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.
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机译:几乎所有的经济理论都以生产函数为前提,无论是在企业层面还是在总体层面。从这个意义上说,生产函数是新古典主流理论的关键概念之一。有非常重要的一类生产函数,通常在微观经济学中进行分析。即$ h $均质的生产函数。此类生产函数包括微观经济学中的许多重要生产函数。特别是众所周知的广义Cobb-Douglas生产函数和ACMS生产函数。在本文中,我们通过生产超曲面研究了$ h $均匀生产函数的几何性质。结果,我们获得了关于$ h $齐次生产函数的一些刻画,这些函数具有不变的规模收益或成为完美的替代品。还给出了广义Cobb-Douglas和ACMS生产函数的一些应用。
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