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Bertrand Complements. Analysis. 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.
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Bertrand Complements Analysis.
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.
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.
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.
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?
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.
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!!
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.
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.
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?
