ECON201PS7

# ECON201PS7 - WELLESLEY COLLEGE DEPARTMENT OF ECONOMICS...

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WELLESLEY COLLEGE DEPARTMENT OF ECONOMICS ECONOMICS 201-03 JOHNSON Problem Set #7 (due IN LECTURE Friday, November 7 th ) 1. P&R, page 550, #6. {You may indeed set up the profit maximizing situation here directly and solve for the labor demand curve [L*(w,P)] before plugging in the numbers given in the text.} 2. A function is homogeneous of degree α in x and y if: f ( t*x , t*y ) = t α * f ( x , y ) So, for instance, if doubling x and y ( t = 2 ) also doubles the value of f (.) , then the function would be homogeneous of degree 1 in x and y, since f(.) has been scaled up by 2 1 , meaning that α = 1 in that case. Alternatively, if that function above is homogeneous of degree 0 ( α = 0 ) in x and y, then doubling both of those variables ( t = 2 ) WOULD NOT CHANGE the value of f(.) , because 2 0 = 1 and we would simply be multiplying f(.) by 1 . Find the homogeneity properties of our familiar producer theory functions below. Once you have figured out the homogeneity properties, explain the economics behind your findings. To simplify your work in this question, I have reproduced our functions from the big example on producer theory we did in lecture. These functions below are for the long run, but you should also be able to consider the short run functions too in terms of their homogeneity properties. If

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## This note was uploaded on 06/15/2010 for the course ECON 201 taught by Professor Johnson during the Fall '08 term at Wellesley College.

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ECON201PS7 - WELLESLEY COLLEGE DEPARTMENT OF ECONOMICS...

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