Monopoly and monopoly behavior
Varian: Intermediate Microeconomics, 8e, chapters 24 and 25
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In this lecture you will learn
• how monopoly chooses optimal price/quantity
• what natural monopoly is and how to regulate it
• what the advantages and disadvantages of patents are
• how to profit on different pricing strategies
• what the equilibrium in monopolistic competition looks like
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Definition of monopoly
Monopoly = market structure with only one firm in the market
Monopolies can may arise for different reasons:
• exclusive ownership of an important input (diamonds, rubber)
• exclusive licences or franchises (Czech Railways, Czech Post Office)
• patents (pharmaceutical industry, mobile technologies, ...)
• natural monopoly = large MES (network industries)
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Maximizing profits
Monopoly maximizes profits:
max
y
π(y) = r(y) − c(y)
First order condition:
MR(y∗
) − MC(y∗
) = 0 ⇐⇒ MR(y∗
) = MC(y∗
)
Second order condition:
MR (y∗
) − MC (y∗
) < 0 ⇐⇒ MC (y∗
) > MR (y∗
)
Profit maximizing monopoly considers output y∗ at which
• marginal revenues equal marginal costs,
• MC is steeper than MR.
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Maximizing profits (cont’d)
If a monopoly has negative profits at y∗, it may not produce y∗.
In the SR, monopoly shuts down, i.e. produces y = 0 if
p(y∗
)y∗
− cv (y∗
) − F < −F ⇐⇒ p(y∗
) < AVC(y∗
),
where cv (y) are variable costs and F fixed costs.
In the LR, monopoly exits the industry if
p(y∗
)y∗
− c(y∗
) < 0 ⇐⇒ p(y∗
) < AC(y∗
).
CAUTION!
Contrary to competitive firms, monopoly does not have a supply curve,
because p(y∗) > MC(y∗) (one price → more quantities).
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Example – a linear demand curve
Demand:
p(y) = a − by
Total revenue:
r(y) = ay − by2
Marginal revenue:
MR(y) = a − 2by
Profit:
π = (p(y∗) − AC(y∗))y∗
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Example – optimum of a monopoly in the SR
Demand function: p(y) = 10 − y
Cost function: c(y) = 2y + F, where F = 10
What is the optimal quantity and the profit of monopoly?
Profit function: π(y) = p(y)y − c(y) = 10y − y2 − 2y − 10
First order condition: 10 − 2y∗ − 2 = 0 ⇐⇒ y∗ = 4
Second order condition: −2 < 0 (the extreme is maximum)
Result: y∗ = 4, π(y∗) = 6
Would the optimal quantity change if F = 20? No. Only π(y∗) = −4
Would y∗ in the LR change if QF = 20?
Yes. Monopoly would exit the market.
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Elasticity and monopoly markup
MR(y) = r (y) = (p(y)y) = p(y) + p (y)y (product rule)
Substituting into the first order condition MR(y∗) = MC(y∗):
p(y∗
) + p (y∗
)y∗
= MC(y∗
)
The relationship between the monopoly markup and the elasticity:
p(y∗
) + p (y∗
)
p(y∗)y∗
p(y∗)
= MC(y∗
)
p(y∗
) 1 + p (y∗
)
y∗
p(y∗)
= MC(y∗
)
p(y∗
) (1 + 1/ (y∗
)) = MC(y∗
)
p∗
MC(y∗)
=
1
1 − 1/| (y∗)|
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EXAMPLE: Elasticity for Coke and Dr. Pepper
Dub´e (JEMS, 2005) – Pepsi = −3,07 and Dr.Pepper = −6,03
If the producers were monopolists: p/MC = 1,48 (Pepsi) 1,2 (Pepper)
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Inefficiency of monopoly
Monopoly: MR(ym) = MC(ym)
Perfect competition: pc = MC(yc)
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Inefficiency of monopoly (cont’d)
With a reduction from yC to ym:
• producer’s surplus PS
changes by A−C
• consumers’ surplus CS
reduces by A + B
• total surplus CS + PS
reduces by B + C =
deadweight loss
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Natural monopoly
Natural monopoly – one firm can satisfy market demand at lower costs
than more firms.
Regulation seems simple
– set pm = MC.
Problem: at this price
natural monopoly is
typically in loss.
Alternative: set price
such that monopoly has
zero profit (pm = AC).
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APPLICATION: The optimal life of a patent
Patent = limited monopoly. What is the optimal length of a patent?
Two effects on consumers. The longer the duration,
• the higher the motivation to innovations (↑ CS),
• the higher the deadweight loss (↓ CS).
In the US the life of a patent is 17 years. Is it optimal?
William Nordhaus (Invention, Growth, and Welfare, 1969) calculated that
for average innovations a patent life of 17 years achieved 90 percent of the
maximum possible consumers’ surplus.
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APPLICATION:
”
Patent thickets“
Patent thicket – a dense web of overlapping intellectual property rights a
firm faces if it wants to commercialize a new technology.
Firms may create a portfolio of patents for strategic purposes.
Each firm’s patents serve as a defense against patent suits.
If e.g. IBM tries to sue HP, HP would do the same to IBM.
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Price discrimination
Three types of price discrimination that differ in their assumptions:
1 Perfect price discrimination (first-degree p. d.)
Monopoly knows the willingness to pay and can sell each unit of
product for the maximum price consumers are willing to pay.
2 Second-degree price discrimination
Monopoly knows that consumers differ in their willingness to pay,
knows their demands, but cannot tell which consumer is which.
3 Third-degree price discrimination
Monopoly knows demands of different groups of consumers, may
charge different prices to different groups, but does not know the
willingness to pay for individual units of product.
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Example – perfect price discrimination
Hana and Lola are the only buyers in a market with a monopoly with
constant MC. Hana has high and Lola low willingness to pay (WTP).
What is the quantity bought by Hana and Lola? What is the profit?
Result:
Hana buys 8 and Lola 3 units.
The monopoly’s profit from Hana = area A; profit from Lola = B.
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Example – perfect p. d. for linear demands
Demands of Hana and Lola: qH = 100 − p and qL = 40 − p
Quantity q, profit π, surpluses CS and PS and deadweight loss DWL?
Result:
Quantity: q = qV + qN = (100 − 20) + (40 − 20) = 80 + 20 = 100
Profit: π = PS = A + B = 80×80
2 + 20×20
2 = 3 400
Consumers’ surplus: CS = 0, deadweight loss: DWL = 0 17 / 40
Real-world examples of perfect price discrimination?
A theoretical concept – does not exist in reality. Imperfect examples:
• markets without posted prices – Asian bazaar, car sales, antique markets,
B2B services, ...
• In 2000 Amazon charged different prices to different consumers for the same
DVDs. After critique Amazon abandoned this practice.
• System Ding from Soutwest airlines offers individual fares to each customer–
but the fares are 30 % below the price of similar flights.
• Priceline (internet airline ticket sales) let the customers to name their price/
willingness to pay. But there was competition in the market. People entered
lower than competitive prices. Priceline had to change its business model.
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Second degree price discrimination
Second degree price discrimination – the result: price depends on
quantity bought by the consumer (also nonlinear pricing).
Problem: The monopoly knows that consumers differ in their willingness
to pay, but cannot tell the WTP of individual consumers – does not
discern consumers with a high WTP.
Solution: The monopoly offers such price-quantity packages that give the
consumers an incentive to self select – high WTP customers choose
package meant for them.
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Example – second-degree price discrimination
The same 2 buyers as in perfect p. d. and zero MC and F.
Situation 1: First let’s assume that the monopoly offers the same package
as in the case of perfect discrimination:
• package 1 – quantity x0
1 for the price A
• package 2 – quantity x0
2 for the price A + B + C
The result of situation 1:
• Lola chooses package 1
and has a CS of 0
• Hana chooses package 1
and has a CS of B
• The monopoly will have
a profit of 2A
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Example – second-degree price discrimination (cont’d)
Situation 2: The monopoly offers:
• package 1 – quantity x0
1 for a price of A
• package 2 – quantity x0
2 for a price of A + C
The result of situation 2:
• Lola chooses package 1
and has a CS of 0
• Hana chooses package 2
and has a CS of B
• Compared to situation 1,
monopoly increases its
profit to 2A + C
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Example – second-degree price discrimination (cont’d)
Situation 3: Compared to situation 2, the monopoly:
• reduces the quantity in package 1 and the price by the triangle area y
• increases the price of package 2 (quantity x2 unchanged) by the area x
The result of situation 3:
• Lola chooses package 1
and has a CS of 0
• Hana chooses package 2
and her CS falls by x
• Compared to situation 2 the
monopoly’s profit increases by
x − y
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Example – second-degree price discrimination (cont’d)
Profit maximization: The monopoly reduces the quantity x1 to xm
1 ,
where the rise in profit from Hana equals the loss from Lola:
• package 1 – quantity xm
1 for a price A
• package 2 – quantity x0
2 for a price A + C + D
The result of profit maximization:
• Lola chooses package 1
and has a CS of 0
• Hana chooses package 2
and has a CS of B
• The monopoly’s profit increases
further to 2A + C + D
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Example – second-degree price discrimination (cont’d)
Two general conclusions:
1 Consumers with a high willingness to pay profit from the presence of
consumers with a low willingness to pay. The monopoly cannot take
their entire CS because they would start buying the product aimed at
low-WTP consumers.
2 Even consumers with a low WTP may be better of with price
discrimination than otherwise. If monopoly was not allowed to price
discriminate, it might supply only to consumers with a high WTP.
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Third-degree price discrimination
Third-degree price discrimination – monopoly knows consumer
demands, can divide consumers in two groups and charge different prices
(can prevent arbitrage).
Difference to
• second-degree p. d. – can tell the consumers apart.
• first-degree p. d. – cannot charge prices equal to the willingness to
pay for each unit of the product.
Examples:
• student discounts with ISIC
• different prices for different
nationalities (books, pills, entrance)
• discounts based on the place of
residence (Disneyland)
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Third-degree price discrimination (cont’d)
Assume that monopoly divides the consumer in two groups (markets) and
arbitrage is not possible.
Inverse demands in markets 1 and 2: p1(y1) and p2(y2)
Cost function of the monopoly: c(y1 + y2)
Monopoly maximizes profit
max
y1,y2
p1(y1)y1 + p2(y2)y2 − c(y1 + y2)
First order conditions:
MR1(y1) = MC(y1 + y2)
MR2(y2) = MC(y1 + y2)
In the optimum, MC equal MR in both markets.
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Example – third-degree price discrimination
Demand in market 1: D1(p1) = 100 − p1 ⇐⇒ p1(y1) = 100 − y1
Demand in market 2: D2(p2) = 100 − 2p2 ⇐⇒ p2(y2) = 50 − y2/2
Cost function of the monopoly: C(y1 + y2) = 20(y1 + y2)
Optimal quantities and prices in both markets and monopoly profit?
First order condition:
MR1 = MC and MR2 = MC
100 − 2y1 = 20 and 50 − y2 = 20
Quantity – solving the first order contitions: y1 = 40 and y2 = 30
Prices – substituting in demands: p1 = 60 and p2 = 35
Monopoly profit: π = 60 × 40 + 35 × 30 − 20(40 + 30) = 2 050
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Example – price discrimination prohibited
Demand in market 1: D1(p1) = 100 − p1 ⇐⇒ p1(y1) = 100 − y1
Demand in market 2: D2(p2) = 100 − 2p2 ⇐⇒ p2(y2) = 50 − y2/2
Cost function of the monopoly: C(y1 + y2) = 20(y1 + y2)
How does the result change if monopoly cannot discriminate?
Monopoly charges only one price =⇒ faces market demand:
D(p) = D1(p1) + D2(p2) = 200 − 3p ⇐⇒ p(y) =
200
3
−
y
3
Next, problem of monopoly – result: y = 70, p = 431
3, π = 1 6331
3
Comparing with price discrimination:
• price between p1 and p2 – sells more in market 1 and less in market 2
• monopoly has a lower profit and consumers higher CS
Is price third-degree price discrimination always bad?
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A specific example with a kinked marked demand
Linear demands in both markets and zero marginal costs:
• With price discrimination: monopoly sells in both markets.
• Without discrimination: if D2 is low, monopoly is only in market 1.
CS is the same in market 1 and lower in market 2 than with discrim.
Consumers better off than with price discrimination.
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Third-degree price discrimination and price elasticity
How do prices depend on price elasticities 1(y1) and 2(y2)?
First-order conditions can be written as
MR1(y1) = p1(y1) 1 −
1
| 1(y1)|
= MC(y1 + y2)
MR2(y2) = p2(y2) 1 −
1
| 2(y2)|
= MC(y1 + y2).
If p1 > p2, then:
1 −
1
| 1(y1)|
< 1 −
1
| 2(y2)|
and thus | 1(y1)| < | 2(y2)|
The market with a less elastic demand will have higher prices.
Intuition: Less price-sensitive consumers pay higher prices.
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CASE: Price discrimination in Disneyland
Why do people living close to Disneyland pay less for the entrance?
They are more price elastic. Lower price might induce more visits.
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Two-part tariff
Two-part tariff consists of
• a fixed fee
• price for one unit of product
Examples:
• amusement park (entrance fee + price per ride)
• tennis club (yearly membership + price per hour)
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Example – Disneyland dilemma
Assumptions: only 1 attraction. 1 visitor with WTP corresponding to the
demand in graph. A monopoly with constant MC for rides.
At ¯p, the revenue
from rides is ¯p¯x.
Entrance fee = CS
Monopoly profit =
profit on rides + CS
Profit not maximized
– lost profit =
deadweight loss
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Example– Disneyland dilemma (cont’d)
At the price p∗ = MC, CS is maximal and profit on rides zero.
Profit of monopoly is maximal, no deadweight loss.
The optimal two-part tariff:
• price p∗ = MC
• fixed fee = CS
Numerical example:
Inverse demand: p = 9 − x
Marginal cost: MC = 3
Solution:
Price: p∗ = MC = 3
Fixed fee: 6×6
2 = 18
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Bundling
Firms often sell products in bundles
Examples:
• computer with operating system
• magazine (bundle of articles)
• MS Office (Word, Excel, PowerPoint)
• ...
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Example – sell product in bundles or separately?
2 customers (A and B) with a different willingness to pay (table)
2 products – word processor W and spreadsheet program E
Monopoly costs: marginal costs MC = 0 and fixed costs F = 100:
Will monopoly sell W and E separately or in a bundle (1+1)?
customer/product word processor (W ) spreadsheet program (E)
A 120 $ 100 $
B 100 $ 120 $
Result:
Separately:
• optimal prices W and E:
p∗
W = 100$ and p∗
E = 100 $
• profit: π = 2p∗
W + 2p∗
E − F =
4 × 100 − 100 = 300 $
Bundle (1+1):
• optimal price of bundle:
p∗
W +E = 220
• profit: π = 2p∗
W +E − F =
2 × 220 − 100 = 340 $
The monopoly has a higher profit from bundling.
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Monopolistic competition
Assumptions:
(1) a large number of independent firms with a differentiated product
(2) free entry and exit
Examples:
• market for clothes and shoes
• many food markets
• market with books, movies, manazines
Condition (1) =⇒ Each firm in a situation of a monopoly:
• each firm faces a downward-sloping demand
• each firm’s choice of quantity/price has no impact on other firms
Condition (2) =⇒ Firms in the LR enter the profitable market
(or exit the market in loss). =⇒ The firm’s demand becomes flatter and
lower (steeper and higher). This process lasts until the profit is 0.
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Monopolistic competition – equilibrium in the LR
In the LR, the equilibrium quantity y∗ is such that D(y∗) = LAC(y∗).
The long-run equilibrium
has two properties:
1 positive DWL, even
though profits are 0
2 firms have excess
capacity – operate to
the left of minLAC
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What should you know?
• Monopoly maximizes profit at a quantity q∗,
at which MC = MR.
• The higher the elasticity of demand at q∗,
the lower p/MC.
• Monopoly does not have supply curve.
• Monopoly is inefficient – it creates
deadweight loss.
• Natural monopoly satisfies demand at lower
AC than more firms.
• Natural monopoly selling efficient quantity
will be probably in loss.
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What should you know? (cont’d)
• Perfect price discrimination leads to the
efficient outcome.
• Monopoly using third-degree p. d. charges
a higher price in the less elastic market.
• Consumers may benefit from price
discrimination – monopoly might be
willing to sell to low-WTP consumers.
• With the same demand, a two-part tariff
leads to the same result as perfect price
discrimination.
• Monopolistically competitive firms are in
a similar situation as monopoly, but they
have zero profits in the LR.
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