COBBDOUGLAS PRODUCTION FUNCTION The CD production function is

COBB-DOUGLAS PRODUCTION FUNCTION

The C-D production function is based on the empirical study of the American manufacturing industry made by Paul H Douglass and C. w Cobb during the period 1899 to 1922. It is a linear homogenious production Function of degree one which takes into the account of two inputs that is, Labour and Capital, for a entire output of the manufacturing industry. The general form of Cobb -Douglass production function can be expressed as-: Q = AL αKβ Here-: Q L = Labour input K α&β = A = Output = Capital input Possitive parametors ( α >0 , β > 0 , α+ β =1 ) =Technical change ( it assumed to be constant( The equation tells that output depends directly on L &K , and that part of output which cannot be explained by L and K is explained by A which is

Properties The following are the important properties of Cobb. Douglass production function-: 1. Constant Returns to Scale C – D production function exhibits constant returns to scale. To prove it , let us increase the quantities of L & K by λ times and output must also increased by λ times. Then the increased output (Q*) will be; Q* = λQ α+β=1 Constant returns to scale α+β>1 Increasing returns to scale α+β<1 Diminishing returns to scale

2. The Average Product (AP) and Marginal Product (MP) of factors The C-D production function tells that the AP & MP of factors is a function of the ratio of the factors. Q = ALαKβ APL = A (K/L)β APK = A (L/K)α MPL = α A (K/L)β MPK = β A (L/K )α 3. Marginal Rate of Substitution between Capital and Labour (MRS LK) The MRS LK can be derived from the C-D production function. MRS LK = ∂Q/∂L ÷ ∂Q /∂K

4. Elasticity of factors substitution The Elasticity of factors substitution of the C-D production function is equal to unity. Its proof, the elasticity of substitution (es) between K&L is defined as; σ = ( f 1 × f 2 )/(f 12 × Q) Here ; f 1 =MPL f 2 = MPK f 12 = cross partial derivative of L& K ∂Q = ∂L × ∂K σ=1 when the elasticity of substitution is unity the production function is homogenious of degree one. That is constant returns to scale

5. Euler’s theorum The application of Euler’s theorum to distribution in an other property of the C-D production function. If the production function Q = f(K/L) is homogenious of degree one , then according to Euler’s theorum Q = L (∂Q/∂L) + K ( ∂Q/∂K ) Apply the general form of C-D production function we get Q = Q

6. Factor intensity In the C-D production function Q = ALαKβ , the factor intensity is measured by the ratio ( α /β ). Higher the ratio , the production function is more labour intensive and lower the ratio , the production function will be capital intensive. 7. Efficiency of production The coefficient ‘A’ in the C-D production function helps in measuring the efficiency in the organisation of the factors of production. If two firms have the same α , β , L and K but produce different quantities of output , this difference may be due to the superior organisation of more efficient firm as against the other. The more efficient firm will have a larger ‘ A ‘ than the other firm

8. Multiplicative Function The C-D production function is a multiplicative function. It means that if an input has zero value , the output will also be zero. This property highlights the fact that all inputs are necessary for production in a firm. 9. Output elasticity It can be defined as the proportionate change in output with a given change in input. The output elasticity of L & K can be calculated with the help of C-D production function : - Output elasticity of labour = ( ∂Q / ∂L ) ÷ ( L / Q ) Output elasticity of capital = ( ∂Q / ∂K ) ÷ (K / Q )

Criticisms The C-D production function considers only two inputs , labour and capital and neglects some important inputs like raw materials , which are used in production. In the C-D production function , the problem of measurement of capital arises because it takes only the quantity of capital available for production. But the full use of the available capital can be made only in periods of fullemployment. This is unrealistic situation. The C-D production function is criticised because it shows constant returns to scale. But constant returns to scale are not an actuality , for either increasing or decreasing returns to scale are applicable to production.

The C-D production function is based on the assumption of substitutability of factors and neglects the complimentarity of factors. This function is based on the assumption of perfect competitionin the factor market which is unrealistic. One of the weakness of C-D production function is the aggregation problem.

Importance The C-D production function has been used widely in empirical studies of manufacturing industries and in inter-industry comparisons. It is used to determine the relative shares of labour and capital in total output. And it is also used to prove Euler’s theorum. Its parametors α and β represents elasticity coefficients that are used for inter-sectoral comparisons. This production function is linear homogenious of degree one which shows constant returns to scale. If α + β >1 - increasing returns to scale α + β <1 - decreasing returns to scale This production function is more than two variables.

Conclusion Thus the practicability of the C-D production function in the manufacturing industry is a doubtful proposition. This is not applicable to agriculture where for intensive cultivation , increasing the quantity of inputs will not raise output proportionately.

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