2. externalities and public goods.pdf
TRANSCRIPT
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Market Failures:
Externalties and Public Goods
Prof. Carlo Cambini
Politecnico di [email protected]
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Externalities
Externalities arise between producers,
between consumers, or betweenproducers and consumers
Externalities are the effects of productionand consumption activities not directly
reflected in the market
They can be negative or positive
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Externalities
Negative
Action by one party imposes a cost on anotherparty
Plant dumps waste in a river, affecting those
downstreamThe firm has no incentive to account for the external
costs that it imposes on those downstream
Production of electricity and emission of excessiveCO2
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Externalities
Positive
Action by one party benefits another party
Homeowner plants a beautiful garden where all the
neighbors benefit from it
Homeowner did not take their benefits into accountwhen deciding to plant
Network externalities: mobile users benefits from abig installed base in order to obtain lower call prices
(for on net calls, but not for off net calls!)
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Negative Externalities and
Inefficiency
Scenario plant dumping waste
Marginal External Cost (MEC) is the increase in costimposed on users downstream for each level ofproduction
Marginal Social Cost (MSC) is MC plus MEC
Equilibrium in a competitive market where marketdemand crosses supply curve
Assumption: the firm has a fixed proportions
production function and cannot alter its inputcombinationsThe only way to reduce waste is to reduce output
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External Costs
MC
S = MCI
P1
q1
P1
Q1
MSC
MSCI
Firm output
Price
Industry output
Price
MEC
MECI
q*
P*
Q*
D
Firm will produce q1 at P1.
There is MEC of production from
the waste released. The MSC is
true cost of production.
The profit maximizing firm
produces at q1 while the
efficient output level is q*.
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Negative Externalities and
Inefficiency
The MC curve for the firm is the marginal cost of
production Firm maximizes profit by producing where MC
equals price in a competitive firm
As firm output increases, external costs on usersalso increase, measured by the marginal
external cost curve
From a social point of view, the firm produces
too much output
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External Costs
Aggregatesocial cost of
negative
externality
By not producing
at the efficient
level, there is a
social cost onsociety.MC
S = MCI
D
P1 P1
q1 Q1
MSC
MSCI
Firm output
Price
Industry output
Price
MEC
MECI
q*
P*
Q*
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Positive (Network) Externalities Economists say that there is a network
externalitywhen the value of a good depends
on the number of other people who use it.
Examples are goods like the telephone
network, the fax machines network, the email
network, or the Internet itself.
Thus, the utility of a single agent i depends not
only on the quantity consumed (q) but also on
the numberN of agents in the market who use
it:),()( qNUqU ii =
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Network externalities We face direct network externalities when the
utility of an agent of type A depends on the
number of agents belonging to the same group
(say network) A:
An additional agent that enter the network
generates a postive externality (positive feedback)
to the existing agents since connectionpossibilities are enlarged (ex. the evolution of
mobile adoption).
The Metcalfes law
),()(,,
qNUqUAAiAi
=
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A simple model (Rohlfs, 1974)
Letp be the (fixed) price to be connected to a
telecom network; the utility function of aconsumers of type [0, 1] (= willingness to pay)
is:
Utility increases if the numbern [0, 1] of
users increases.
=connectnoif0
connectsif)1()(
pnU
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A simple model (Rohlfs, 1974)
Denote with the consumer indifferent
between being connected or not, for a given pricep and number of users n.
For the marginal consumer, the price limit is
given by:
In equilibrium, the number of potential users
should be equal to the number of existing users,
i.e. = n.
~
0)~
1( = pn
~
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A simple model (Rohlfs, 1974)
Thus, in equilibrium we have:
Two equilibria, one stable and one unstable.
is called the critical mass
)~
1(~
=pp
0
p
1/2n
1
0
0 0
L H
L0
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A simple model (Rohlfs, 1974)
What is the critical mass? The minimum level of
coverage/penetration that a network/technologyshould reach in order to remain in the market.
If you fail, you will exit the market.
Relevant concept in high-tech industries:compatible vs. incompatible products.
Relevant role of price and its impact on the
coverage level.
Important factors: switching costs and lock in
effect
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Market analysis in presence of network
externalities
From social point of view, the optimal coverage is
the level that maximes welfare, given by the sum ofconsumer net surplus and firms profit, i.e.:
W= Gross Surplus P*Q(P) + P*Q(P) C(Q) == Gross Surplus C(Q)
where Gross Surplus =
and in equilibrium n =
=
2
~~
)1(
2~
0
ndn
~
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Market analysis in presence of network
externalities
From social point of view, it is easy to show that
a 100% coverage should be reached (almost for c< 0.5).
Costi,
Benefici
0
0,1
c = 0,5
0,2
0,3
0,4
0,5
0,2 0,4 0,6 0,8 1
c = 0,25
c = 0,1
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Market analysis in presence of network
externalities
Should a private firm choose to cover all the
marlet or not?In monopoly:
FOC:Costi,Ricavi
0
0,1
c = 0,5
0,2
0,3
0,4
0,5
0,2 0,4 0,6 0,8 1
c = 0,25
c = 0,1
~~
)~
1(~~~
)~
( ccp ==
0~
3~
2 2 = c
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Market analysis in presence of network
externalities
Using simulation we determine the optimal
coverage/penetration rate:
0,6710
0,6110,1
0,5410,2
0,510,25
010,5
MonopolyEfficiencyCost c
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Network externalities
It is important to understand that if the value of the
network increases through interconnection (due toMetcalfe law), then there should be a way to divide
that increase in value so to make all participants
better off. If the pie gets bigger, everyone can get a larger
price. However, the increased size of the pie also
means that threats not to interconnect becomemore significant. And, of course, a larger pie is a
more tempting target for someone to try to snatch
than a smaller one.
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Network externalities
If two networks of size n1 and n2 interconnect (with n1>> n2 ), what increase in value accrues to each one?
Applying Metcalfes law:
Each network gets equal value from interconnecting!!
This calculation, simple though it is, gives someinsight into why peering, or settlement-freeinterconnection, is common among large backboneproviders. The gains from interconnection are splitmore-or-less equally, even among somewhat differentsize networks.
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Network externalities
But not all networks are willing to interconnect
on a payment-free basis.What happens if one network acquires the
other (say 1 acquires 2)?
Network 1 captures twice as much value by
buying out network 2 rather thaninterconnecting with it. Essentially the threat ofnon-connection increases the larger networksbargaining power.
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Indirect network externalities
We face indirect network externalities when
the utility of an agent belonging to a group(say network) A depends on the number of
agents of the group B and viceversa:
Example: all the so called intermediation
market
==
)),(()(
)),(()(
,,
,,
qNNUqU
qNNUqU
ABBiBi
BAAiAi
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Indirect network externalities
Example (from Armstrong, 2004):
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Indirect network externalities
Example (from Armstrong, 2004):
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Indirect network externalities
Example (from Armstrong, 2004):
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Indirect network externalities
Example (from Armstrong, 2004):
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Indirect network externalities In all the examples, we have a (physical or virtual)
platform that intermediate between the two groups of
agent. When we have several groups of agents that interact
via one or more platform, we say that we face a two-sided market
Surplus is created or destroyed only when groupsinteract, but this interaction should be mediated insome way.
In these cases, the surplus enjoyed by a member ofone group depends on the number of the agent of theother group that join the same platform
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Two-side markets
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Two-side markets
Business strategy for the platform: getting both
side on board. Only maximizing the number ofagent in both side of the market permit to createhigher surplus in the market
Pricing issues: prices are related to: a) relativeimpact of the positive externality; b) level of priceelasticity.
Tariff level and tariff structure
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Two-side markets: a simple model
Two-sided market. Price competition.
with eij 0 and e12e21 < 1
Note:
ifD(p2) increases (due to a decrease ofp2), positive
effect also on the market demand 1, raising by e21D(p2).
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Two-side markets: a simple model
Benchmark model. Independent platform:
suppose each market served by one platform:
We obtain:
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Two-side markets: a simple model
Now suppose only one platform serves all
markets:
Price equilibrium:
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Two-side markets: a simple model
Case I: intermediate level of indirect
externalities
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Two-side markets: a simple model
Case II: high externality from 2 to 1 (i.e. e21 >
e12)
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Two-side markets: a simple model
Case III: high externality from 1 to 2 (i.e. e21