ajaz_eco_204_2012_2013_chapter_12_Long_Run_CMP_PP

# D the price of owned capital and only state all

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Unformatted text preview: he depreciation of capital, in each period? State all assumptions and show all calculations. (b) Derive an expression for ( ), the value of capital in period , in terms of ( ) and show all calculations. and only. State all assumptions (c) Derive an expression for ( ), the user cost of capital in period , in terms of ( ) ( ) assumptions and show all calculations. (d) “The price of (owned) capital and only. State all ( ) falls over time”: True or false? State all assumptions and show all calculations. (12.15) A company uses labor ( ), capital ( ) and materials ( ) to produce output ( ). The production function is: Suppose capital is fixed at so that: (a) Does the company have increasing, constant or decreasing returns with respect to labor and materials? (b) Suppose , , , , . Derive the optimal demand for labor, materials and the short run cost function. Is the cost function consistent with the company’s returns to labor and materials? (c) Will a dollar increase in impact cost more or less or the same as a dollar increase in ? 8 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. Solutions (12.1) 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)? Answer The problem is: () () () () () () Setup the Lagrangian objective function: () [ () [ The FOC and Kuhn-Tucker conditions are: () () [ [ From the KT conditions the signs of the Lagrange multipliers are: (12.2) 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)? Answer The problem is: 9 ECO 204 Chapter 12: Practice Problem...
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