ajaz_eco_204_2012_2013_chapter_12_Long_Run_CMP_PP

Eco 204 s ajaz hussain do not distribute the 1st

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Unformatted text preview: e Cobb-Douglas form we know that for so that . As such, we can drop the non-negativity constraints: we must use some power and labor () Now: () Setup the Lagrangian: () () [ The FOCs are: 36 ECO 204 Chapter 12: Practice Problems & Solutions for The Long Run Cost Minimization Problem in ECO 204 (this version 2012-2013) University of Toronto, Department of Economics (STG). ECO 204, S. Ajaz Hussain. Do not distribute. [ The 1st FOC implies: The 2nd FOC implies: Equating the ’s yields the familiar “the optimal input bundle is where the iso-quant is tangent to the iso-cost” result: This allows us to isolate power (or for that matter labor) in terms of labor (power). For instance: 37 ECO 204 Chapter 12: Practice Problems & Solutions for The Long Run Cost Minimization Problem in ECO 204 (this version 2012-2013) University of Toronto, Department of Economics (STG). ECO 204, S. Ajaz Hussain. Do not distribute. We can substitute this in the 3rd FOC: [ ( ) ( ) ( ) ( ) ( Now, we are told that Substitute the expression for ) which means that: to get: ( ) 38 ECO 204 Chapter 12: Practice Problems & Solutions for The Long Run Cost Minimization Problem in ECO 204 (this version 2012-2013) University of Toronto, Department of Economics (STG). ECO 204, S. Ajaz Hussain. Do not distribute. ( ) ( ) ( ( Substitute ) ) to get: ( ) (12.12) This question is based on the HBS case The Aluminum Industry in 1994. The following table contains the cost structure of the average CIS primary aluminum smelter, the average state primary aluminum smelter, and the average rational primary aluminum smelter (please note that cumulative capacity below is the total capacity of all smelters within a category (for example, the total cumulative capacity of all CIS smelters is 1.788 million tons per year): All cost figures are $/t Variable costs are in BOLD Smelter Country Company Average Capacity (‘000s tpy) Total electricity cost Total alumina cost Other raw materials Average CIS Average State Smelter Smelter Ave...
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