ajaz_eco_204_2012_2013_chapter_12_Long_Run_CMP_PP

Show all calculations below answer at the optimum to

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Unformatted text preview: for a unit of sugar, it must be that: Thus, holding all other inputs constant, the “sub” production function for sweeteners is: As such, the production function becomes: ( ) ( ) (g) For the production function in part (f), calculate the optimal inputs and cost function of producing target output . Show all calculations below. Answer At the optimum, to produce target output it must be that: 27 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. ( ) This implies: Notice there are 5 unknowns ( as: ) but only 4 equations. To handle such an equation, express the cost function () () We know that: The cost function becomes: () () ( ) () () ( ) ( ) This is a linear function is 1 unknown, sugar ( ). The slope is ( the cost function becomes: ) The intercept is ( ). If 28 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. C(q) {Ps - 2PF} Sugar In this case, the optimal amount of sugar is zero. This makes sense because sugar and fructose are perfect substitutes, where a unit of sugar is the same as 2 units of fructose (i.e. the “sweetener” iso-quant has slope -2). If the “cost function” is steeper than the iso-quant, then we should use no sugar. This happens when: Therefore, if the optimal inputs are: () The cost function becomes: 29 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. () () ( ) ( )( ) () On the other hand, if ( ) ( ( ) ) Ajax will use only sugar as a sweetener: The cost function becomes: () () ( ) ( ( )( ) () ) ( ) ( () ( ) ) (h) What is the elasticity of t...
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