Cobb-Douglas Production Function in Business Economics
Learn about the Cobb-Douglas Production Function, a key concept in Business Economics that explains the relationship between output and inputs like labor and capital. Discover its properties and implications for firms' production decisions.
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COURSE: B.COM. (HONOURS) PAPER NAME BUSINESS ECONOMICS TOPIC COBB - DOUGLAS PRODUCTION FUNCTION YEAR- THIRD SEMESTER-6 SESSION -2019-2020 DATE OF LECTURE: 05/05/2020 PREPARED BY DR. KAMALIKA CHAKRABORTY ASSISTANT PROFESSOR (DEPARTMENT OF ECONOMICS) KHATRA ADIBASI MAHAVIDYALAYA, BANKURA, WEST BENGAL
Cobb - Douglas Production Function The Cobb Douglas is widely used to represent the relationship of an output and two inputs. The Cobb Douglas function is of the form: Q(L,K) =A? ? where: Q = total L = labor input (the total number of person-hours worked in a year) K = capital input A = total factor productivity(efficiency coefficient ) and are the output elasticity of labor and capital, respectively. These values are constants determined by available technology.
C-D production function is a homogeneous function, the degree of homogeneity of the function being + Properties of Cobb-Douglas Production Function which is Homogeneous of Degree One: The C-D production function of degree one may be written Q=AL K1- The properties of this function are (i) Average of L and K, i.e., APL, APK would be the functions of L-K or K-L ratio. (ii) In the case of C-D production function both MPLand MPKto be functions of L-K ratio. (iii) In the case of C-D production function the APLand MPLcurves and the APKand MPKcurves, all would be downward sloping.
(iv) In the case of C-D production function, coefficient of partial elasticity of Q w.r.t. a change in L, K remaining constant, would be EQL= = constant, and the coefficient of partial elasticity of Q w.r.t. a change in K, L remaining constant, would be EQL= 1 = constant. (v) For the C-D production function, the isoquants of the firm would be negatively sloped and these curves would be convex to the origin. (vi) For the C-D function, the expansion path of the firm would be a straight line.
(viii) For C-D production function, total output would be exhausted if the inputs L and K are paid at the rate of their respective marginal product, i.e., L. MPL+ K. MPK= Q. (ix) For C-D production function , if labour (L) and capital (K) are paid at the rate of their respective MPs, then the relative shares of labour and capital would be and 1 respectively. (x) Elasticity of substitution between labour and capital in case of C-D production function is equal to one.
