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THE FIRM 2 2.0. Introduction In the first lesson, we learnt that the production function represents the maximum possible output. We now turn to the study of the minimum expenditure of attaining this maximum output. It is the cost function. 2.1. Objectives • To define the cost function and understand its properties. • To learn how to derive the cost function. • To learn the duality between the cost function and the production function. 2.2. The Cost Function It is defined as the minimum cost of producing a given output level during a given period of time. The cost function is expressed as a function of input prices and output i.e. ( ) ( ) [ ] y V X WX Y W C i ∈ = : min , Where W is a vector of strictly positive input prices. X is a vector of strictly positive inputs and, [ ] n n X W X W X W WX + + + = ... 2 2 1 1 The cost function depends o n technology since the only constraint to the minimization problem expressed above is that X must be capable of producing at least output y . 2.2.1. Properties of a Cost Function 1. Non-ne gat ivi ty proper ty i.e . ( ) 0 > y w C i 0 > ∀ w , 0 > y 1

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