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ajaz_eco_204_2012_2013_chapter_12_Long_Run_CMP

# Almost surely an exogenously given wouldnt equal

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Unformatted text preview: rs, and declining balance depreciation: & Declining balance depreciation () Above the salvage value was (artificially set) to be ( ) exogenously given salvage value ( ) ( ) ( ) What would happen if in fact there was an ? Almost surely, an exogenously given ( ) wouldn’t equal ( ) ( ). To rectify this problem we can choose a different constant percentage factor. First notice that in: 13 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. () the “constant depreciation factor” is from ( ( ⏟ ) If the firm does indeed have an exogenously given salvage value that differs ( ) one can “fix” this by assuming a different constant proportion (say ) ( ) calculated via ( ) ( ) ( ) equals the exogenously given salvage value. Here is how: let () Where the constant ⏟ ( ( ) is to be determined. To see how, we note that: () But ( ) ) which ensures that ( ) () ) so that: () ( ) () ( ) ( ) ( )( ) Now by recursive substitution: () ( )( ) ){ ( ( ) )} ( ( ){ ( ) ( ) ( ) )} ( ) ( ) Again by recursive substitution one can show (and you should show): () ( ) ( ) ( ) ( ) ( ) ( ( ) ( ) () In summary, with declining balance depreciation: () ( ) () Now, with an exogenously given salvage value ( ) we can de...
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