Bertrand 1883 price competition Both firms choose prices

Bertrand (1883) price competition. • Both firms choose prices simultaneously and have constant marginal cost c. • Firm one chooses p 1. Firm two chooses p 2. • Consumers buy from the lowest price firm. (If p 1=p 2, each firm gets half the consumers. ) • An equilibrium is a choice of prices p 1 and p 2 such that – firm 1 wouldn’t want to change his price given p 2. – firm 2 wouldn’t want to change her price given p 1.

Bertrand Equilibrium • Take firm 1’s decision if p 2 is strictly bigger than c: – If he sets p 1>p 2, then he earns 0. – If he sets p 1=p 2, then he earns 1/2*D(p 2)*(p 2 -c). – If he sets p 1 such that c<p 1<p 2 he earns D(p 1)*(p 1 -c). • For a large enough p 1 that is still less than p 2, we have: – D(p 1)*(p 1 -c)>1/2*D(p 2)*(p 2 -c). • Each has incentive to slightly undercut the other. • Equilibrium is that both firms charge p 1=p 2=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¢ • March 1994 25¢ (in Staten Island) 40¢ • July 1994 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)=3 q. Price Maxp (p-3)*(15 -p) What is the choice of p. This is the monopoly price and quantity! Maxq 1, q 2 (15 -q 1 -q 2)*(q 1+q 2)-3(q 1+q 2).

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 pricematching 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).

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?