Algebraic Production Functions and Their Uses Before Cobb-Douglas

the production function relates total product P to the labor L, capital C, land T (terrain), and other inputs that combine to produce it. The function expresses a technological relationship. It describes the maximum output obtainable, at the existing state of technological knowledge, from given amounts of factor inputs. Put differently, a production function is simply a set of recipes or techniques for combining inputs to produce output. Only efficient techniques qualify for inclusion in the function, however, namely those yielding maximum output from any given combination of inputs. Production functions apply at the level of the individual firm and the macro economy at large. At the micro level, economists use production functions to generate cost functions and input demand schedules for the firm. The famous profit-maximizing conditions of optimal factor hire derive from such microeconomic functions. At the level of the macro economy, analysts use aggregate production functions to explain the determination of factor income shares and to specify the relative contributions of technological progress and expansion of factor supplies to economic growth.