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 p1=p2, each firm gets half the consumers.) • An

equilibrium

such that is a choice of prices p1 and p2 – firm 1 wouldn’t want to change his price given p2. – firm 2 wouldn’t want to change her price given p1.

Bertrand Equilibrium

• Take firm 1’s decision if p2 is strictly bigger than c: – If he sets p1>p2, then he earns 0.

– If he sets p1=p2, then he earns 1/2*D(p2)*(p2-c).

– If he sets p1 such that c

• For a large enough p1 that is still less than p2, we have: – D(p1)*(p1-c)>1/2*D(p2)*(p2-c).

• Each has incentive to slightly undercut the other.

• Equilibrium is that both firms charge p1=p2=c.

• Not so famous Kaplan & Wettstein (2000) paper shows that there may be other equilibria with positive profits if there aren’t restrictions on D(p).

Cooperation in Bertrand Comp.

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

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.

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 Max p (p-3)*(15-p) • What is the choice of p.

• This is the monopoly price and quantity! • Max q1,q2 (15-q1-q2)*(q1+q2)-3(q1+q2).

Anti-competitive practices.

• In the 80’s, Crazy Eddie said that he will beat any price since he is insane. • Today, many companies have

price-beating matching

policies.

and

price-

• 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).

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 B’s net price be to customers?

• B has a price-matching policy. If B charges a price of 9, what is firm A’s best choice of a price. • If both firms have price of 9, does either have an incentive to undercut the other?