Consider a situation where network effects are very strong, so that Assumption 2.4 on page 28 is violated. More precisely, let there be 60 A-oriented consumers and 60 B-oriented consumers, where UA def =  2qA − pA buy A 2qB − pB − 100 buy B, UB def =  2qA − pA − 100 buy A 2qB − pB buy B. Answer the following questions.

(a) Prove that there does not exist an UPE where 60 consumers buy brand A and 60 consumers buy brand B.

(b) Find the price charged by each firm in an equilibrium where all the 120 consumers buy brand A only.