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ajaz_eco_204_2012_2013_chapter_12_Long_Run_CMP

# Function as as constant as as as constant as note

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Unformatted text preview: nition: () () () Thus: () () () (){ () () () Next, we prove that: { By definition: () ( () ) If we double inputs then (using the definition of returns to scale): () } ( ) () () () () { () () Finally we prove that: } By definition: () 47 ECO 204 Chapter 12: a Firm’s Cost Minimization Problem (this version 2012-2013) University of Toronto, Department of Economics (STG). ECO 204, S. Ajaz Hussain. Do not distribute. () () We know that: () } { 9 Complements Long Run Cost Minimization Problem We now consider a company which produces output by using essential inputs as complements (fixed proportions). For examples, a flight requites a certain number of pilots and attendants. The general complementary inputs long run production function is: ( ) Notice that each input is essential for production because if any input, say input #1, is zero then: ( ) As such, requires strictly positive amounts of each input. For simplicity, let’s look at a firm that uses essential and “complementary” inputs to produce output. Its long run CMP is: ( and as ) Since all inputs are essential for p...
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