Network Competition:
II. Price discrimination
J ean-Jacques Laffont
Patrick Rey
J ean Tirole
M a a r t e n W i s m a n s
M i c h i e l U b i n k
( 2 0 0 7 6 2 0 7 )
( 2 0 0 7 6 2 0 4 )
Agenda
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Introduction
The model
Main insights
Propositions
Conclusions
Companion article
• Framework of interconnection agreements
between rival operators
• Studied competition between interconnected
networks
• Assumption of non-discriminatory pricing
Our article
• Relaxes the assumption of non-discriminatory
pricing
• Shows that the nature of competition is affected
by price discrimination (in the entry and mature
phase of the industry)
Free competition
• Unconstrained interconnection agreements
• Entrants may be handicaped (entry phase)
• Enforce collusive behavior (mature phase)
Our article
Fixed cost and marginal cost
• Marginal cost technically determined for on-net call
• Depends on interconnection price of rival network
for off-net call
Assumptions
• Percentage of calls terminating on net is equal
to the fraction of consumers subscribing to the
network
• The interconnection price charged by the two
companies is equal
• Two differentiated networks in the market have full
coverage and can serve all consumers
The model
Total marginal cost
C= 2C0 + C1
C0 = MC originating and terminating
C1 = MC in between
D emand stucture is differentiated à la H otelling
The model
Pi = On-net prices
^Pi = Of-net prices
i = Market share
a = Unit access charge
The model
Fixed cost and marginal cost
• Marginal cost technically determined for on-net call
• Depends on interconnection price of rival network
for off-net call
The model
Consumer Welfare is given by:
v(p) = Consumer variable net surplus
Consumer expectations and
market shares
Price discrimination creates positive, tariff-mediated,
network externalities. Customers of network i are better
off the more (fewer) consumers join it if pi < p^i
(pi > p^i)
This article only focusses on a stable equilibrium
situation
Main insights (1)
• Network interconnection eliminates network
externalities under nondiscriminatory pricing
• Positive (negative) network externalities exist if
the access price embodies a markup (discount)
relative to marginal cost
Main insights (2)
• Ratio of off- and on-net call prices reflects the
relative markup on access
• Price discrimination introduces a wastefull
distortion in the consumers’ marginal rate of
substitution between on- and off-net calls
Main insights ( 3 )
• Trigger intense competition for market share. The
bigger the market share, the less off-net cost have to be
paid
• When the networks are poor substitutes, price
discrimination decreases the double markup for on-net
calls and raises it for off-net calls; This price dispersion
benefits those whose net surplus function is convex
• A full coverage incumbent can squeeze out smaller
competitors by raising interconnection prices
(anticompetitive concerns)
Stable symmetric equilibrium
When
=0
a = Unit access charge (the charge asked by a
rival firm for an off-net call)
c0 = Marginal costs of terminating end of call
m = Markup on access (relative to total cost of call)
Stable symmetric equilibrium
The proportionality rule ( Lemma 1) says:
Because 1 + m = 0, there is an unique equilibrium
under discriminatory pricing that is symmetric and
moreover stable. (The price of on and off-net calls is
equal)
Optimimal access charge
Aw = Unit access charge that is socially preferred
aπ = Unit access charge that maximizes profit
σ: = Index of substitutability.
When: σ = 0:
When: σ > 0:
aw < aπ = c0 Then:
aw < c0 < aπ Then:
and profit is maximized
An small increase in the substitutability parameter σ
first increases both aw and aπ and cares fore monopoly
prices. If σ gets larger people are more interested in
substituting providers and logically aπ and p decrease
again.
Impact of price
discrimination
Price discrimination may increase social welfare when
applied to competition between equals:
(i) Price discrimination may alleviate double marginalization
(ii) Price discrimination intensifies competition
1.
D ouble marginalization
If the two networks are poor substitutes and if there is
a markup on access (a > c0 ), social welfare is higher
under price discrimination than under uniform pricing.
The function W(p) reaches a max at p=c. Since all
prices exceed the monopoly price because of the
markup, a mean-preserving price spread stricly raises
social welfare.
2.
Intensified Competition
Price discrimination lowers the average price for small
markups.
Pd = On-net price under discrimination
^Pd = Off-net price under discrimination
Pu = Price under uniform pricing
Nonlinear pricing
Firms know their consumers’ variable surplus function
Firms set two-part tariffs
Network i therefore charges:
Fi = Fixed fee (subscriber line charge)
Ti = Total revenue
Qi = Consumption of on-net calls
^Qi = Consumption of of-net calls
Nonlinear pricing
In a competition with nonlinear tariffs, if the access
charge is small (a close to C0) or the networks are
poor substitues, then:
(i) There exists a unique equilibrium (dynamic and
stable)
(ii) The marginal prices are the perceived marginal
costs Pi = c and ^Pi = (1+m)c
1. Unique equilibrium
Market shares are:
This defines a stable shared market equilibrium (from
the point of view of consumer behavior) if
which holds if either
is small enough.
2. Marginal prices
By fixing the market shares, a network i maximizes
over its marginal prices Pi and ^Pi. Marginal-cost
pricing is obtained, thus:
Pi = C
^Pi = (1 + m)c
Blockaded entry
A sufficient condition for the full-coverage
incumbent to enjoy the full monopoly profit is that
the entrant's coverage not exceed:
μ0 = Minimum coverage that makes network 1 to enjoy full
monopoly profit
v(pm) = Consumer’s variable net surplus with monopoly price
v(pR) = Consumer’s variable net surplus with Ramsey price
Conclusions
Two key points of departure from the nondiscriminatory pricing analysis:
Raising costs through high access prices,
leads to more intense competition for market
share. Not necessarily to higher prices and
profitability
• Price discrimination by a dominant operator
should be opposed by potential entrants and
customers. Entrants should be protected.
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