Intermediate Microeconomics
Monopoly
1
Pure Monopoly

A Monopolized market has only a single seller.

Examples?

XM radio?

Microsoft?

Walmart in a small town?
2
Monopolies

So what causes monopolies?

Legal Constraints:
 e.g patents for new drugs

Ownership of a fixed resource
 e.g. toll highway, land in a given area.

Collusion
 e.g. several producers act as one (OPEC)

Large economies of scale (natural monopolies)
 e.g. land line phone service, utilities, Google? Microsoft?
3
Monopolies

Why are we concerned about Monopolies?
4
Implications of Monopoly

Key to Monopoly: Seller is not a price taker!


Specifically, since monopolist chooses market supply, it essentially
picks a point on the market demand curve to operate on.
This means that for a monopolist, equilibrium price is a function of the
quantity they supply, so they effectively get to choose both
 i.e. choose where to operate on p(q) (“Inverse Demand Curve”)
$
QD(p) or p(q)
Q
5
Monopolist’s Problem

In perfect competition, a firm wanted to choose a quantity to maximize
profits, given it is a “price taker”.
max π(q) = R(q) – C(q)
= pq – C(q)


To find profit maximizing q, we take derivative of π(q) and set it equal to zero,

This gives
p - MC(q*) = 0
“First Order Condition” (FOC)

or equivalently, keep producing until MC(q*) = p
Like any firm, a monopolist wants to choose quantity to maximize profits,
but by doing so effectively chooses price as well.
max π(q) = R(q) – C(q)
= p(q)q – C(q)
So what will be profit maximization condition for the monopolist?
6
Monopolist’s Problem
$
c(Q)
R(Q) = p(Q)Q
q
π(Q)
7
Marginal Revenue for Monopolist

Profit max condition is always MR(q*) = MC(q*) (from FOC)



For firm in perfect competition, firm is a price taker so MR(q) = p for all q.
For monopolist: MR(q*) = [p’(q*)q* + p(q*)]

Since p(q) is the inverse of the market demand curve, we know p’(q) < 0.

Therefore, [p’(q)q + p(q)] < p(q), implying MR(q) < p(q) (i.e. marginal
revenue from producing and selling another unit is less than price)

What is intuition?
Ex: Consider a Market Demand Curve: QD(p) = 400 – 5p



What is Equation for the Inverse Demand curve?
What is Equation for Marginal Revenue curve?
Graphically?
8
Monopolist Behavior

Consider a monopolist:

Cost function given by C(q) = q2 + 8q + 20
Market Demand Curve of QD(p) = 400 – 5p.

What will be equilibrium price and quantity?

Graphically?

9
Profit Maximization and Demand Elasticity

Recall that R(q) = p(q)q


So MR(q) = p’(q) q + p(q)
= p(q)[p’(q) q/p(q) + 1]
Recall ε(p) = Q’(p) p/Q(p)
= slope of demand curve times price divided by quantity


So 1/ε = slope of inverse demand curve times quantity divided by price
= p’(q) q/p(q)
So MR(q) = p(q)[1/ε + 1]

Recalling ε < 0, what does this tell us about output under a monopoly
and demand elasticity, recognizing that Monopolist will choose q to
equate MR(q) to MC(q)?
10
Profit Maximization and Demand Elasticity

We can actually learn even more from elasticity.

In competitive markets, firms produced until
p = MC(q*)

Alternatively, monopolist supplies until MR(q*) = MC(q*), or until:
p(q*)[1/ε + 1] = MC(q*)

Re-writing we get:
p(q*) = MC(q*)ε /[ε +1]

So how does monopoly “mark-up” depend on elasticity of demand?
11
Monopoly and Efficiency

The key implication of a Pareto Efficient
outcome is that all possible gains from trade are
exhausted.

Will this be true in a monopolized market?


Consider first what it means for all gains from
trade to be exhausted.
 Output is produced as long as marginal cost of
last unit is less than what a consumer is
willing to pay for that unit.
How do we know this won’t be true under a profit
maximizing monopolist? How would we see this
graphically?
12
Taxing a Monopolist

What if government imposes a tax on monopolist equal to $t/unit
sold. Will this somehow increase efficiency?

Consider again monopolist with MC(q) = 2Q + 8 that faces a demand
curve such that MR(Q) = 80 – 2Q/5
 We know that without tax, Q = 30 and p = 74
 What will change with tax of t = $12?

Graphically?
13
Entry

If a monopolist is making all these economic profits, can this
monopoly be maintained?


Entry constrained by law (patents, patronage/political favors)
Natural Monopoly - firm’s technology has economies-of-scale large
enough for it to supply the whole market at a lower average cost than is
possible with more than one firm in the market.

Essentially very high fixed costs of entry.
 Examples?
14
Monopoly Policy

Under natural monopoly it is best for one firm to supply whole
market.

To prevent inefficiencies of monopoly, there are a couple of strategies.
 Have government run/regulate industry.
 e.g. Utilities, postal service?

Break-up monopolist
 Especially relevant when declining marginal cost structure due to
high entry costs (e.g. software, drugs)

Block mergers that could allow monopolies to form in the first place.
 Problems?
15