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 p1=p2, each firm gets half the consumers.) An equilibrium is a choice of prices p1 and p2 such that –firm 1 wouldn’t want to change his price given p2. –firm 2 wouldn’t want to change her price given p1.

2. 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<p1<p2 he earns D(p1)*(p1-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).

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 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).

6. 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 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 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?