Chapter Twenty-Six Factor Markets
Chapter Twenty-Six Factor Markets
What Do We Do in This Chapter? We study how a monopolist behave in the factor market
What Do We Do in This Chapter? We study how a monopolist behave in the factor market
A Competitive Firm's Input Demands A purely competitive firm is a price- taker in its output and input markets. It buys additional units of input i until the extra cost of extra unit exceeds the extra revenue generated by that input unit. MRPi(xi)=Wi
A Competitive Firm’s Input Demands A purely competitive firm is a pricetaker in its output and input markets. It buys additional units of input i until the extra cost of extra unit exceeds the extra revenue generated by that input unit. MRPi xi wi ( ) * =
A Competitive Firm's Input Demands For the competitive firm the marginal revenue of a unit of input i is MRP(X)=P×MP(X)
A Competitive Firm’s Input Demands For the competitive firm the marginal revenue of a unit of input i is MRPi xi p MPi xi ( ) = ( )
A Monopolist's Demands for Inputs What if the firm is a monopolist in its output market while still being a price-taker in its input markets? (The other extreme case is called monopsony:A singe buyer with infinite sellers)
A Monopolist’s Demands for Inputs What if the firm is a monopolist in its output market while still being a price-taker in its input markets? (The other extreme case is called monopsony: A singe buyer with infinite sellers)
A Monopolist's Demands for Inputs Suppose the firm uses two inputs to produce a single output. The firm's production function is y=f(X1,X2). So the firm's profit is II(X1,x2)=p(y)y-W1X1-w2x2
A Monopolist’s Demands for Inputs Suppose the firm uses two inputs to produce a single output. The firm’s production function is So the firm’s profit is y = f(x ,x ). 1 2 (x ,x ) p(y)y w x w x . 1 2 = − 1 1 − 2 2
A Monopolist's Demands for Inputs y=f(X1,X2). II(X1,x2)=p(y)y-W1X1-w2x2. The profit-maximizing input levels are determined by aΠ_d(p(y)y)ay 6x1 dy axi -w1=0 and and(p(y)y)ay -w2=0. 0X2 dy 02
A Monopolist’s Demands for Inputs y = f(x ,x ). 1 2 (x ,x ) p(y)y w x w x . 1 2 = − 1 1 − 2 2 The profit-maximizing input levels are determined by x d p y y dy y x w 1 1 = − 1 = 0 ( ( ) ) x d p y y dy y x w 2 2 = − 2 = 0 ( ( ) ) . and
A Monopolist's Demands for Inputs That is, MRP)=d(P()y)y=MR(Y)xMP(xi)=WI dy axi MRP(xi)=d(P(V)y)y=MR(y)x MP2(x2)=W2 dy 0x2
A Monopolist’s Demands for Inputs That is, MRP x d p y y dy y x MR y MP x w m 1 1 1 1 1 1 ( ) ( ( ) ) ( ) ( ) * * = = = MRP x d p y y dy y x MR y MP x w m 1 1 2 2 2 2 ( ) ( ( ) ) ( ) ( ) * * = = =
A Monopolist's Demands for Inputs That is, MRP(X1) _d(p(y)y)y=MR(y)xMPi(xi)=W1 dy ax1 MRP(xi)=d(P(y)y)ay =MR(y)x MP2(x2)=W2 dy 0x2 d(p(y)y)/dy MR(y)p for all y 0 so the marginal revenue product curve for a monopolist's input is lower for all y >0 than is the marginal revenue product curve for a perfectly competitive firm
A Monopolist’s Demands for Inputs That is, MRP x d p y y dy y x MR y MP x w m 1 1 1 1 1 1 ( ) ( ( ) ) ( ) ( ) * * = = = d(p(y)y)/dy = MR(y) 0 so the marginal revenue product curve for a monopolist’s input is lower for all y >0 than is the marginal revenue product curve for a perfectly competitive firm. MRP x d p y y dy y x MR y MP x w m 1 1 2 2 2 2 ( ) ( ( ) ) ( ) ( ) * * = = =
A Monopolist's Demands for Inputs $/input unit p×MP1(X) MR(y)×MP(X) X
A Monopolist’s Demands for Inputs MR y MPi xi ( ) ( ) p MPi xi ( ) xi $/input unit