Bertrand Complements

1. Bertrand Complements Analysis.

2. What are complements? • Two firms each choose a price. • Total price was the sum of the two prices. • Demand was set by the total price. • What on earth fits this story? • Computer and screen. • Computer and operating system. • Shoes and shoelaces. • Plane ticket and airport use.

3. Krugman, NY times • Who is Krugman? • Krugman has lately been known for his anti-Bush columns. • Would he be, in favor, of breaking up a monopolist such as Microsoft? • In his column “MICROSOFT: WHAT NEXT?” written in April 2000. He says the following.

4. What next? • Baron Wilhelm von Gates was the lord of two castles along the Rhine. • From these castles he was able to demand money from all the travellers who passed by. • This made him wealthy, but also much disliked. Eventually the Holy Roman Emperor split up the Gates domain and give one to the Baron’s nephew. • But the results of this breakup were not quite what the emperor's legal department had promised.

5. Price Competition with complements. • Take the demand=15-p, and mc=3 of the monopolist in the experiment. • The optimal price for him to charge is 9. • Let us say that instead of a monopolist there are two separate companies. • For instance, one selling Windows and the other Office. • The marginal cost of either is now 1.5. Why? • The demand is now 15-(p1+p2). Why?

6. What is the equilibrium? • Firm 1 chooses p1 to max (p1-1.5)(15-p1-p2) • Firm 2 chooses p2 to max (p2-1.5)(15-p1-p2) • p1=(13.5-p2)/2+1.5 • p2=(13.5-p1)/2+1.5 • Solving yields p1=p2=5.5.

7. Who wins? • Do the shareholders gain? • Profit with the monopolist was 36. • Profit with either firm is (p1-1.5)(15-p1-p2)=(5.5-1.5)(15-5.5-5.5)=4*4=16 • Combined profit is 32. • Do the users gain? • Well the price WAS 9. Now it is 11 for both!!

8. Returning to Krugman • Travellers complained that things had gotten even worse. • They faced two different robber barons, but were paying more for each trip. • Moreover, the combined income of the baron and his nephew was less than the baron alone before. • But this diminished revenue was the result not of lower tolls but of reduced business. • Before the breakup, von Gates had an incentive to exercise restraint in his extortion: better to keep the tolls low enough that river commerce was not impeded. • Any restraint on his part would simply give his nephew an opportunity to raise his own demands -- and his nephew made the same calculation. • So their combined tolls became too high even for their own good. • The ill-considered imperial response only made things worse, punishing not just the baron but everyone else.

9. Someone paid attention to Krugman for once. • Sept. 2001. The US Department of Justice has announced that it will no longer push to have software giant Microsoft broken up.

10. Homework • There is a very Beersheva to Haifa train line. Travellers either go between • Haifa and Tel Aviv with demand 12-p • Tel Aviv and Beersheva 12-p • Haifa and Beersheva. 18-p • Say it is all owned by one profit maximizing monopolist with marginal cost of zero. For simplicity assume that the monopolist must set the price of the Haifa-Beersheva route equal to the sum of the other two. What would he charge for all three routes? • Now say the government thinks it needs to add competition to the rail industry. It divides things into two companies. One takes care of the Haifa-Tel Aviv route and the other the Tel Aviv-Beersheva route. The price of the combined trip is the sum of the other two. • What are the new prices? • Who wins and who loses?