PRODUCTION FUNCTIONS

PRODUCTION FUNCTIONS1. ALTERNATIVEREPRESENTATIONS OFTECHNOLOGYThe technology that is available to a firm can be represented in a variety ofways. The most general are those based on correspondences and technology set for a given PRODUCTION process is de-fined asT={(x,y) : x Rn+,y Rm:+x can produce y}where x is a vector of inputs and y is a vector of outputs. The set consists ofthose combinations of x and y such that y can be produced from the given Output Correspondence and the Output is often convenient to define a PRODUCTION correspondence andthe associated output :The output correspondence P, maps inputs x Rn+into subsets of outputs, , P:Rn+ 2Rm+. A correspondence is different from a function in that agiven domain is mapped into a set as compared to a single real variable(or number) as in a :The output set for a given technology, P(x), is the set of all output vectorsy Rm+that are obtainable from the input vector x Rn+.

PRODUCTION FUNCTIONS 3 outputit is sometimesuseful to represent the technology of the firm with a math-ematical function that gives the maximum output attainable from a given vector of inputs. This function is called a production function and is defined as f(x) = max y [y:(x,y) ∈ T] = max y [y: x ∈ V(y)] = max y ∈ P(x) [y] (2)

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