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Rubinstein2005-page100

# Rubinstein2005-page100 - vector Î p 2 z is continuous 3...

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October 21, 2005 12:18 master Sheet number 98 Page number 82 82 Lecture Seven Figure 7.2 Profit maximization. and on the consumer’s preferences. Thus, the producer’s problem is similar to that of the consumer’s dual problem. (See fig. 7.2.) Properties of the Supply and Profit Functions Let us turn to some of the properties of the supply and profit func- tions. The properties and their proofs are analogous to the properties and proofs in the discussion of the consumer’s dual problem. Supply Function 1. z p ) = z ( p ) . (The producer’s preferences are induced by the price vector
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Unformatted text preview: vector Î» p .) 2. z is continuous. 3. Assume the supply Function is well defned. IF z ( p ) 6= z ( p ) , we have ( p âˆ’ p ) [ z ( p ) âˆ’ z ( p ) ] = p [ z ( p ) âˆ’ z ( p ) ] + p [ z ( p ) âˆ’ z ( p ) ] > 0. In particular, iF (only) the k th price increases, z k increases; that is, iF k is an output ( z k > 0), the supply oF k increases; and iF k is an input ( z k < 0), the demand For k decreases. Note that this result, called the law of supply , applies to the standard supply...
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