Chapter 27 Factor Markets

1. Chapter 27 Factor Markets • Key Concept: a monopsony is the situation where there is a single buyer. • FOC: pf’(x)=w(x)+w’(x)x.

2. Chapter 27 Factor Markets • In Chap. 20 we only consider a competitive output and a competitive input market. • That is, a firm is a price taker in the output/input market. • We can now relax this a bit.

3. We first consider a monopoly in the output market and reexamine its factor demand. • Looking from the point of view of the use of factor x, a monopolist • maxy p(y)y-c(y)

4. maxx p(y)y-c(y) • Looking at the revenue term p(y)y • (ΔR/Δy) (Δy/Δx) • =MRyMPx • =p(y) [1-1/|(y)|] MPx • =MRPx • Marginal revenue product

6. maxx p(y)y-c(y) • maxx p(y)y-wx • MRPx = w

7. A monopsony is the situation where there is a single buyer. • The buyer is called a monopsonist. • For simplicity assume the monopsonist sells in a competitive market.

8. The profit maximization of a monopsonist is • maxx  • =pf(x)-w(x)x • where w(x) gives the factor price when the monopsonist employs x amount of factor. • In other words, w(x) is the inverse factor supply curve.

9. maxx  = pf(x)-w(x)x • The FOC becomes pf’(x)=w(x)+w’(x)x. • The LHS is the value of marginal product. The RHS is new. • To use one more x, the marginal unit costs w(x). However, since supply is upward sloping, all units employed before cost more too.

10. We can do some algebra. • w(x)+w’(x)x • =w(x)[1+w’(x)x/w(x)] • =w(x)[1+1/(x)] • where (x) is the factor supply elasticity

11. As in what we’ve discussed for a firm’s revenue, we can now define the marginal expenditure and average expenditure in the factor market. • ME= w(x)[1+1/(x)] • AE=w(x)x/x=w(x) • ME>AE • This is due to (x)>0. Moreover when supply is upward sloping, ME>AE.

12. We can graphically illustrate the optimum. • If w(x)=a+bx, then to min w(x)x, FOC becomes w(x)+w’(x)x or a+bx+bx or a+2bx (twice as steep)

14. Let us talk about the effect of minimum wage. • If the labor market is competitive and that the government sets a minimum wage higher than the equilibrium, the supply of labor will exceed the demand for labor at the higher minimum wage.

16. If the labor market is dominated by a monopsonist, thingsare very different. • If the government sets the minimum wage equal to that would prevail in a competitive market, the ME becomes flat until point (Lc, Wc). • The monopsonist will increase employment.

18. We examine one interesting market structure where a monopolist produces output that is used as a factor input by another monopolist.

19. Upstream monopolist produces x with constant marginal cost of c. • Downstream monopolist produces y=f(x). • For simplicity, assume f is identity or y=x. • The inverse demand for downstream is p(y)=a-by.

20. Solve the downstream maximization first. • If the upstream charges k for per unit of x used, downstream • max p(y)y-ky = (a-by)y-ky • MR=a-2by=k

21. MR=a-2by=k • For upstream, this means for the price k it charges, it will be able to sell k=a-2bx. In other words, the MR of downstream is the demand of the upstream. • Upstream max kx-cx=(a-2bx)x-cx • FOC: a-4bx=c • x=(a-c)/4b.

23. Had the two monopolists merged, then the merged monopolist would • max (a-by)y-cy • FOC a-2by=c • y=(a-c)/2b

24. The upstream monopolist raises its price above its marginal cost and then the downstream monopolist raises its price above the already marked-up cost. • There is a double markup. • The price is not only too high from a social point of view. It is too high from the viewpoint of maximizing total monopoly profits.

25. Chapter 27 Factor Markets • Key Concept: a monopsony is the situation where there is a single buyer. • FOC: pf’(x)=w(x)+w’(x)x.