ajaz_eco_204_2012_2013_chapter_12_Long_Run_CMP

# Eco 204 s ajaz hussain do not distribute notice a

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Unformatted text preview: ) ( )( ) ( )} ( ){ ( ( ) ( )} ( ) ( ) Again by recursive substitution one can show (and you should show): () ( ) ( ) ( ) ( ) ( ) ( ) 12 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. Notice a pattern? In fact, if you kept going back a total of periods you would get: () ( ) ( ) ( ) ( ) ( ( ) ) ( ⏟ ( ) ( ) ) ( ) () () In summary, with declining balance depreciation: () And since ( ) ( ( ) ( ) () ) we have: () From the expression ( ) ( ) () ( ) we can endogenously set the salvage value at time () ( ) as: () Here the salvage value is determined endogenously because with a time dependent depreciation cost there is no reason why ( ) ( ) ( ) should be the same as an exogenously specified salvage value and therefore the salvage value is artificially set to be ( ) ( ) ( ). For example, the following graph shows the value of capital over time given that it was purchased for \$500m, has a useful life of 10 yea...
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