ajaz_eco_204_2012_2013_chapter_13_Short_Run_CMP_PP

# The only variable input here is labor now if we

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Unformatted text preview: here is labor. Now: If we double labor levels, the new output is: ( ) Observe: corresponds to increasing returns in labor since: corresponds to constant returns in labor: corresponds to deccreasing returns in labor: There is no connection between returns and returns to scale. For example: This has decreasing returns to labor ( ) but constant returns to scale ( ). (b) What is the percentage change in output due to a 1% increase in labor? Interpret the elasticity in light of the answer in part (a). Answer The production function is: 5 ECO 204 Chapter 13: Practice Problems & Solutions for The Short 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: When : Doubling labor more than doubles output, i.e. increasing returns. When : Doubling labor doubles output, i.e. constant returns. When : Doubling labor less than doubles output, i.e. decreasing returns. (c) Derive the optimal (short term) demand for labor. Why doesn’t optimal labor depend on wages? Answer Notice we can drop the constraint , since the production function is Cobb-Douglas. Therefore, the Lagrangian (this includes the constant total fixed cost ) is: The FOCs are: From the second FOC: [ 6 ECO 204 Chapter 13: Practice Problems & Solutions for The Short 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. Observe that optimal labor does not depend on wages. This is because there are two inputs: fixing capital and target output necessarily yields a unique choice for labor. Seen another way, look at the iso-quant below -- here, optimal labor is “picked off” from the iso-quant. K Fixed Capital = k q L Optimal L (...
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## This document was uploaded on 01/19/2014.

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