ajaz_eco_204_2012_2013_chapter_12_Long_Run_CMP_PP

54 eco 204 chapter 12 practice problems solutions for

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Unformatted text preview: ) A 1% increase in TFC raises the average rational smelter’s loss by 2.92% or from a loss of ($14,373) to a loss of ($14,793). 54 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. (12.13) Ajax Bus Company (ABC) operates a bus service between Robarts library and the Rotman School of Management. Each ABC bus (capital) carries 100 passengers and requires a driver and a conductor (labor). Let number of buses/day, number of workers (labor) per day, and number of passengers/day. Denote the price of leasing (or owning) buses per day by and daily wages by (assume that drivers and conductors have the same daily wage). In this question, all inputs are variable. ( ) (a) If ABC wishes to carry passengers per day, what is the optimal (cost minimizing) number of buses and labor per day? That is, solve the problem: ( ) Answer This problem cannot be solved by the Lagrangian method since the production function is not differentiable everywhere. Instead, note that at the optimal choice of inputs it must be that: ( Notice And: ) is solved in chapter 11 practice problems (11.8) part (a). This implies: ( ) And: ( ) That is: This makes sense: 100 passengers required 1 bus ( ) and two workers ( ) 55 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. (b) Derive ABC’s (long-run) cost function. Please show all calculations below and state any assumptions. Answer From above: The cost function is: () () () (c) This question should be answered independently of all other questions (i.e. the numbers given here for and are for this question only). Suppose and can be either $20 with probability ¾ or $40 with probability ¼. Calculate ABC’s expected cost of carrying passengers. Please show all calculations below. Answer From above: () Here with certainty; wages are uncertain and are expected to be: Thus, the expected cost will be: [ ( )] [ ( )] [ ( )] 56 ECO 204 Chapter 12: Practice Problems & Solutions for The Long Run...
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