\f1. In the 'v'ertical Product Differentiation model studied in lectures. let the qualities of the products of firms A and B be [IA 2 Lie 2 I initially. What classic game does the resu tting competition in prices resemble. and what are the associated equilibrium profits? Suppose an inventor offers Firm A exclusive rights to a production technology that would increase its quality to out = F without affecting the marginal production cost (while o3 : 1 still}. in return for a lumpsum fee F. Firm A believes that, if it rejects the offer, the inventor will reach an agreement with Firm B {so that of; = 7". [3,4 = 1}. before the firms simultaneously name prices. What is the highest value of F that Firm A might be willing to pay {justify your answer)? Illustrate graphically the subgameperfect Nash equilibrium that would ensue if F = 1. [25 marks] 2. Consider the Hotelling duopoly model with combative advertising studied in lec tures. with product characteristics .11 = {1,12 = 1, and disutilityr cost t = 1. Hence. the total cost incurred by a consumer with tastes I E [(1.1] when buying from seller 15 {1,2} is p,- + |x xi| of. The cost of advertising effort a.- is mg, where c 2} is the cost of advertising parameter. Suppose Firm One is unable to do any advertising (Le. :11 = [1}. but Firm Two has the option to launch an advertising campaign that will require 1 unit of advertising effort {oz 2 1}. before the two firms simultaneously name prices. Alternatively. Firm Two can choose not to advertise (a; = [1}. What is the highest value of n: such that the optimal decision of Firm Two is to ad vertise? Justify your answer. [25 marks] 3. Fiecall the Entry Deterrence model with quantity competition and capacity pre commitment. In particular. suppose the demand price function is P {Q} = 1 Q, the constant unit cost of capacity {output} is 112 and the cost of entry is such that the Entrant would prefer to stay out when the lncumbent's output quantity 11 r c} 1.13