On some geometric properties of $h$-homogeneous production functions in microeconomics

Bang-Yen Chen

Almost all economic theories presuppose a production function, either on the firm level or the aggregate level. In this sense the production function is one of the key concepts of mainstream neoclassical theories. There is a very important class of production functions that are often analyzed in microeconomics; namely, $h$-homogeneous production functions. This class of production functions includes many important production functions in microeconomics; in particular, the well-known generalized Cobb-Douglas production function and the ACMS production function. In this paper we study geometric properties of $h$-homogeneous production functions via production hypersurfaces. As consequences, we obtain some characterizations for an $h$-homogeneous production function to have constant return to scale or to be a perfect substitute. Some applications to generalized Cobb-Douglas and ACMS production functions are also given.