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Production Functions

The input-output relational statement specifying the technology or what is called ‘Production function’. Earlier we have stated the production function for either a single product or joint-project or multiproduct firm. Conceptually, the production centre is like the black box wherein magical operation takes place as a result the flows of input get processed into flows of output of goods and service either in a single period or over a multiperiod.

1. Cobb-Douglas type: Q = Q(L,K)

Q = AL^∝ k^1–∝ where ‘A’ is a constant (index of efficiency),∝ and 1 – ∝ indicate returns to factors labor and capital. These power term added together are called ‘function coefficient’ (∝ + 1–∝) =1 ‘constant returns to scale in production economics’.

2. Leontief type: Q = minimum where ‘a’ and ‘b’ are constants. In this case of fixed proportion function, there is no scope (technological feasibility lacking) for substitution between factors.

3. Linear types: At the other extreme, there may be cases where there is no limit to the substitutability between factors, such that a multi-vitiate production function work out to be a single-variable liner production function, Q = aL or bK where ‘a’ or ‘b’ represent factor proportionality.

4. CES type: The cob-Douglas type stated earlier, with function coefficient equal to 1 is a special case of Constant Elasticity of Substitution (CES) type. In other CES type, constant may take any other value (other than one.) Q = B [gh^–h + (1 – g)K^–h ]^–1/h is a CES type production function, with B, G and h as constants; h > – 1.

5. VES type: If the function coefficient does not remains constant,

But varies in the productive process, pay over shifts, then it is Variable Elasticity of Substitution (VES).