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• 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.
• The monopolist maxy (=R(y)-C(y)) and
so the 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.
• Then 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). 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. (PC
is a special case where p’(y)=0.)
• 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). Another way to read
this is since demand is downward sloping,
so AR(y) decreases with y, when AR
decreases, MR must be lower than AR.
• For linear demand p=a-by, so MR(y)=aby+(-b)y=a-2by.
• 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.
• Consider a monopolist. If the monopolist
is levied a quantity tax of t dollars, what
will occur?
• 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. But this is
not generally true. Suppose the demand is
of constant elasticity. Then p[1+1/]=c+t.
Thus ∆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.
• 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.