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ajaz_eco_204_2012_2013_chapter_12_Long_Run_CMP_PP

Since the lagrange multiplier corresponds to an

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Unformatted text preview: s & 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. () () () () () () Setup the Lagrangian objective function: () [ () [ The FOCs and Kuhn-Tucker condition are: () () [ [ From the KT condition: zero, or negative. Since the Lagrange multiplier corresponds to an equality constraint, it can be positive, (12.3) Consider the following profit maximization problem: () () What can be said about the firm’s capacity if at the optimal solution to illustrate your answer. Do NOT solve the Profit Maximization Problem. ? Give a brief explanation and use graphs Answer The problem is: () () () () () () Setup the Lagrangian objective function: () () [ [ By the envelope theorem: 10 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. If it means that a small increase in capacity will have a positive impact on profits. This is only possible if the () current capacity is strictly less than the unconstrained profit maximizing output (i.e. the output where ( )) () ( ). See example below for firm with linear demand curve: or that currently Firm (Decreasing Returns) Firm (Constant Returns) () () () () () () Firm’s Demand () () () () Firm’s Demand (12.4) Consider a company that has purchased (not leased) capital to produce a target output . Assume straight line depreciation, zero salvage value, and constant opportunity cost rate of return. What are: ● the lowest and highest values of owned capital ● the lowest and highest prices of owned capital? Give a brief explanation and show all necessary calculations. Answer The value of capital at time is: () ( ) () Assuming straight line depreciation and zero salvage value we have: () () Thus: () ( ) () ( () ) Note: () () (...
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