ajaz_eco_204_2012_2013_chapter_12_Long_Run_CMP_PP

D the price of owned capital and only state all

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

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...
View Full Document

Ask a homework question - tutors are online