ajaz_eco_204_2012_2013_chapter_12_Long_Run_CMP_PP

The highest value of capital is at and the lowest

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Unformatted text preview: ) () () () 11 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. In general: () () () () () () ( )[ This is a decreasing function of . The highest value of capital is at () and the lowest value of capital is at time ( )[ () since: () ( )[ The price of capital at time is: () () () () Note that opportunity cost at time = opportunity cost rate of return at time Value of capital at time Assuming straight line depreciation and zero salvage value we have ( ) () () () From above ( ) ( )[ () () () () and so: () () so that: () () ( ) ( )[ () () With constant opportunity cost rate of return ( ) ( )[ ( ) and so: () () ( [ ) This is also a decreasing function of . The highest price of capital is at () () ( [ ) () ( ) ( ) 12 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. and the lowest price of capital is at time since: () () [ ( () ) (12.5)-[PART A] A company with market power has constant returns. Setup, solve, and derive the conditions for the various Kuhn-Tucker cases of the following general Profit Maximization Problem given that the company can charge a uniform price or 1st degree price discrimination prices: () () ⏟ You must express all first order conditions and the conditions for the Kuhn-Tucker various cases in terms of marginal revenue and marginal cost only. State all assumptions and show all calculations. Answer A company with market power solves the following Profit Maximization Problem (PMP): () () Observe how price is a function of output. Recall that all inequality constraints must be expressed in the form ( ) Therefore: . () () () () Having expressed all constraints in terms of ( ) , form the Lagrangian: [ () () [ () () [ The FOC is: (()) ⏟ (...
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This document was uploaded on 01/19/2014.

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