Lecture 10b: A Network Competition Model Laffont, Tirole,

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Lecture 10b A Network Competition
ModelLaffont, Tirole, Rey (1998a,b) RAND
Journal of Economics
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Outline of Model

• Demand system in which individuals are
  distributed according to their preferences over
  networks.
• Consumers have two choices which network to join
  and how many calls to make.
• Prices chosen by the firms affect network
  affiliation, as well as the number of calls.
• Model formalizes pricing game between the
  competing firms and analyzes the effect of
  changes in termination fees on the equilibrium
  prices.

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Cost Specification

• Marginal cost of origination and the marginal
  cost of termination are equal to c0.
• The marginal cost of transmission c1.
• Termination fee denoted by a. We assume that
  a is common to all networks (regulation).
• In Israel changes in a in Agurot per minute
• 2004 45 2005 32 2008 22 2011 8.37

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Cost of On-Net Off Net Calls

• The total cost of an on-net call, i.e., a call
  that originates and terminates on the same
  network is c?2c0c1.
• The total cost to the network for an off-net
  call, i.e., a call that originates on one network
  and terminates on another network is
• ??ac0c1.

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Demand for Phone Calls

• We assume a constant elasticity of demand for
  phone calls
• q(p)p-?.
• q is quantity (minutes) and p is the price per
  unit (minute).
• ?gt1 is the elasticity of demand.

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Demand for Calls Continued

• We assume that the price of on-net and
  off-net calls are the same denoted by p.
• Consumers net surplus from calls is given by
• v(p) p-(?-1)/( ?-1).

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Balanced Calling Pattern

• We assume that there is a balanced calling
  pattern. This means
• A consumer has an equal chance of calling any
  other consumer with cellular service.
• The fraction of calls originating on one network
  and terminating on that network (on-net calls) is
  equal to the percent of the consumers that
  subscribe to that network.

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Which Network to Join

• Hotelling model Two networks located at opposite
  ends of the unit line.
• We normalize the size of the market to one.
• Consumer preferences distributed uniformly over
  the line.
• We assume that the market is fully covered, that
  is, all consumers subscribe to one of the
  cellular networks

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Which Network to Join

• Benefit to a consumer located at x joining net 1
• u1(p1,x)w1(p1)- tx,
• where w1(p1)? v(p1) (1- ?) v(p1)v(p1)
• ? is the market share of firm 1.
• Hence, u1( p1,x)v(p1)- tx
• Since we assumed that the market is fully
  covered, (1-?) is the market share of firm 2.
• Benefit to a consumer located at x joining net 2
• u2( p2,x) v(p2) t(1-x),

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Network Size in Equilibrium

• In equilibrium, the marginal consumer x ?.
• Hence, the marginal consumer is defined by
• u1( p1,?) u2( p2,?)
• OR
• ? ½v(p1)-v(p2)/2t½?v(p1)-v(p2), where
  ?1/2t.
• ? measures the degree of substitutability among
  networks. When ? is small (t is large), there is
  little substitutability between networks.

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Firm Profits and Oligopoly Equilibrium

• Profits of network 1 are given by
• ?1(p1 p2) ? ?(p1-c)q(p1)?(1- ?)p1 - ?
  q(p1)(1-?)?(a-c0)q(p2)

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First Term of Profit Function

• The first term in the profit function,
  ??(p1-c)q(p1), represents the profits from on-net
  calls that originate on network one
• The first ? is the fraction of subscribers that
  join network one, the second ? is the percent of
  calls made on-net by the subscribers of network
  one. (p1 - c) is the margin per on-net call and
  q(p1) is the number of calls.

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Second Term of Profit Function

• The second term of the profit function
  ?(1-?)p1 - ? q(p1)
  ?(1-?)p1-(ac0c1)q(p1) represents the profits
  from off-net calls that originate on network one
  ? is the fraction of subscribers that join
  network one, (1-?) is the percent of calls made
  off-net, q(p1) is the total number of off-net
  calls per subscriber and p1 - (ac0c1) is the
  margin per off-net call. This is because network
  one incurs the cost of origination, c0, the cost
  of transmission, c1, and the termination fee, a,
  that is paid to network two.

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Third Term of Profit Function

• The third term, (1-?)?(a-c0)q(p2), represents
  revenue from calls that originate on network two
  and terminate on network one. (1-?) is the
  fraction of subscribers that join network two, ?
  is the percent of calls made off-net (to network
  one) and q(p2) is the total number of off-net
  calls per subscriber, and (a-c0) is the margin
  per call. This is because the revenue per call
  is a and the cost of terminating the call that
  originates on network two is c0.

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Equilibrium Prices

• Equilibrium prices are found by differentiating
  the profit functions with respect to p1 and p2
  and setting these equations equal to zero.
• If a stable, symmetric equilibrium exists
  (p1p2p),
• p increases in a. (Thus, when a falls, p falls)
• Thus, the access charge is an instrument of tacit
  collusion.
• Why? See next slide!

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Intuition for Result ?1(p1 p2) ?
?(p1-c)q(p1)?(1- ?)p1 - ? q(p1)(1-?)?(a-c0)q(p
2) But second term can be written ?(1-?)p1-(a
c0c1)(c0-c0)q(p1)?(1-?)p1-c
q(p1)-?(1-?)a-c0q(p1) Thus, ?1(p1 p2)
?(p1-c)q(p1) (1-?)?(a-c0)q(p2)-q(p1) ?1(p1
p2) Retail profit access
revenue/deficit term Note If p1gt p2, firm 1
has positive revenue from access. And when a is
well above a-c0, this provides a strong incentive
not to lower prices