= Cobb-Douglas Production Function = The '''Cobb-Douglas production function''' is a formulation of the production function, typically given inputs of labor and capital. <> ---- == Formulation == The basic Cobb-Douglas function is: Y(L,K) = AL^a^K^b^ Where... * L is '''labor''' and K is '''capital''', the classical economic inputs * A is '''total factor productivity''', essentially the catch-all residual term, generally thought of as intrinsically-productive technology or human capital * ^a^ and ^b^ represent '''output elasticities''', generally thought of as technological effects on specific inputs' efficiencies, somewhere in the non-inclusive range of 0 and 1. The output elasticities of a Cobb-Douglas function can also be characterized in terms of '''returns to scale'''. For example, if there is just one input... * ...and a 100% increase to the input causes a 100% increase to the output (i.e., '''constant''' returns to scale), then the output elasticity ''must'' be 1. * ...and a 100% increase to the input causes a >100% increase to the output (i.e., '''increasing''' returns to scale), then the output elasticity ''must'' be >1. * ...and a 100% increase to the input causes a <100% increase to the output (i.e., '''decreasing''' returns to scale), then the output elasticity ''must'' be <1. ---- == History == This production function was developed by Charles Cobb and Paul Douglas. They fit decades of aggregated U.S. economic data to this model and estimated the output elasticities for the U.S. economy. ---- CategoryRicottone