Lecture 6: Strategic commitment

1

• Lecture 6 Strategic commitment
• applications to entry and exit (II)
• Entry, Capacity and Price Competition Gelman
  Salop, 1983, Bell Journal of Economics, 14
  315-325. Simplified version in section 8.4.4,
  Shy, 198-200.
• Paper examines the role of precommitment in
  strategic interaction between a dominant
  incumbent firm and an entrant
• A small competitor partially offsets its demand
  disadvanatge by engaging in capacity limitation
  and discount pricing.
• Strategy credibly reduces the threat posed to the
  dominant incumbent firm and makes retaliation
  more costly
• This is an example of Judo economics in which a
  small firm uses its rivals large size to its own
  advantage

2

• Model in General
• Homogeneous Products
• Incumbent is at least as efficient as entrant,
  i.e., c1? c2.
• Two-stage game
• Stage 1 Entrant chooses capacity (k2) price
  (p2).
• Stage 2 Incumbent chooses price (p1).
• If incumbent matches price, it takes the whole
  market (and it has the capacity to serve the
  whole market.)
• Without capacity or if k2?, incumbent takes the
  whole market.

3

• Incumbent has two strategies (I) Deter entry
  (II) accommodate entry.
• Deterrence profits ?D (p1p2) (p2-c1)D(p2)
• Accommodation Profits The incumbent chooses p1 gt
  p2, and allows the entrant to sell all of its
  output. The incumbent is then a monopolist on
  the residual demand curve. (They assume
  reservation-price rationing so that the entrant
  gets the k2 consumers with the highest
  valuation.)
• ?A (p1-c1)D(p1)-k2 (where p1 is the
  monopoly price)

k2
4

• Hence the entrant chooses so that ?D ? ?A.
• As p2 increases, ?D increases. As k2 increases,
  ?A decreases.
• Thus there is a tradeoff between p2 and k2. If
  the entrant chooses to large a capacity or too
  high a price, the incument will respond by
  deterring entry.
• Hence the entrant underinvests in order not to
  provoke a response from the incumbent. This is
  an example of a puppy-dog strategy.

5

• Numerical Example
• Let P100-Q, and let c1c20.
• Hence D(p1)-k2 100- p1-k2
• Hence to find ?A, maximize p1 (100-p1-k2)
• FOC imply that p1 (100- k2)/2.
• Hence ?A (100- k2)2/4.
• ?D p2D(p2) p2(100- p2).
• ?A ?D implies that (100- k2)2/4 p2(100- p2).

6

• Solving yields p2 100-(200- k2)k2.5 /2.
• Clearly, there is an inverse relationship between
  p2 and k2 for the entrant.
• As increases, profits increase, but must fall to
  insure that the constraint (?A ?D) holds.
  Otherwise the incumbent will deter entry.
• In the first stage, entrant maximizes ?E p2k2,
  where p2 100-(200- k2)k2.5 /2. This needs
  to be solved numerically.

7

• Finally we need to check that p2ltp1. Otherwise,
  the entrant will not make any sales.
• p2 100-(200- k2)k2.5 /2 lt p1 (100- k2)/2
  implies
• (200- k2)k2.5 gt k2, which implies
• (200- k2)k2 gt k22, which implies
• 200k2 gt 2k22, which implies
• 100 gt k2.
• This is true because demand function is P100-Q.