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

5. Factor demand by a monopolist.
Since the marginal revenue product curve (MRP) lies beneath the curve measuring the value of the marginal product (pMP), the factor demand by a monopolist must be less than the factor demand by the same firm if it behaves competitively.

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)

13. Monopsony.
The firm operates where the marginal revenue from hiring an extra unit of the factor equals the marginal cost of that extra unit.

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.

15. Minimum wage.
Panel A shows the effect of a minimum wage in a competitive labor market. At the competitive wage, wc, employment would be Lc. At the minimum wage, w, employment is only Lmw. Panel B shows the effect of a minimum wage in a monopsonized labor market. Under monopsony, the wage is wm and employment is Lm, which is less than the employment in the competitive labor market. If the minimum wage is set to wc, employment will increase to Lc.

16. If the labor market is dominated by a monopsonist, things are 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.

17. Minimum wage.
Panel A shows the effect of a minimum wage in a competitive labor market. At the competitive wage, wc, employment would be Lc. At the minimum wage, w, employment is only Lmw. Panel B shows the effect of a minimum wage in a monopsonized labor market. Under monopsony, the wage is wm and employment is Lm, which is less than the employment in the competitive labor market. If the minimum wage is set to wc, employment will increase to Lc.

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.

22. Upstream and downstream monopoly.
The downstream monopolist faces the (inverse) demand curve p(y). The marginal revenue associated with this demand curve is MRD(y). This in turn is the demand curve facing the upstream monopolist, and the associated marginal revenue curve is MRU(y). The integrated monopolist produces at y∗ i ; the nonintegrated monopolist produces at y∗ m.

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.