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Rubinstein2005-page99

# Rubinstein2005-page99 - 12:18 master Sheet number 97 Page...

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Unformatted text preview: October 21, 2005 12:18 master Sheet number 97 Page number 81 Production 81 logical constraints on the producer is by a production function which specifies, for any positive vector of inputs v ∈ R K − 1 + , the maximum amount of commodity K that can be produced. If we start from technology Z , we can derive the production func- tion by defining f ( v ) = max { x | ( − v , x ) ∈ Z } . Alternatively, if we start from the production function f , we can derive the “technology” by defining Z ( f ) = { ( − w , x ) | x ≤ y and w ≥ v for some y = f ( v ) } . If the function f satisfies the assumptions of f ( ) = 0, continuity, and concavity, then Z ( f ) satisfies the above assumptions. The Supply Function We will now discuss the producer’s behavior. The producer’s prob- lem is defined as max z ∈ Z pz . The existence of a unique solution for the producer problem re- quires some additional assumptions such as that Z be bounded from above (that is, there is some bound B such that...
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