ajaz_eco_204_2012_2013_chapter_12_Long_Run_CMP

The equation above implies that so that but

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Unformatted text preview: t line depreciation cost in period ( () ⏟ () () Notice that this is independent of so we can write this as: () For simplicity, let’s initially assume that ( ) () so that: () From above we had ( ) ( ) ( ) and setting ( ) () yields: ( ) Here’s how we derive an expression for ( ) in terms of the “parameters”: ( ) the purchase price; ; and ) life of the capital. The equation above implies that ( ( ) so that: () But ( ) ( ) () ( ) ( ( ) ( ) ( ) ) ( ) you’d get: () () ( so that: Carrying on recursively back to But since ) the useful ( ) () we have: () () () () () ( ){ } 10 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 have ( ) Let’s check if this formula is correct: at () ( ){ } ( ){ } ( ) which is correct; at we have which is also right since we assumed zero salvage value. 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 years, zero salvage value, and straight line depreciation: & Straight line depreciation () What if the salvage value was positive (i.e. the capital is worth something at th...
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