Lec 5 Production - 1 Prot maximization and cost...

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1 Pro&t maximization and cost min- imization = max x 1 ;x 2 pf ( x 1 ;x 2 ) w 1 x 1 w 2 x 2 = max q;x 1 ;x 2 pq ( w 1 x 1 + w 2 x 2 ) s.t. q = f ( x 1 ;x 2 ) which may also be rewritten as = max q pq c ( w 1 ;w 2 ;q ) c ( w 1 ;w 2 ;q ) = min x 1 ;x 2 w 1 x 1 w 2 x 2 s.t. q = f ( x 1 ;x 2 ) of output q and input prices w 1 and w 2 , what is the cheapest cost of producing it? This cheapest cost can be written as a cost function c ( w 1 ;w 2 ;q ) . Stage 2: Given a cost function c ( w 1 ;w 2 ;q ) and the price of output p , how much output should the &rm produce and sell?
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Properties of production function Production function: Q = f ( K;L ) Holding L Q is increasing in K . Holding K Q is increasing in L . Long run - all factors of production variable including going in or out of business.
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Lec 5 Production - 1 Prot maximization and cost...

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