Classification of quasi‐product production models with minimal isoquants

Abstract

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.