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ajaz_eco_204_2012_2013_chapter_16_Market_Power_PP

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University of Toronto, Department of Economics (STG). ECO 204, S. Ajaz Hussain. Do not distribute. 1 ECO 204 Chapter 16: Practice Problems & Solutions for Analysis of Firms with Market Power in ECO 204 (this version 2012-2013) Department of Economics (STG), ECO 204, Sayed Ajaz Hussain _________________________________________________________________________________________________ P RACTICE P ROBLEMS W ITH S OLUTIONS TO : C HAPTER 16 : Analysis of Firms with Market Power Updated: 4/14/2013 Question 16.1 Write down ● the Lagrangian objective function ● the first order conditions and (any) Kuhn-Tucker conditions for the following profit maximization problem (do NOT solve the problem): ( ) ( ) What are the possible “signs” of the Lagrange multipliers (i.e. positive, zero, negative)? Question 16.2 Write down ● the Lagrangian objective function ● the first order conditions and (any) Kuhn-Tucker conditions for the following profit maximization problem (do NOT solve the problem): ( ) ( ) What are the possible “signs" of the Lagrange multipliers (i.e. positive, zero, negative)? Question 16.3 True or false: if a firm with market power is producing the revenue maximizing output at a uniform price then the absolute value of the price elasticity must be equal to 1 (i.e. | | )? Give a brief explanation and use graphs to illustrate your answer. Do NOT solve the Revenue Maximization Problem. Question 16.4 True or false: a firm with ample capacity and market power charging optimal 1 st degree price discrimination prices will produce the same total output as if it were charging the “perfectly competitive” uniform price? Do NOT solve any profit maximization problems and use graphs to illustrate your answer. Question 16.5 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 1 st 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. Question 16.6 The economist, Hugo Salgado, estimated the following demand models for Intel and AMD PC (personal computer) “CPU chips” (Central Processing Units):
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University of Toronto, Department of Economics (STG). ECO 204, S. Ajaz Hussain. Do not distribute. 2 ECO 204 Chapter 16: Practice Problems & Solutions for Analysis of Firms with Market Power in ECO 204 (this version 2012-2013) The subscripts and refer to “AMD” and “Intel” respectively w here CPU and quantity of CPUs (millions). Notice these demand models are of the form ( ) and ( ) respectively. Hugo also estimated AMD and Intel’s average variable cost: Throughout this final exam assume that AMD and Intel: are in the short run have ample capacity ● and will always produce strictly positive output (i.e. ).
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