2. Comparing Market Structures with Differentiated Goods [50 total] The market for widgets is dominated by two firms which produce differentiated versions of the widget. Patents prevent any other firms from entering the market. The firms face demand curves as follows: 91 = 360 - P1 + 0.5p2 92 = 360 - P2 + 0.5p1 Equivalently, the firms' inverse demand curves are given by: P1 = 720 - 4/3 91 - 2/3 92 P2 = 720 -/3 92 -2/3 91 The firms have identical, constant marginal costs of E60 per unit: MC1 = MC2 = 60 a) Bertrand Duopoly: Compute each firm's price at the Nash equilibrium of the simultaneous Bertrand game. [7] b) Cournot Duopoly: Compute each firm's output at the Nash equilibrium of the simultaneous Cournot game. [7] c) Price versus quantity competition: Explain the intuition behind the conclusion that price competition is fiercer than quantity competition. Refer to the concepts of strategic complements and strategic substitutes. [10] d) Price competition with sequential choice: Compute each firm's price at the subgame perfect equilibrium of the sequential game when firm I is the leader, and the firms compete on price. [8] e) Stackelberg Duopoly: Compute each firm's output at the subgame perfect equilibrium of the sequential game when firm I is the leader, and the firms compete on quantity. [8] f) Price versus quantity competition with sequential choice: Why is there generally a first-mover advantage under sequential quantity competition and a second-mover advantage under sequential price competition? [or]