ajaz_eco_204_2012_2013_chapter_17__18_PP

Show all calculations and state any assumptions hints

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Unformatted text preview: of output and is the same answer as the marginal cost calculated from the cost function: () () 38 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. (d) Use the Kuhn-Tucker/Lagrangian method to calculate D & H’s profit maximizing outputs, prices and (any) Lagrange multipliers in all 3 markets in April 2010. Show all calculations and state any assumptions. Hints: Don’t forget the constraint that total output capacity and that . Answer: D & H solves the problem: From question 1 we can deduce the total capacity as = Dolce & Havana: January – March 2010 January February 10 30 20 10 20 20 $9,000 $21,000 $5,000 $3,500 $2,000 $2,000 Units Sold in NYC: Units Sold in Boston: Units Sold in Toronto: NYC Revenues: Boston Revenues: Toronto Revenues: Available (Unused) Capacity Number of individual customers in NYC Number of individual customers in Boston March 20 10 20 $16,000 $3,500 $2,000 50 50 10 10 10 5 5 5 10 + 20 + 20 + 50 = 100 Total Capacity 40 30 + 10 + 20 + 40 = 100 20 + 10 + 20 + 50 = 100 The problem becomes: Since D & H has signed a contract is a constant so that we can simplify the problem: Re-express this as: ( ) ( ) 39 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. Substituting: We get: ( ( ( ) ) ) ( ( ) ) ( ) This is an inequality constrained problem and can be solved by the Kuhn-Tucker method: [ The FOCs and KT conditions are: ( Start by checking ( ) Possibility #1: ) and implies: Equate the FOCs: 40 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. A...
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