On the properties of the sato production function

Production function with only one output plays one of the key roles in the theory of the firm. Some of the common examples of production functions in the main microeconomic literature are, for example, CES, Cobb-Douglas or Leontief production function. In order to be a production function, a given mathematical function must satisfy certain properties. Various properties of the CES, Cobb-Douglas and Leontief production functions are proved and very well known in general. However, one of the not so common production functions is the “Sato function”. In this paper, we prove that Sato function satisfies the necessary assumptions for a function to be a production function. These requirements are continuity, strict monotonicity, strict quasiconcavity and that a positive amount of output requires positive amounts of some of the inputs. To the best of our knowledge, our results are new and unknown in the microeconomic literature.