Post on 12-Jan-2016
Lecture # 16Lecture # 16
MonopolyMonopoly
Lecturer: Martin ParedesLecturer: Martin Paredes
2
1. The Monopolist's Profit Maximization Problem
The Profit Maximization Condition Equilibrium
2. The Inverse Elasticity Pricing Rule3. The Welfare Economics of Monopoly
3
Definition: A monopoly market consists of a single seller facing many buyers.
Assumption: There are barriers to entry.
4
The monopolist's objective is to maximise profits:
Max (Q) = TR(Q) – TC(Q) = P(Q)· Q – C(Q) Q
where P(Q) is the (inverse) market demand curve.
5
Profit maximizing condition for a monopolist:
dTR(Q) = dTC(Q) …or… MR(Q) = MC(Q) dQ dQ
In other words, the monopolist sets output so that the marginal profit of additional production is just zero.
6
Recall that a perfect competitor sets P = MC, because MR = P.
This is not true for the monopolist because the demand it faces is NOT flat.
As a result, MR < P
7
Since TR(Q) = P(Q) · Q, then:
dTR(Q) = MR(Q) = P(Q) + dP(Q) · QdQ dQ
In perfect competition, demand is flat, meaning dP(Q)/dQ = 0, so MR = P.
For a monopoly, demand is downward-sloping, meaning dP(Q)/dQ < 0, so MR < P.
8
Example: Marginal Revenue
P0 P0
P1
C
A B
Q0Q0+1q q+1
Competitive firm Monopolist
Demand facing firm
Demand facing firm
A B
Price Price
Firm output Firm output
9
The MR curve lies below the demand curve.
Price
Quantity
P(Q), the (inverse) demand curve
Q0
P(Q0)
Example: Marginal Revenue Curve and Demand
10
The MR curve lies below the demand curve.
Price
Quantity
P(Q), the (inverse) demand curve
MR(Q), the marginal revenue curve
Q0
P(Q0)
MR(Q0)
Example: Marginal Revenue Curve and Demand
11
Example: Marginal revenue for linear demands
Suppose demand is linear: P(Q) = a – bQ
Total revenue is TR = Q*P(Q) = aQ – bQ2
Marginal revenue is: MR = dTR = a – 2bQdQ
So, for linear demands, marginal revenue has twice the slope of demand.
12
Definition: An agent has market power if she can affect the price that prevails in the market through her own actions.
Sometimes this is thought of as the degree to which a firm can raise price above marginal cost.
13
In the short run, the monopolist shuts down if the profit-maximising price does not cover AVC (or average non-sunk costs).
In the long run, the monopolist shuts down if the profit-maximising price does not cover AC.
14
Example: Profit maximisation Suppose: P(Q) = 100 – Q
TC(Q) = 100 + 20Q + Q2
Marginal revenue is: MR = dTR = 100 – 2QdQ
Marginal cost is: MC = dTC = 20 + 2QdQ
MR = MC ==> 100 – 2Q = 20 + 2Q ==>Q* = 20P* = 80
15
Example: Profit maximisation In equilibrium Q* = 20
P* = 80
Observe that: AVC = 20 + Q* = 40AC = 100 + 20 +
Q* = 45 Q* Hence, P* > AVC and P* > AC
16
Example: Positive Profits for Monopolist
Price
Quantity
Demand curve
100
100
17
Example: Positive Profits for Monopolist
Price
Quantity
Demand curve
MR
100
50 100
18
Example: Positive Profits for Monopolist
Price
Quantity
Demand curve
MR
MC
20
100
50 100
19
Example: Positive Profits for Monopolist
Price
Quantity
Demand curve
MR
MC
20
100
50 10020
20
Example: Positive Profits for Monopolist
Price
Quantity
Demand curve
MR
MC
20
100
50 10020
80E
21
Example: Positive Profits for Monopolist
Price
Quantity
Demand curve
MR
20
80
MC
AVC
20
100
50 100
E
22
Example: Positive Profits for Monopolist
Price
Quantity
Demand curve
MR
20
80
MC
AVC
20
100
50 100
EAC
23
Example: Positive Profits for Monopolist
Price
Quantity
Demand curve
MR
20
80
MC
AVC
20
100
50 100
EAC
: Profits
24
Notes: 1. A monopolist has less incentive to
increase output than the perfect competitor: for the monopolist, an increase in output causes a reduction in its price.
2. Profits can remain positive in the long run because of the assumption that there are barriers to entry.
25
Notes: 3. A monopolist does not have a supply
curve: because price is determined endogenously by the demand:
The monopolist picks a preferred point on the demand curve.
Alternative view: the monopolist chooses output to maximize profits subject to the constraint that price be determined by the demand curve.
26
We can rewrite the MR curve as follows:MR = P + dP · Q
dQ = P + dP · Q · P
dQ P = P 1 + dP · Q
dQ P = P 1 + 1
( )( )
27
Given that is the price elasticity of demand:
When demand is elastic ( < -1), then the marginal revenue is positive (MR > 0).
When demand is unit elastic ( = -1), then the marginal revenue is zero (MR= 0).
When demand is inelastic ( > -1), then the marginal revenue is negative (MR < 0).
28
Example: Elastic Region of Linear Demand Curve
Quantity
Price
a/b
a
Demand
29
Example: Elastic Region of Linear Demand Curve
Quantity
Price
a/2b a/b
a
MR
Demand
30
Example: Elastic Region of Linear Demand Curve
Quantity
Price
a/2b a/b
aElastic region ( < -1), MR > 0
MR
Demand
31
Example: Elastic Region of Linear Demand Curve
Quantity
Price
a/2b a/b
aElastic region ( < -1), MR > 0
Inelastic region (0>>-1), MR<0MR
Demand
32
Example: Elastic Region of Linear Demand Curve
Quantity
Price
a/2b a/b
aElastic region ( < -1), MR > 0
Inelastic region (0>>-1), MR<0
Unit elastic (=-1), MR=0
MR
Demand
33
A monopolist will only operate on the elastic region of the market demand curve
Note: As demand becomes more elastic at each point, marginal revenue approaches price.
34
The monopolist will produce at MR = MC, but we also found that:
MR = P 1 + 1
Then: P 1 + 1 = MC
or: P – MC = – 1 P
( )( )
35
Definition: The Lerner Index of market power is the price-cost margin, (P*-MC)/P*.
It measures the monopolist's ability to price above marginal cost, which in turn depends on the elasticity of demand.
The Lerner index ranges between 0 (for the competitive firm) and 1 (for a monopolist facing a unit elastic demand).
36
A monopoly equilibrium entails a dead-weight loss.
For the following analysis, suppose the supply curve in perfect competition is equal to the marginal cost curve of the monopolist.
37
Example: Welfare Effects of Perfect Competition
Supply
Demand
MR
PC
QC
38
Example: Welfare Effects of Perfect Competition
Supply
Demand
MR
PC
QC
: Consumer Surplus
: Producer Surplus
39
Example: Welfare Effects of Monopoly
MC
Demand
MR
PC
QC
40
Example: Welfare Effects of Monopoly
MC
Demand
MR
PC
QCQM
PM
41
Example: Welfare Effects of Monopoly
MC
Demand
MR
PC
QCQM
PM
: Consumer Surplus
42
Example: Welfare Effects of Monopoly
MC
Demand
MR
PC
QCQM
PM
: Consumer Surplus
: Producer Surplus
43
Example: Welfare Effects of Monopoly
MC
Demand
MR
PC
QCQM
PM
: Consumer Surplus
: Producer Surplus
: Deadweight Loss
44
1. A monopoly market consists of a single seller facing many buyers (utilities, postal services).
2. A monopolist's profit maximization condition is to set marginal revenue equal to marginal cost.
3. Marginal revenue generally is lower than price. How much less depends on the elasticity of demand.
45
4. A monopolist never produces on the inelastic portion of demand since, in the inelastic region, raising price and reducing quantity make total revenues rise and total costs fall!
5. The Lerner Index is a measure of market power, often used in antitrust analysis.
6. A monopoly equilibrium entails a dead-weight loss.