Price Competition

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Price Competition

• Bertrand Model
• Assumptions
• Homogenous good
• both firms C1 C2 0
• Consumers are willing to pay 10.
• The total number of consumers is N.

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Price Competition

• How will consumers respond to a price
  differential?
• Price Competition.
• The Nash equilibrium
• P1 P2 0

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• There are N consumers, and each of them is
  willing to pay 10 for the product.
• If the two firms can cooperative,
• P10,
• Profit1Profit2 10N/2

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• But how can they achieve it?
• Price collusion but it is usually illegal
  difficult to maintain.

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How to change the game?

• How to achieve the collusive outcome more easily?

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1. Upstream Joint Company

• F1 F2 form a joint company U, providing a key
  input to both firms.
• Without the key input, F1 F2 cannot produce.
• After F1 F2 buy the key inputs from the joint
  company, they continue to engage in the price
  competition.

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• When the joint firm sells the key input at X,
  their unit production costs become X,
  respectively.
• The price competition brings the final price X.
  Each firm does not make any profit from the final
  sales.

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• However, the joint company makes Xn profits by
  selling the key input to the two firms.
• F1 F2 have ½ shares of the joint firm.
• Thus, the final profit by each firm is ½ Xn.

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• What is the optimal X? Thats is 10. The profit
  level for the joint firm is 10n.
• The two firms split the profit equally, and each
  firms profits 10n/2.

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2. Cross Licensing

• Firms 1 and 2 have similar technologies.
• They make licensing contracts each other.
• Licensing fee is r.
• Production cost is increased by r.

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• A cross-license is simply an agreement between
  two companies that grants each the right to
  practice the others patents.
• Rather than blocking each other and going to
  court or ceasing production, the two enter into a
  cross-license.

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• The patent system, while surely a spur to
  innovation overall, is in danger of imposing an
  unnecessary drag on innovation by enabling
  multiple rights owners to tax new products,
  processes and even business methods.
• The vast number of patents currently being issued
  creates a very real danger that a single product
  or service will infringe on many patents.
• The essence of science is cumulative
  investigation combined with hypothesis testing.
  The notion of cumulative innovation, each
  discovery building on many previous findings, is
  central to the scientific method.

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Government Concerns

• Anti competitive effects
• Pro competitive effects
• Double mark-up problem
• If the two technologies are complementary with
  each other, there is a double-mark up problem.

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Connection Fee

• 1) ATT and competitors
• In the past, ATT declined a connection between
  ATT and other local firms. However, by law, it
  must allow the connection.

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Connection Fee

• 2) Cellular Phone and Fixed Line
• When someone makes a call from a cellular phone
  to a fixed line, he pays service fees to the
  cellular service provider. However, as the call
  is connected to the fixed line phone, the
  cellular service provider must pay some amount of
  fees to the fixed line company.

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Connection Fee

• 3) Long Distance Call or International Call
• When we make a phone call to New York, we pay
  service fees to HK phone companies. However, as
  the phone call is connected to New York, using
  the phone networks of New York, HK phone
  companies need to pay some amount of fees to US
  companies.

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Connection Fee

• Questions
• What is the strategy use of connection fees?
• Under deregulation, can we allow telephone firms
  to choose the fees?

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Telecommunication

• Two telephone service sectors A and B
• The cost of providing each service is c.
• There are multiple firms in each sector.
• Suppose that ? consumers are in sector A, and
  (1-?) are in sector B.

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• We assume a balanced calling pattern.
• That is, the traffic inside sector A is ??.
• The out-going traffic from sector A to sector B
  is ?(1- ?).
• The out-going traffic from sector B to sector A
  is (1- ?)?.

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Telecommunication

• The connection fee is denoted by a.
• The cost of serving each customer in sector A
  ?c(1-?)(ca) c(1-?)a
• Note that the cost increases with a.

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• When several firms compete each other to get
  customers in each sector, the price will go down
  to the cost, c(1-?)a.
• Profits in sector A
• ?p- c(1-?)a ?(1-?)a ?(1-?)a.
• Profit comes from only the access fee sector, not
  from your own customers.

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Telecommunication

• From your own customers, the net profit is zero,
  because the price is the same as the cost.
• However, there is a transfer from firms in the
  other sector. Actually, you make money from
  customers on the other Telephone Company.