ajaz_eco_204_2012_2013_chapter_12_Long_Run_CMP_PP

Eco 204 s ajaz hussain do not distribute 451 1181

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Unformatted text preview: rage Rational Smelter CIS All over All over CIS State Rational 243.73 120.74 121.53 148.62 454.49 292.29 382.13 407.27 348.49 63.69 163.57 120.62 39 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. 4.51 11.81 10.34 76.92 56.72 73.91 39.57 46.45 53.84 17.80 62.73 194.19 68.76 53.17 37.82 67.11 52.48 86.58 1,788.07 (All CIS) 2,826.95 (All state) 16,962.17 (All rational) 740.14 1,135.25 873.15 Plant power and fuel Consumables Maintenance Labor Freight General and administrative Cumulative capacity (‘000s of tons/year) (all smelters in a category) Total variable costs per ton ($/ton) = () (a) Solve the profit maximizing problem for the average rational primary aluminum smelter: () Here price of aluminum/ton, Total fixed Cost, ( ) = Total variable cost and capacity. Assume . Show all calculations. Answer Since the case reports cost figures in “$ per ton” we assume that all smelter’s have constant returns so that: () () () This will be useful below. Now, a smelter’s profit maximization problem (PMP) is: () Note that smelters are price takers so that form ( ) . Therefore: is a constant. Recall that all inequality constraints must be expressed in the () () 40 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. Having expressed all constraints in terms of ( ) , form the Lagrangian: [ () [ () [ The FOC is: () The Kuhn-Tucker conditions are: [ Notice there are 4 possible cases that must be checked: q=0 λ2 = 0 (Check when λ2 ≥ 0) (Check when q ≥ 0) q = qc λ1 = 0 q = qc λ1 = 0 (Check when λ1 ≥ 0 ) (Check when q ≤ qc) (Check when λ1 ≥ 0 ) (Check when q ≤ qc) Case A Case B Case C Case D Case A 41 ECO 204 Chapter 12: Practice Problems & Solutions for The Long Run Co...
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This document was uploaded on 01/19/2014.

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