ECON 30524 - Bocconi University. Strategic Decision Making and Markets BESS - 30458. MOCK GENERAL EXAM: Second Part. Q&A

ECON 30524 - Bocconi University. Strategic Decision Making and Markets BESS - 30458. GENERAL EXAM: Second Part. Q&A Exercise 1 Consider a market populated by 100 consumers. Each of them is willing to buy one unit of product X if the price does not exceed 50. There exist 2 firms in the market, producing a perfectly homogeneous good and facing no capacity constraint. Firm H has a constant marginal cost cH = 10 and firm L has a constant marginal cost cL = 0. The two firms set prices simultaneously for an infinite number of periods. Imagine that at period t = 1 each firm sets the monopoly price. In each of the following periods (t ≥ 2) firm i (with i = H; L) sets the monopoly price if it observes that in the previous period both competitors chose that price; in this case the two firms share evenly the market demand. If in the previous period at least one competitor chose a price different from the monopoly price, firm i sets forever the price p∗ i that it would set in the Nash Equilibrium of the one-shot game. Exercise 2 Consider a market in which (inverse) demand is given by p = 30 − Q. Three firms operate in the market and compete `a la Cournot. They have the same marginal cost equal to 10 and the same fixed cost F = 5. The three firms sell homogeneous products. (i) Compute the Nash equilibrium of the one-shot game in which firms choose quantities simultaneously. Compute the equilibrium output of each firm, the equilibrium price and the equilibrium profits of each firm. Each firm solves the following maximization problem maxqi(30−q1−q2−q3−10)qi taking strategies of co-players as given. From the FOC and symmetry, one can derive the equilibrium output of each firm q∗b = 30−4 10 = 6: Equilibrium price is p∗b = 15; and equilibrium profit of each firm is π∗b = (15 − 10) ∗ 5 − 5 = 20: Assume that firms 1 and 2 decide to merge. The merger does not produce any efficiency gain. (ii) Compute the post-merger Nash equilibrium of the one-shot game. Compute the equilibrium output of each firm, the equilibrium price and the equilibrium profits of each firm. If firms 1 and 2 merge and they do not produce efficiency gains, we have two firms instead of three that compete under Cournot competition, the firm resulting from the merger, whose output is denoted as qM and the outsider, whose output is denoted as q3. Each firm solves the following problem: maxqi(30 − qM − q3 − 10)qi, so that equilibrium output is q∗post = 30−3 10 = 20 3 , the equilibrium price is p∗post = 50 3 and the equilibrium profits of each firm are πM∗post = 400 9 − 10 (because in the absence of efficiency gains the merger entity pays twice the fixed cost F ) and