Digital Markets

Assignment 9

This is the first installment of a “final assignment.” I will add questions.


1.      Question 1 sets you up to do some legal reasoning in question 2. This is based on the Ahlborn/Evans and Larouche papers.


  1. What are the two complaints against Microsoft?
  2. Referring to Magill, Bronner and IMS, in European law, do firms have a right to refuse supply?
  3. Review the four elements of the IMS test for refusal to supply. Do all need to be satisfied, or just one of them?
  4. In European law, is tying a per se offense?
  5. Having read these papers, what do you think “objective justification” means?
  6. In the U.S., there is almost always a “rule of reason” defense to an antitrust complaint. The defense is that the disputed conduct leads to cost reductions or some other efficient outcome, and this outweighs any harm to competition. Referring to pages 615-616 of Larouche, what does he think about the efficiency defense in the European law?


2.      This is a speculative question that will encourage you to contemplate what refusal-to-supply means.


  1.  Review the TradeComet complaint. What is the legal basis cited in the complaint? (When the legal argument is fleshed out, it will probably have much more than this.)
  2. On the basis of what you learned in Microsoft, would a refusal-to-deal argument have a chance of succeeding in Europe? Try to make an argument, using the IMS test, or other legal arguments you learned in Microsoft.
  3. Come to a conclusion about whether Google’s (alleged) treatment of TradeComet reduces competition or welfare. As a judge trained in economics, and assuming that the stated facts hold up, would you hold for TradeComet on economic grounds?


3.      Consider a two player game similar to the one discussed in class (Avery et al 1999): In this question there is no Center. Instead there is a profit maximizing seller. The payoffs in this game are


player A

player B












a)      What is the equilibrium under the profit maximizing price?

b)      What is the profit maximizing price? (Consider only pure strict equilibrium).

c)      What is the social optimum (The sum of buyers’ payoffs)? Is it attained in equilibrium?

4.    Continuing the setup of problem 3, suppose the seller may price discriminate. She can set a first period price p1 and a second period price p2.

a)      Show that CC and WW cannot be more profitable under price discrimination. (Hint: use the participation constraints). 

b)      What are the profit maximizing prices? What is the equilibrium?

c)      What is the social optimum? What can you say about price discrimination and efficiency in this context?

5.  This is a modeling exercise to help you think about the economic consequences of tying. However, tying is multifaceted, so you would not want to draw broad conclusions from a simple model such as this. The model is very simple to make it tractable. After you solve it, you might want to change the assumptions on demand to make it richer.


      Assume there is an operating system (e.g., Windows) and two substitute applications (e.g., WMP and Real Player). To use either application, the user must have the operating system. The proprietor of the operating system is also the proprietor of WMP, and the two products might be tied.


The only reason consumers would buy the operating system is to run an application – it has no independent value. All consumers have willingness to pay 1 for firm 1’s application, but the willingness to pay of a random consumer for application 2 is a random variable θ. Assume that θ is uniformly distribution on [0,2] and there is a total mass of consumers equal to 2. Thus half the consumers have a higher willingness to pay for application 2 than for application 1.


a) Suppose that everyone owns the OS, and the firms compete on price to sell their applications. There is no tying. A consumer will choose application 1 if 1-p1>0 and 1-p1>θ-p2, and will choose application 2 if θ-p2>0 and 1-p1<θ-p2. Verify that the numbers of buyers are as follows for the two applications:




if p1>1

D1(p1,p2) =




max { (1-p1+p2), 2 }





if p2>2

D2(p1,p2) =




max { (1+p1-p2), 2 }



Suppose the two firms compete on price. The profit functions are p1D1(p1,p2) and p2D2(p1,p2).

What are the Nash-equilibrium prices p1,p2? (Nash equilibrium is where neither firm wants to change its price, conditional on the other firms’ price.)


b) Now suppose that the OS and application 1 are tied, and sold at a common price p1. To consume application 2, a user must have the OS, so the consumer must buy the tied product as well as application 2. Suppose the tied product is sold at price p1=1. Show that the demand for application 2 is



if p2>1

D2 (p1,p2) =







What is the most profitable price for application 2?

Does tying increase firm 1’s profit?

Does tying increase the total number of buyers?

Does tying increase/decrease welfare?