Lecture 10b: A Network Competition Model Laffont, Tirole, & Rey (1998a,b) RAND Journal of Economics

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.

Cost Specification Marginal cost of origination and the marginal cost of termination are equal to c 0. The marginal cost of transmission: c 1. 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

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  2c 0 +c 1. 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  a+c 0 +c 1.

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).  >1 is the elasticity of demand.

Demand for Calls Continued We assume that the price of “on-net” and “off-net” calls are the same denoted by p. Consumer’s net surplus from calls is given by v(p)= p -(  -1) /(  -1).

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.

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

Which Network to Join Benefit to a consumer located at x joining net #1 u 1 (p 1,x)=w 1 (p 1 )- tx, where w 1 (p 1 )=  v(p 1 ) + (1-  ) v(p 1 )=v(p 1 )  is the market share of firm 1. Hence, u 1 ( p 1,x)=v(p 1 )- 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 u 2 ( p 2,x)= v(p 2 )– t(1-x),

Network Size in Equilibrium In equilibrium, the marginal consumer x= . Hence, the marginal consumer is defined by u 1 ( p 1,  )= u 2 ( p 2,  ) OR  = ½+[v(p 1 )-v(p 2 )]/2t=½+  [v(p 1 )-v(p 2 )], where  =1/2t.  measures the degree of substitutability among networks. When  is small (t is large), there is little substitutability between networks.

Firm Profits and Oligopoly Equilibrium Profits of network 1 are given by  1 (p 1 ; p 2 ) =   (p 1 -c)q(p 1 )+  (1-  )[p 1 -  ]q(p 1 )+(1-  )  (a-c 0 )q(p 2 )

First Term of Profit Function The first term in the profit function,  (p 1 -c)q(p 1 ), 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. (p 1 - c) is the margin per on-net call and q(p 1 ) is the number of calls.

Second Term of Profit Function The second term of the profit function  (1-  )[p 1 -  ]q(p 1 ) =  (1-  )[p 1 -(a+c 0 +c 1 )]q(p 1 ) 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(p 1 ) is the total number of off-net calls per subscriber and [p 1 - (a+c 0 +c 1 )] is the margin per off-net call. This is because network one incurs the cost of origination, c 0, the cost of transmission, c 1, and the termination fee, a, that is paid to network two.

Third Term of Profit Function  The third term, (1-  )  (a-c 0 )q(p 2 ), 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(p 2 ) is the total number of off-net calls per subscriber, and (a-c 0 ) 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 c 0.

Equilibrium Prices Equilibrium prices are found by differentiating the profit functions with respect to p 1 and p 2 and setting these equations equal to zero. If a stable, symmetric equilibrium exists (p 1 *=p 2 *=p*), p* increases in a. (Thus, when a falls, p* falls) Thus, the access charge is an instrument of tacit collusion. Why? See next slide!

Intuition for Result  1 (p 1 ; p 2 ) =   (p 1 -c)q(p 1 )+  (1-  )[p 1 -  ]q(p 1 )+(1-  )  (a-c 0 )q(p 2 ) But second term can be written:  (1-  )[p 1 -(a+c 0 +c 1 )+(c 0 -c 0 )]q(p 1 )=  (1-  )[p 1 -c] q(p 1 )-  (1-  )[a-c 0 ]q(p 1 ) Thus,  1 (p 1 ; p 2 ) =  (p 1 -c)q(p 1 ) + (1-  )  (a-c 0 )[q(p 2 )-q(p 1 )]  1 (p 1 ; p 2 ) = Retail profit + access ‘revenue/deficit’ term Note: If p 1 > p 2, firm 1 has positive revenue from access. And when a is well above a-c 0, this provides a strong incentive not to lower prices