<P> In general, economic output is not a (mathematical) function of input, because any given set of inputs can be used to produce a range of outputs . To satisfy the mathematical definition of a function, a production function is customarily assumed to specify the maximum output obtainable from a given set of inputs . The production function, therefore, describes a boundary or frontier representing the limit of output obtainable from each feasible combination of input . (Alternatively, a production function can be defined as the specification of the minimum input requirements needed to produce designated quantities of output .) Assuming that maximum output is obtained from given inputs allows economists to abstract away from technological and managerial problems associated with realizing such a technical maximum, and to focus exclusively on the problem of allocative efficiency, associated with the economic choice of how much of a factor input to use, or the degree to which one factor may be substituted for another . In the production function itself, the relationship of output to inputs is non-monetary; that is, a production function relates physical inputs to physical outputs, and prices and costs are not reflected in the function . </P> <P> In the decision frame of a firm making economic choices regarding production--how much of each factor input to use to produce how much output--and facing market prices for output and inputs, the production function represents the possibilities afforded by an exogenous technology . Under certain assumptions, the production function can be used to derive a marginal product for each factor . The profit - maximizing firm in perfect competition (taking output and input prices as given) will choose to add input right up to the point where the marginal cost of additional input matches the marginal product in additional output . This implies an ideal division of the income generated from output into an income due to each input factor of production, equal to the marginal product of each input . </P> <P> The inputs to the production function are commonly termed factors of production and may represent primary factors, which are stocks . Classically, the primary factors of production were Land, Labour and Capital . Primary factors do not become part of the output product, nor are the primary factors, themselves, transformed in the production process . The production function, as a theoretical construct, may be abstracting away from the secondary factors and intermediate products consumed in a production process . The production function is not a full model of the production process: it deliberately abstracts from inherent aspects of physical production processes that some would argue are essential, including error, entropy or waste, and the consumption of energy or the co-production of pollution . Moreover, production functions do not ordinarily model the business processes, either, ignoring the role of strategic and operational business management . (For a primer on the fundamental elements of microeconomic production theory, see production theory basics). </P> <P> The production function is central to the marginalist focus of neoclassical economics, its definition of efficiency as allocative efficiency, its analysis of how market prices can govern the achievement of allocative efficiency in a decentralized economy, and an analysis of the distribution of income, which attributes factor income to the marginal product of factor input . </P>

Functions of capital as a factor of production