ajaz_eco_204_2012_2013_chapter_17__18_PP

Eco 204 s ajaz hussain do not distribute the prices

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Unformatted text preview: jaz Hussain. Do not distribute. ( ) We have two equations: Adding the two equations: The 1st FOC implies: ( This violates the condition that Possibility #2: ) and cannot be a solution. The 1st and 2nd FOCs imply: These imply: With this, all KT conditions are satisfied. The solution is: 41 ECO 204 Chapter 17 & 18: Practice Problems & Solutions for Firms with Market Power: Business Apps and Price Discrimination in ECO 204 (this version 2012-2013) University of Toronto, Department of Economics (STG). ECO 204, S. Ajaz Hussain. Do not distribute. The prices will be: ( ) () 42 ECO 204 Chapter 17 & 18: Practice Problems & Solutions for Firms with Market Power: Business Apps and Price Discrimination in ECO 204 (this version 2012-2013) University of Toronto, Department of Economics (STG). ECO 204, S. Ajaz Hussain. Do not distribute. (e) Now suppose there is a possibility of arbitrage between (i) NYC and Boston and (ii) between Boston and Toronto. Assume the cost of arbitrage between NYC and Boston is $300 and the cost of arbitrage between Boston and Toronto is $200. Use the Kuhn-Tucker/Lagrangian method to calculate the optimal outputs, prices and (any) Lagrange multipliers for all 3 markets in April 2010. Answer From above: Note that: Therefore, arbitrage is profitable. To prevent arbitrage D & H could set the price differential exactly equal to the cost of arbitrage so that the problem becomes: Using our calculations in part (a) this becomes: The constraints can be re-expressed as: ( ) And: 43 ECO 204 Chapter 17 & 18: Practice Problems & Solutions for Firms with Market Power: Business Apps and Price Discrimination in ECO 204 (this version 2012-2013) University of Toronto, Department of Economics (STG). ECO 204, S. Ajaz Hussain. Do not distribute. The problem becomes: Form the Lagrangian: [ [ [ The FOCs and KT conditions are: ( Start by checking ( Possibility #1: ) ) . which implies: Notice that the FOC: Implies that: 44 ECO 204 Chapter 17 & 18: Practice Problems & Solutions for Firms w...
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