proportional marginal rate of substitution (PMRS) property and with constant elasticity of substitution (CES) property is a challenging problem [3][4][5][6][7] and several classification results were obtained in the last years for different production functions, such as homogeneous, homothetic, quasi-sum and quasi-product production functions [8][9][10][11]. Other notable results concerning the above production models were recently derived using a differential geometric approach [12][13][14][15][16][17][18][19][20][21][22][23][24][25]. This treatment is based on the fact that one can associate a graph hypersurface to any production function and it is remarkable that one can relate basic concepts from production theory with some differential geometric invariants (intrinsic and extrinsic) of the associated hypersurface [26,27].…”