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Production Function, Lecture Notes - Economics

Economics

Post: September 8th, 2011
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Production functions
Production functions
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PRODUCTION FUNCTIONS 1. A LTERNATIVE R EPRESENTATIONS OF T ECHNOLOGY The technology that is available to a firm can be represented in a variety of ways. The most general are those based on correspondences and sets. 1.1. Technology Sets. The technology set for a given production process is defined as T = {(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 of those combinations of x and y such that y can be produced from the given x. 1.2. The Output Correspondence and the Output Set. 1.2.1. Definitions. It is often convenient to define a production correspondence and the associated output set. 1: The output correspondence P, maps inputs x ∈ Rn into subsets of outputs, + m i.e., P: Rn → 2R+ . A correspondence is different from a function in that a + given domain is mapped into a set as compared to a single real variable (or number) as in a function. 2: The output set for a given technology, P(x), is ..

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