Bertrand (1883) price competition.

1
Bertrand (1883) price competition.

• Both firms choose prices simultaneously and have
  constant marginal cost c.
• Firm one chooses p1. Firm two chooses p2.
• Consumers buy from the lowest price firm. (If
  p1p2, each firm gets half the consumers.)
• An equilibrium is a choice of prices p1 and p2
  such that
• firm 1 wouldnt want to change his price given
  p2.
• firm 2 wouldnt want to change her price given p1.

2
Bertrand Equilibrium

• Take firm 1s decision if p2 is strictly bigger
  than c
• If he sets p1gtp2, then he earns 0.
• If he sets p1p2, then he earns 1/2D(p2)(p2-c).
• If he sets p1 such that cltp1ltp2 he earns
  D(p1)(p1-c).
• For a large enough p1 that is still less than p2,
  we have
• D(p1)(p1-c)gt1/2D(p2)(p2-c).
• Each has incentive to slightly undercut the
  other.
• Equilibrium is that both firms charge p1p2c.
• Not so famous Kaplan Wettstein (2000) paper
  shows that there may be other equilibria with
  positive profits if there arent restrictions on
  D(p).

3
Cooperation in Bertrand Comp.

• A Case The New York Post v. the New York Daily
  News
• January 1994 40 40
• February 1994 50 40
• March 1994 25 (in Staten Island) 40
• July 1994 50 50

4
What happened?

• Until Feb 1994 both papers were sold at 40.
• Then the Post raised its price to 50 but the
  News held to 40 (since it was used to being the
  first mover).
• So in March the Post dropped its Staten Island
  price to 25 but kept its price elsewhere at 50,
• until News raised its price to 50 in July,
  having lost market share in Staten Island to the
  Post. No longer leader.
• So both were now priced at 50 everywhere in NYC.

5
Collusion

• If firms get together to set prices or limit
  quantities what would they choose. As in your
  experiment.
• D(p)15-p and c(q)3q.
• Price Maxp (p-3)(15-p)
• What is the choice of p.
• This is the monopoly price and quantity!
• Maxq1,q2 (15-q1-q2)(q1q2)-3(q1q2).

6
Anti-competitive practices.

• In the 80s, Crazy Eddie said that he will beat
  any price since he is insane.
• Today, many companies have price-beating and
  price-matching policies.
• A price-matching policy (just saw it in an add
  for Nationwide) is simply if you (a customer) can
  find a price lower than ours, we will match it. A
  price beating policy is that we will beat any
  price that you can find. (It is NOT explicitly
  setting a price lower or equal to your
  competitors.)
• They seem very much in favor of competition
  consumers are able to get the lower price.
• In fact, they are not. By having such a policy a
  stores avoid loosing customers and thus are able
  to charge a high initial price (yet another
  paper by this Kaplan guy).

7
Price-matching

• Marginal cost is 3 and demand is 15-p.
• There are two firms A and B. Customers buy from
  the lowest price firm. Assume if both firms
  charge the same price customers go to the closest
  firm.
• What are profits if both charge 9?
• Without price matching policies, what happens if
  firm A charges a price of 8?
• Now if B has a price matching policy, then what
  will Bs net price be to customers?
• B has a price-matching policy. If B charges a
  price of 9, what is firm As best choice of a
  price.
• If both firms have price of 9, does either have
  an incentive to undercut the other?