Cobb-Douglas Production Function In Hindi कॉब-डगलस उत्पादन फलन https://youtu.be/BMJTU8ADyAU
Definition: The Constant Elasticity of Substitution Production Function or CES implies, that any change in the input factors, results in the constant change in the output. In CES, the elasticity of substitution is constant and may not necessarily be equal to one or unity.
The CES production function is a neoclassical production function that displays constant elasticity of substitution. In other words, the production technology has a constant percentage change in factor (e.g. labour and capital) proportions due to a percentage change in marginal rate of technical substitution. The two factor (capital, labor) CES production function introduced by Solow, and later made popular by Arrow, Chenery, Minhas, and Solow
As its name suggests, the CES production function exhibits constant elasticity of substitution between capital and labor. Leontief, linear and Cobb–Douglas functions are special cases of the CES production function.
Constant Elasticity Of Substitution Production Function
Q = A [α K-θ + (l-α)L-θ] -1/θ
Q is Total output.
K is capital, and L is labour.
A is the efficiency parameter indicating the state of technology and organizational aspects of production.
α (alpha) is the distribution parameter or capital intensity factor coefficient concerned with the relative factor shares in the total output.
θ (theta) is the substitution parameter which determines the elasticity of substitution.
1. The CES function is homogenous of degree one. If we increase the inputs С and L in the CES function by n-fold, output Q will also increase by n-fold.
Thus like the Cobb-Douglas production function, the CES function displays constant returns to scale.
2. In the CES production function, the average and marginal products in the variables С and L are homogeneous of degree zero like all linearly homogeneous production functions.
3. From the above property, the slope of an isoquant, i.e., the MRTS of capital for labour can be shown to be convex to the origin.
4. The parameter (theta) in the CES production function determines the elasticity of substitution. In this function, the elasticity of substitution,
σ = 1/ 1 + θ
5. As a corollary of the above, if L and С inputs are substitutable ∞ for each other an increase in С will require less of L for a given output. As a result, the MP of L will increase. Thus, the MP of an input will increase when the other input is increased.
CES function vs. CD function:
Differences between the CES function and the CD production function:
1. The CD function is based on the observation that the wage rate is a constant proportion of output per head. On the other hand, the CES function is based on the observation that output per head is a changing proportion of wage rate.
2. The CES production function is based on larger parameters than the CD production function and as such allows factors to be either substitutes or complements. The CD function is, on the other hand, based on the assumption of substitutability of factors and neglects the complementarity of factors. Thus the CES function has wider scope and applicability.
3. The CES production function can be extended to more than two inputs, unlike the CD function which is applicable to only two inputs.
4. In the CES function, the elasticity of substitution is constant but not necessarily equal to unity. It ranges from 0 to ∞. But the CD function is related to elasticity equal to unity. Thus the CD function is a special case of the CES function.
5. The CES function covers constant, increasing and decreasing returns to scale, while the CD function relates to only constant returns to scale.