COBB DOUGLAS PRODUCTION FUNCTION THEORY

1. COBB DOUGLAS PRODUCTION FUNCTION THEORY By GOURAV DHOLWAL KRUPA SAGAR REDDY

2. Background Definition Equation Properties of theory Usage Criticisms Flow of presentation

3. Background During 1900–1947, Charles Cobb and Paul Douglas formulated and tested the Cobb–Douglas production function through various statistical evidence.

4. The Cobb–Douglas functional form of production functions is widely used to represent the relationship of an output and two inputs. Definition

5. The function they used to model production was of the form: P(L,K) = BL α K β where: P = total production (the monetary value of all goods produced in a year) L = labor input (the total number of person-hours worked in a year) K = capital input (the monetary worth of all machinery, equipment, and buildings) B = total factor productivity(efficiency coefficient ) α and β are the output elasticity of labor and capital, respectively. These values are constants determined by available technology. Equation

6. Labour L Capital K Production P

7. Question Production Function Estimation. Washington-Pacific, Inc., manufactures and sells lumber, plywood, veneer, particle board, medium-density fiber board, and laminated beams. The company has estimated the following multiplicative production function for basic lumber products in the Pacific Northwest market: Q = output, L = labor input in worker hours, K = capital input in machine hours and E = energy input in BTUs (British Thermal Unit)

8. MARGINAL PRODUCTION Marginal product of labor : If the production function is denoted by X = P(L,K), then the partial derivative dP / dL is the rate at which production changes with respect to the amount of labor. Economists call it the marginal production with respect to labor or the marginal productivity of labor . MP L =AP L .b 1 PROPERTIES

9. Marginal productive of capital The partial derivative dP / dK is the rate of change of production with respect to capital and is called the marginal productivity of capital MP K =AP K .b 2

10. It is amount by which the quantity of input has to be reduced when one extra unit of another input is used so that output remain constant. MRTS is slope of isoquant curve MRTS = MPL/MPK =b1/b2.K/L Marginal rate of technical substitution

11. σ= percentage change in K/L/ or percentage change in MRTS sigma will be equal to one so this function is perfectly substitutable function Elasticity of factor substitution

12. We can know whether production is taking place in labour intensity or capital intensity It can be determined by the ratio of coefficient constant of labour to coefficient constant of capital if b 1 /b 2 > 1 then it is labour intensive and vice versa Factor intensity

13. Refers to a technical property of production that examines changes in output subsequent to a proportional change in all inputs (where all inputs increase by a constant factor). If output increases by that same proportional change then there are constant returns to scale (CRTS), sometimes referred to simply as returns to scale. If output increases by less than that proportional change, there are decreasing returns to scale (DRS). If output increases by more than that proportion, there are increasing returns to scale (IRS) Return to scale

14. When two firms are doing production with same unit of capital, labour , raw material and everything but there is difference in the out put of production this occur due to difference in the efficiency in usage of labour and capital B is the coefficient constant of the production in the equation Efficiency of production

15. This section will demonstrate the usage of the production formula using real world data Usage Year 1889 1890 1891 1892 1919 1920 P 100 101 112 122 218 231 L 100 105 110 117 196 194 K 100 107 114 122 387 407 Economic data of the American economy during the period 1889 - 1920 .

16. Cont. Cobb and Douglas used the method of least squares to fit the data of Table 1 to the function: P(L,K ) = 1.01(L 0.75 )(K 0.25 ) For example, if the values for the years 1904 and 1920 were plugged in: P(121 , 138) = 1.01(1210.75)(1380.25) = 126.3 P(194 , 407) = 1.01(1940.75)(4070.25 )= 235.8 which are quite close to the actual values, 122 and 231 respectively. The production function P(L,K) = bL α _K_ β has subsequently been used in many settings, ranging from individual firms to global economic questions. It has become known as the Cobb-Douglas production function.

17. Lack of micro foundations The Cobb–Douglas production function was not developed on the basis of any knowledge of engineering, technology, or management of the production process Criticism