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ABSTRACT
The production function explains a basic technological relationship between scarce resources, or inputs, and output. This paper offers a brief overview of the historical significance and operational role of the production function in business and economics. The origin and development of this function over time is initially explored. Several various production functions that have played an important historical role in economics are explained. These consist of some well known functions, such as the Cobb-Douglas, Constant Elasticity of Substitution (CES), and Generalized and Leontief production functions. This paper also covers some relatively newer production functions, such as the Arrow, Chenery, Minhas, and Solow (ACMS) functions, the transcendental logarithmic (translog), and other flexible forms of the production function. Several important characteristics of the production function are also explained in this paper. These would include, but are not limited to, items such as the returns to scale of the function, the separability of the function, the homogeneity of the function, the homotheticity of the function, the output elasticity of factors (inputs), and the degree of input substitutability that each function exhibits. Also explored are some of the duality issues that potentially exist between certain production and cost functions. The information contained in this paper could act as a pedagogical aide in any microeconomics-based course or in a production management class. It could also play a role in certain marketing courses, especially at the graduate level.
Keywords: Production function; returns to scale; cost functions
INTRODUCTION
The use of scarce resources is a major topic in economics. The relationship that explains the technology of the firm is called the production function. This function demonstrates the relationship between these scarce resources and the output of a firm. Production theories have existed long before Adam Smith, but were only refined, in a mathematical sense, during the late 19th century. When concerned with a one output firm, the production function is a very simple construct. It tells us the maximum quantity of a particular output that can be produced using various combinations of inputs given certain technical knowledge. We can think of the production function as a type of transformation function where inputs are transformed into output via a managerial process. There are also production sets and input requirement sets...