Search results “Elasticities of substitution and complementarity determining”

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
Where,
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.
Its Properties:
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.

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Production Function In Hindi / उत्पादन फलन क्या है?https://youtu.be/zM_2i0AvbeM
Production function relates quantities of physical output of a production process to quantities of physical inputs or factor of production Q=𝑓(𝐿,𝐾,𝑇,….𝑛)
The Cobb-Douglas production function is based on the empirical study of the American manufacturing industry made by Paul Douglas and Charles Cobb. It is a linear homogeneous production function of degree one which takes into account two inputs, labour and capital, for the entire output of the manufacturing industry.
𝑄=𝐴𝐿^𝑎 𝑘^𝛽
Q = total production (the real value of all goods produced in a year
L = labour input (the total number of person-hours worked in a year
K = capital input (the real value of all machinery, equipment, and buildings)
A = The equation tells that output depends directly on L and K, and that part of output which cannot be explained by L and K is explained by A which is the ‘residual’, often called technical change.
α and 𝛽 are the output elasticities of capital and labour, respectively. These values are constants determined by available technology.
Properties of Cobb Douglas production function (𝑄=𝐴𝐿^𝑎 𝑘^𝛽)
Cobb-Douglas production is linear homogenous.
In cobb-Douglas returns to scale is constant that means if labor and capital is increased in some proportion will increases in same proportion.
For production purposes there is always be require labour and capital. Without any of these two factor, production is not possible.
According to the cobb-Douglas production function if one factor of production is kept constant and the other quantity of the other factor of production is increased then the marginal productivity of variable factor is reduced.
Elasticity of technical substitution is unity.
The production function solved by Cobb-Douglas had 1/4 contribution of capital to the increase in manufacturing industry and 3/4 of labour so that the C-D production function is Q = AL3/4 K1/4
Importance of Cobb - Douglas production function:
1. It has been used widely in empirical studies of manufacturing industries and in inter-industry comparisons.
2. It is used to determine the relative shares of labour and capital in total output.
3. It is used to prove Euler’s Theorem.
4. Its parameters a and b represent elasticity coefficients that are used for inter-sectoral comparisons.
.5. This production function is linear homogeneous of degree one which shows constant returns to scale
6. Economists have extended this production function to more than two variables.
Criticism of Cobb - Douglas production function:
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. It is, therefore, not possible to generalize this function to more than two inputs.
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.
It is not possible to change all inputs to bring a proportionate change in the outputs of all the industries. Some inputs are scarce and cannot be increased in the same proportion as abundant inputs. On the other hand, inputs like machines, entrepreneurship, etc. are indivisible.
4. The C-D production function is based on the assumption of substitutability of factors and neglects the complementarity of factors.
5. This function is based on the assumption of perfect competition in the factor market which is unrealistic. If, however, this assumption is dropped, the coefficients α and β do not represent factor shares.

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