Classification of quasi-sum production functions with Allen determinants

Abstract

In this paper, we derive an explicit formula for the determinant of Allen's matrix of quasi-sum production functions. We completely classify the quasi-sum production functions by using their Allen determinants. Further, we give some geometric applications of Allen determinants.

Rotational surfaces in isotropic spaces satisfying weingarten conditions

“…The rotational surfaces given by (3) and (4) are locally isometric and thus we only consider the ones of the form (3).…”

“…The work of surfaces with certain properties in the isotropic 3-space I 3 has important applications in several applied sciences, e.g., computer science, image processing, architectural design and microeconomics, see [3,4,6,8,[30][31][32]. Differential geometry of isotropic spaces has been introduced by K. Strubecker [38], H. Sachs [33][34][35], D. Palman [28] and others.…”

Classification of factorable surfaces in the pseudo-Galilean space

“…When the graphs of production functions in microeconomics have NGC, one can realize a "good" analysis of isoquants by projections, without losing essential information about their geometry (see [1,19]). By motivating these, we target to study the factorable surfaces in the pseudo Galilean space G In this paper, we classify the factorable surfaces with NGC and minimal ones in G 1 3 .…”

Galilean geometry of corresponding surfaces to production models in economics

“…The authors in [6] called such matrices the Allen's matrix and classified some production functions by using the singularity of the Allen matrices [3][4][5][6].…”

“…Chen, et al [10,17] investigated the graph hypersurfaces of the production models via the isotropic geometry. For further study of graph hypersurfaces of production functions we refer the reader to [3][4][5][6][9][10][11][12][13][14][15].…”