1. Chapter 25 Monopoly
Key Concept: Monopolist chooses y so that p(y)+p’(y)y=MC(y).
This is inefficient because for efficiency, the comparison should be p(y)=MC(y).
Since typically p’(y)<0, it will underproduce.

2. Chapter 25 Monopoly
Consider the opposite extreme where there is only one firm in the industry. Then it makes no sense to assume that the firm is a price taker.

3. The monopolist
maxy  where =R(y)-C(y)
FOC becomes MR(y)=MC(y)
Since the monopolist faces the market demand curve, let p(y) denote the price on the demand when the quantity is y.

4. MR(y)=d(p(y)y)/dy=MC(y)
FOC becomes p(y)+p’(y)y=MC(y)
The LHS has the usual economic interpretation that raising one unit of quantity could raise the revenue by p(y) because the marginal unit will bring in revenue of p(y).

5. FOC becomes p(y)+p’(y)y=MC(y)
However, at the same time, since demand is downward sloping, to sell one more unit, the price has to be lower.
The lower price will decrease the revenue for all the units sold before.
Perfect competition is a special case where p’(y)=0.

6. MR(y)
=p(y)+p’(y)y
=p(y)[1+p’(y)y/p(y)]
=p(y)[1+1/(y)]
Note that average revenue AR is p(y)y/y=p(y).
Since normally (y)<0, so MR(y)<p(y)=AR(y).

7. MR(y)<p(y)=AR(y)
Another way to read this is since demand is downward sloping, so AR(y) decreases with y.
AR decreases if and only if MR must be lower than AR.

8. Coupled with MC, we can find the optimum.
This confirms again that a monopolist will only operate at the portion where |(y)|>1.
Moreover, for a given demand, the monopolist chooses an optimal output. Hence it is meaningless to talk about the supply curve of a monopolist.

9. Fig. 24.1

10. MR(y)=p(y)+p’(y)y=p(y)[1+p’(y)y/p(y)]=p(y)[1+1/(y)].
For linear demand p=a-by, so MR(y)=a-by+(-b)y=a-2by.
The MR curve is twice as steep as the demand curve.

11. MR(y)=p(y)+p’(y)y=p(y)[1+p’(y)y/p(y)]=p(y)[1+1/(y)]=p(y)[1-1/|(y)|].
Setting MR=MC gives
p(y)[1-1/|(y)|]=MC
p(y)=MC/[1-1/|(y)|]
Price is a markup over MC because |(y)|>1.

12. Consider a monopolist.
If the monopolist is levied a quantity tax of t dollars, what will occur?

13. If the demand is linear and the monopolist has a constant MC curve, then we can illustrate by a graph that the price will increase by only t/2.
First, MC shifts up by t.
Then by “twice as steep,” we get…

14. Fig. 24.3

15. But this is not generally true.
Suppose the demand is of constant elasticity.
p[1+1/]=c+t
∆p/∆t=1/[1+1/]
Since typically <-1, so ∆p/∆t>1. In words, the monopolist passes more than the amount of the tax t.

16. The inefficiency of the monopolist can be seen from its FOC.
The monopolist chooses output so that MR(y)=p(y)+p’(y)y=MC(y).
However for efficiency, we only care about p(y) and MC(y). Since p’(y)y<0, the monopolist will underproduce.

17. Fig. 24.4

18. Fig. 24.5

19. A monopolist underproduces.
Regulators could eliminate the inefficiency by setting price equal to MC.
But this could run into the problem that the monopolist may make a negative profit at such a price.

20. The monopolist may then be regulated to operate at (pAC, yAC).

21. A natural monopoly.
If a natural monopolist operates where price equals marginal cost, then it will produce an efficient level of output, yMC, but it will be unable to cover its costs. If it is required to produce an output where price equals average cost, yAC, then it will cover its costs, but will produce too little output relative to the efficient amount.

22. The cause of a monopolist typically depends on the comparison between the minimum efficient scale of production and the market size.

23. Demand relative to minimum efficient scale.
(A) If demand is large relative to the minimum efficient scale, a competitive market is likely to result. (B) If it is small, a monopolistic industry structure is possible.

24. Chapter 25 Monopoly
Key Concept: Monopolist chooses y so that p(y)+p’(y)y=MC(y).
This is inefficient because for efficiency, the comparison should be p(y)=MC(y).
Since typically p’(y)<0, it will underproduce.