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Lecture_22_Factor_Markets

# Lecture_22_Factor_Markets - Lecture 22 Factor Markets c...

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Lecture 22: Factor Markets c ° 2008 Je/rey A. Miron Outline 1. Introduction 2. Monopoly in the Output Market 3. Monopsony 4. Upstream and Downstream Monopolies 1 Introduction The analysis in earlier lectures examined factor demands for a °rm facing competitive output and input markets. In some interesting cases, however, the assumption of a competitive market (for either the output or the input) is not realistic. This lecture considers what happens to factor demands when the assumption of competition does not hold in one or both markets. Some of the results here are not enormously important in practice, but they are nice reviews of earlier material and clean applications of the tools already developed. 2 Monopoly in the Output Market When choosing how much of a factor to hire, a °rm always makes the same cal- culation: it compares the marginal revenue from using a bit more of this factor to the marginal cost. This general rule takes di/erent speci°c forms depending on the circumstances. We assume now that the °rm is a monopolist and uses one factor of production. We can therefore write the production function as 1

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y = f ( x ) and the revenue the °rm receives is R ( y ) = p ( y ) y Suppose the °rm considers increasing x a little bit. Then the e/ect on revenue is @R ( y ) @x = @R ( f ( x )) @x = @p ( f ( x )) f ( x ) @x = p ( f ( x )) f 0 ( x ) + f ( x ) p 0 ( f ( x )) f 0 ( x ) = [ p ( y ) + yp 0 ( y )] f 0 ( x ) = p ( y ) ° 1 + yp 0 ( y ) p ( y ) ± f 0 ( x ) = p ( y ) ° 1 + 1 ° ± MP x This can also be written as @R ( y ) @x = MR y MP x That is, the e/ect of an increase in x on revenue is the e/ect of the MP of x times the e/ect of increasing x on the °rm±s MR . The overall expression is known as the marginal revenue product . The MRP is a generalization of the competitive case. Under competition, the elasticity of demand is in°nite and the formula collapses to @R ( y ) @x = pMP x since for a competitive °rm marginal revenue equals price. In this case, therefore, the MRP is just equal to the value marginal product , where that value is determined by the market price. 2
It is useful to think about the how the value MP compares to the revenue MP . The MRP must always be less than the value MP since an increase in x by a monopolist means an increase in the amount of y , and this causes a decrease in p . This result °ts with fact that a monopolist wants to produce less than a °rm acting competitively, so the monopolist also purchases less of the input.

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Lecture_22_Factor_Markets - Lecture 22 Factor Markets c...

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