Cobb-Douglas Production Function and Its Properties.pdf - Cobb-Douglas Production Function and Its Properties Economics Discussion Cobb-Douglas

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10/4/2019 Cobb-Douglas Production Function and Its Properties 1/14 Economics Discussion Economics Discussion Cobb-Douglas Production Function and Its Properties Article Shared by ADVERTISEMENTS: While discussing the production theory of the firm, economists C. W. Cobb and P. H. Douglas used a special form of production function, which is known as the Cobb-Douglas Production Function. Cobb-Douglas (C-D) production function is of the form Q = AL K (8.100) where L = quantity used of labour ADVERTISEMENTS: K = quantity used of capital Q = quantity of output produced A, α, β = positive constants. Actually, the parameter A is the efficiency parameter. It serves as an indicator of the state of technology. The higher the value of A, the higher would be the level of output that can be produced by any particular combination of the inputs. ADVERTISEMENTS: α β Economic Models, Equilibrium, Statics and Dynamics Read Next Story
10/4/2019 Cobb-Douglas Production Function and Its Properties 2/14 Also α and β are the distribution parameters. They have to do with the relative factor shares in the product. Here it is assumed that the firm uses two inputs, labour (L) and capital (K) and produces only one product (Q). Properties of the Cobb-Douglas Production Function: The C-D production functions possess a number of important properties which have made it widely useful in the analysis of economic theories. We shall now discuss them. C-D production function (8.100) is a homogeneous function, the degree of homogeneity of the function being α + β. For here we obtain A (tL) (tK) = t A L K = t Q (8.100a) ADVERTISEMENTS: where t is a positive real number. We obtain from (8.100a) that if L and K are increased by the factor t, Q would increase by the factor t . Also (8.100a) gives us that the condition for the C-D function (8.100) to become homogeneous of degree one (or linearly homogeneous) is α + β = 1. (8.101) α β α + β α β a +β α +β Economic Models, Equilibrium, Statics and Dynamics Read Next Story
10/4/2019 Cobb-Douglas Production Function and Its Properties 3/14 In that case, (8.100) would give us that if L and K are increased by the factor t, then Q would also increase by the factor t. If the C-D production function is homogeneous of any degree α + β as in (8.100) and (8.100a), then (8.100) may be called the generalized version of the C-D function. On the other hand, if the C-D function is homogeneous of degree one as given by (8.100) and (8.101), then the function is called a linearly homogeneous C-D function. Properties of Cobb-Douglas Production Function, Homogeneous of Degree One: The C-D production function of degree one may be written Q=AL K .α + β= 1 (8.102) The properties of this function, i.e., (8,102), are ADVERTISEMENTS: (i) Average and marginal products of L and K, i.e., AP , AP , MP , and MP would all be the functions of L-K or K-L ratio. Let us now

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