ajaz_eco_204_2012_2013_chapter_17__18_PP

# Answer the total cost of manufacturing jackets is now

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Unformatted text preview: 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. (c) Show that the monthly cost function for manufacturing the target output is: () [You will need this cost function for other questions. From the cost function above, note that the total variable cost of () serving the NYC market is , the total variable cost of serving the Boston market is () () and the total variable cost of serving the Toronto market is. Answer: The total cost of manufacturing jackets is: () Now so that: () ( () ) ( () ) () We need to calculate materials required to produce the target output . The Cost Minimization Problem (CMP) is: () () () ( () ) ( ) () There are many ways to solve the problem. Since we’re not asked for the Lagrange multiplier, the easiest way to solve the problem is by substituting the constraint into the objective – re-express the CMP as: () () 36 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. Substitute constraint into objective: () () [Optional] The second way to solve the problem is by the Lagrangian method: () [ The FOCs are: The 2nd FOC implies that: Substituting in objective yields the cost function: () Even though the question doesn’t ask for we can solve for it. Substituting in 1st FOC: 37 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. () ( ) By the way, note that by the envelope theorem, is the change in the optimized objective (in this case total cost) when the constraint is relaxed by 1 unit. That is, is the marginal cost of producing another unit...
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