monopoly chapter 24 - ucsb department of...
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Monopoly Quantity & Price Welfare
MonopolyChapter 24
monoply.gif (GIF Image, 289x289 pixels) http://i4.photobucket.com/albums/y144/AlwaysWondering1/monoply.gif?...
1 of 1 4/23/2009 2:35 AM
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Monopoly Quantity & Price Welfare
Motivating Questions
What price and quantity does a monopoly choose?
What are the welfare effects of monopoly?
What are the effects of taxes on monopolies?
Is monopoly every justified/efficient?
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Monopoly Quantity & Price Welfare
What is a monopoly?
A monopoly is a sole supplier of a good.
The monopolist’s demand curve is the market demand curve.
Price maker not a price taker
Can set price (quantity is constrained by demand curverelationship)
Or: chooses quantity, which determines price
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Monopoly Quantity & Price Welfare
What causes monopolies?
Legal fiat: US Postal Service
Patent: drugs, technology; intellectual property
Sole ownership of a resource: toll road
Cartel: OPEC
Large economies of scale: local utilities
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Monopoly Quantity & Price Welfare
Government & Monopoly
Monopoly is heavily regulated
Antitrust Law: abuse of monopoly power is a felony
Dept. of Justice (DOJ) has antitrust division
Federal Trade Commission (FTC) has regulatory oversight
But govt. creates monopolies (USPS) and issuespatents/copyrights that grant monopoly power.
If if monopoly is so bad, why does the government enable it insome cases?
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Monopoly Quantity & Price Welfare
What quantity maximizes profits?
Setup the problem:
For any firm, profit is given by
Π(y) = R(y)− C (y),
where R(y) is revenue and C (y) is cost.
Profit maximization problem:
maxy
R(y)− C (y)
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Monopoly Quantity & Price Welfare
What quantity maximizes profits?
Graphical analysis:
y
$R(y) = p(y)y
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Monopoly Quantity & Price Welfare
What quantity maximizes profits?
Graphical analysis:
$R(y) = p(y)y
c(y)
y
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Monopoly Quantity & Price Welfare
What quantity maximizes profits?
Graphical analysis:
$R(y) = p(y)y
c(y)
y
Π(y)
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Monopoly Quantity & Price Welfare
What quantity maximizes profits?
Graphical analysis:
$R(y) = p(y)y
c(y)
y
Π(y)
y*
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Monopoly Quantity & Price Welfare
What quantity maximizes profits?
Graphical analysis:
$R(y) = p(y)y
c(y)
y
Π(y)
y*
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Monopoly Quantity & Price Welfare
What quantity maximizes profits?
Graphical analysis:
$R(y) = p(y)y
c(y)
y
Π(y)
y*
At the profit-maximizing output level, the slopes of the revenueand cost curves are equal:MR(y∗) = MC (y∗).
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Monopoly Quantity & Price Welfare
What quantity maximizes profits?
Algebraic analysis:
Optimality condition:
dΠ(y)
dy= 0 =⇒ R ′(y)− C ′(y) = 0 =⇒ R ′(y) = C ′(y)
At the profit maximizing quantity, y∗:
MR(y) = MC (y)
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Monopoly Quantity & Price Welfare
What quantity maximizes profits?
Algebraic analysis:
If the market is competitive, the firm takes p as given/fixed(demand curve is flat)In that case, R(y) = py , where p is constant, so MR(y) = p.Profit-maximizing condition: p = MC
y
$D = MR = p
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Monopoly Quantity & Price Welfare
What quantity maximizes profits?
Algebraic analysis:
Monopoly is not a price taker, though
Demand slopes down
Recall MR(y) = P(y) + P∗(y)y is below P(y)Marginal Revenue curve for a Monopoly
y
price
Demand
MR
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Monopoly Quantity & Price Welfare
What quantity maximizes profits?
Algebraic analysis:
Choose quantity y∗ s.t. MR = MCSet price according to P(y∗)Profit-maximizing condition: p = MCPrice is marked-up over marginal cost p > MC
Example on Graph
yDemandMR
price
ym=2
pm = 8
MC
MC = MR
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Monopoly Quantity & Price Welfare
Monopoly: Example
Inverse Demand: P(y) = 10− y , so marginal revenue is. . .
Clicker Vote:A) MR = −1B) MR = 10− y
2C) MR = 10− yD) MR = 10− 2y
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Monopoly Quantity & Price Welfare
Monopoly: Example
Inverse Demand: P(y) = 10− y , so marginal revenue isMR(y) = 10− 2y .
Cost function: C (y) = 2y + y2, so MC (y) = 2 + 2y
Optimality condition:
MR = MC =⇒ 10− 2y = 2 + 2y
So ym = 84 = 2
. . . and pm = P(ym) = 10− 2 = 8
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Monopoly Quantity & Price Welfare
Monopoly: ExampleExample on Graph
yDemandMR
price
ym=2
pm = 8
MC
MC = MR
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Monopoly Quantity & Price Welfare
Monopoly Price and Elasticity of Demand
How does the monopoly price relate to the elasticity of demand?
MR = p(y) + ydp(y)
dy= p(y)[1 +
y
p(y)
dp(y)
dy]
Recall that
ε =p(y)
y
dy
dp(y).
So
MR = p(y)[1 +1
ε].
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Monopoly Quantity & Price Welfare
Monopoly Price and Elasticity of Demand
How does the monopoly price relate to the elasticity of demand?
MR = p(y)[1 + 1ε ] and MR = MC , so MC = p(y)[1 + 1
ε ].
Rewrite as
p(y) =MC
1 + 1ε
Note that MR, p > 0 implies ε < −1
This means that a monopolist chooses an output level atwhich demand is elastic.
Intuition: if on inelastic part, cutting output (raising price)increases revenue (and maybe lowers costs)
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Monopoly Quantity & Price Welfare
Monopoly Price and Elasticity of Demand
How does the monopoly price relate to the elasticity of demand?
p(y) =MC
1 + 1ε
Because elasticity is negative (demand slopes down), price isalways above MC
Markup pricing: price is marginal cost plus a “markup”. Whathappens to the markup as demand becomes less elastic?
Monopolist increases price
Example: if ε = −3, p(y) = 3MC2 ; if ε = −2, p(y) = 2MC
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Monopoly Quantity & Price Welfare
Perfect Competition vs. Monopoly
Price and Quantity: given a cost function, how does the behaviorof a monopolist compare to that of a competitive firm?
Perfect Competition versus Monopoly
y
Demand
MR
price
ym
pm
MC
pc
yc
pm > pc and ym < y c
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Monopoly Quantity & Price Welfare
Inefficiency of Monopoly
What are the welfare effects of monopoly? Who gains andwho loses?
Since pm > pc , seller gains, consumers lose
But since ym < y c , we know that there are unrealized gainsfrom trade. So the losses outweigh the gains: there is somewelfare loss.
The deadweight loss (DWL) is the societal loss in welfare. Itmeasure the inefficiency of monopoly relative to thecompetitive outcome.
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Monopoly Quantity & Price Welfare
Calculating the DWL of MonopolyCalculating Deadweight Loss of Monopoly
y
Demand
MR
price
ym
pm
MC
pc
yc
CB
A
C
In competitive equilibrium
Consumer surplus = A + B+ C
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Monopoly Quantity & Price Welfare
Calculating the DWL of MonopolyCalculating Deadweight Loss of Monopoly
y
DemandMR
price
ym
pm
MC
pc
yc
CB
A
C
DE
In competitive equilibrium
Producer surplus = D + E
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Monopoly Quantity & Price Welfare
Calculating the DWL of MonopolyCalculating Deadweight Loss of Monopoly
y
DemandMR
price
ym
pm
MC
pc
yc
C
DE
In competitive equilibrium
Total surplus = A + B + C + D + E
A
BC
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Monopoly Quantity & Price Welfare
Calculating the DWL of MonopolyCalculating Deadweight Loss of Monopoly
y
DemandMR
price
ym
pm
MC
pc
yc
CB
A
C
In Monopoly case
Producer surplus = B + D
DE
B
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Monopoly Quantity & Price Welfare
Calculating the DWL of MonopolyCalculating Deadweight Loss of Monopoly
y
Demand
MR
price
ym
pm
MC
pc
yc
CB
A
C
In Monopoly case
Consumer surplus = A
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Monopoly Quantity & Price Welfare
Calculating the DWL of MonopolyCalculating Deadweight Loss of Monopoly
y
DemandMR
price
ym
pm
MC
pc
yc
B
In Monopoly case
Total surplus = A + B + D
DWL = (A + B + C + D + E) – (A + B + D) = C + E
D
B
A
C
E
MC(ym)
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Monopoly Quantity & Price Welfare
Inefficiency of Monopoly
The need for regulation
Competitive market provides greater surplus than monopoly
Can changing from a monopolistic market to a competitiveone make everyone (consumers and monopolist) better off(Pareto improving)?
In other words, is there room for a Pareto improving deal inwhich a monopolist agrees to act like a competitive firm?
No, because this will make the firm worse off
Thus, the DWL of monopoly rationalizes antitrust laws
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Monopoly Quantity & Price Welfare
Example (continued)
Inverse demand: P(y) = 10− y
Marginal cost: MC (y) = 2 + 2y
Recall: pm = 8 and ym = 2
What is the competitive equilibrium?
Use p = MC
P(y c) = 10− y c = 2 + 2y = MC (y c)
So y c = 83 and pc = 22
3
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Monopoly Quantity & Price Welfare
Example (continued)
So what is the DWL of monopoly?
We can calculate DWL using
DWL =1
2[P(ym)−MC (ym)][y c − ym]
Aside: in general, this is an approximation. Because of lineardemand, MC, here it is exact.
So DWL is
DWL =1
2[8− 6][
8
3− 2] =
2
3