    # Properties Of CES And Cobb Douglas Production Function Producer's Equilibrium Or Optimisation Or Least Cost Combination Of Factors

Producer’s equilibrium or optimisation occurs when he earns maximum profit with optimal combinations of factors. A profit maximisation firm faces two choices of optimal combination of factors.

1. To minimise its cost for a given output and
1. To maximise its productivity for a given cost

Thus the least cost combination of factors denotes to a firm producing the major volume of productivity from a given cost and producing a given level of productivity with the minimum cost when the factors are combined in an optimum manner.

The Cobb Douglas Production Function

The Cobb Douglas production function is based on the empirical analysis of the American manufacturing industry made by Paul.H.Douglas and C.W.Cobb. “It is a linear homogeneous production function of degree one which takes into account two inputs, labour and capital, for the entire productivity of the manufacturing industry.” The Cobb-Douglas production function is expressed as below

Q = Ala Cb
Where Q is the production or output, L and C are inputs of labour and capital respectively. A, a and b are positive parameters where = a > O, b > O.

The equation describes that productivity depends directly on L and C and that part of output which cannot be explained by L and C are explained by A which is the residual, often called technical change.

The CES Production Function

It means Constant Elasticity of Substitution or CES Function.

Properties

1. The CES function is standardised of degree one. Thus like Cobb-Douglas production function, the ES function displays constant returns to scale.
1. In the CES production function, the average and marginal products in the variables C and L are standardised of degree zero like all linear standardised production functions.
1. From the above property the incline of an Isoquant i.e. Marginal rate of Technical Substitution MRTS of capital for labour can be represented convex to the origin.
1. As a consequence of the above, if L and C are substitutable (infinity) for each other an increase in C will require less of L for a given productivity. As a consequent, the MP of L will increase. Thus the MP of an input will increase when the other input is increased.

Merits

It has the following merits and they are listed below.

1. The CES function is a standardised of grade one, it is more general, it covers all type of returns
1. This function takes account of a number of parameters
1. This functions takes account of raw materials among its inputs
1. CES functions are very easy to approximate and are free from impractical postulations.

Limitations

1. This production function regards only two inputs. It can be comprehensive to more than two units.  However, it becomes very complex and intricate arithmetically to use it for more than two inputs.
1. The distribution parameter or capital intensity factor co-efficient α is not dimensionless.
1. If data are fitted to the CES function, the value of the competence a parameter cannot be made independent of the other units representing in this production function.
1. If the CES function is used to explain the production of a firm, it cannot be used to explain the aggregate production function of all the firms in the industry. Thus it involves the problem of aggregation of production function of diverse firms in the industry.
1. It suffers from the drawback that elasticity of substitution amidst any part of inputs is the same which does not materialize to be realistic.
1. In approximation of the parameters of CES production function we may come across a large number of problems like choice of exogenous variables, judgment procedure and the problem of multi collinear.
1. There is little possibility of identifying the production function under technological change.

Conclusion

Despite these limits, CES functions is constructive in its application to prove Euler’s theorem, to reveal constant returns to scale to show that average and marginal products are standardised degree zero and to determine the elasticity of substitution.

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