Presentation on theme: "Cournot versus Stackelberg n Cournot duopoly (simultaneous quantity competition) n Stackelberg duopoly (sequential quantity competition) x2x2 x1x1 x1x2x1x2."— Presentation transcript:
Cournot versus Stackelberg n Cournot duopoly (simultaneous quantity competition) n Stackelberg duopoly (sequential quantity competition) x2x2 x1x1 x1x2x1x2
Homogeneous duopoly (linear case) n Two firms (i=1,2) produce a homogenous goods. n Outputs: x 1 and x 2, X= x 1 +x 2 n Marginal costs: MC 1 and MC 2 n Inverse demand function: n Profit function of firm 1:
Cournot-Nash equilibrium n Profit functions: n Reaction functions: n Nash equilibrium:
Computing the Cournot equilibrium (accommodation) n Profit function of firm 1 n Reaction function of firm 1 n Nash equilibrium
Depicting the Cournot equilibrium x 1 Cournot-Nash equilibrium C x 2
Exercise (Cournot) n Find the equilibrium in a Cournot competition. Suppose that the demand function is given by p(X) = 24 - X and the costs per unit by c 1 = 3, c 2 = 2.
Common interests n c 1, c 2 obtaining government subsidies and negotiating with labor unions n a , b advertising by the chemistry industrie
Exercise (taxes in a duopoly) Two firms in a duopoly offer petrol. The demand function is given by p(X)=5-0.5X. Unit costs are c 1 =0.2 and c 2 =0.5. a) Find the Cournot equilibrium and calculate the price. b) Now suppose that the government imposes a quantity tax t (eco tax). Who ends up paying it?
Two approaches to cost leadership n Direct approach (reduction of own marginal costs) - change of ratio between fixed and variable costs -investments in research and development (R&D) n Indirect approach (“raising rivals’ costs”) -sabotage -minimum wages, enviromental legislation
Direct approach, analytically n n Direct approach (reduction of your own marginal costs): 0 =0 directstrategic effecteffect
Direct approach, graphically x 2 x 1 equilibria: increase in production of firm 1 marginal cost reduction of firm 1
Indirect approach, analytically n n Indirect approach (raising rival’s cost): =0 <0 <0 =0 directstrategic effecteffect
Indirect approach, graphically increase of marginal costs of firm 2 x 2 x 1 equilibria: increase in production of firm 1
Reaction curve in the linear case x 1 x 2 Note: alone leads to a price of.
Blockaded entry, graphically x 2 x 1 C M firm 1 as a monopolist
Blockaded entry n Entry is blockaded for each firm: n Entry is blockaded for firm 2:
Blockaded entry (overview) c 2 c 1 duopoly no supply firm 1 as a monopolist firm 2 as a monopolist
Exercise (Strategic trade policy) n Two firms, one domestic (d), the other foreign (f), engage in Cournot competition on a market in a third country. Assume n The domestic government subsidizes its firm’s exports using a unit subsidy s. n Which subsidy s maximizes domestic welfare
The Herfindahl index n The Herfindahl index measures the concentration in an industry. n Exercise: Which market is the most concentrated: l 2 firms with equal market shares, l 3 firms with shares of 0.8, 0.1 and 0.1 or l 3 firms with shares of 0.6, 0.2 and 0.2 ?
n firms in Cournot competition n Total industry output: n Firm i’s profit function: n Firm i’s marginal revenue :
Lerner index of monopoly power n First order condition: n Lerner index for one firm: n Lerner index for the industry:
Stackelberg equilibrium n Profit function n Follower’s reaction function n Leader’s optimal quantity n Nash equilibrium:
Finding the profit-maximizing point on the follower's reaction curve Accommodation x 1 x 2 Blockade or deterrence
Computing the Stackelberg equilibrium (accommodation) n Reaction function of firm 2: n Profit function of firm 1: n Nash equilibrium with and
Depicting the Stackelberg outcome (both firms produce) x 2 x 1 quantities in a Stackelberg equilibrium C S
Exercise (Equilibria) n Which is an equilibrium in the Stackelberg model? n Are there any additional Nash equilibria ?
Cournot versus Stackelberg II n Profit function of firm 1 n First order condition for firm 1 direct effectfollower effect Cournot: 0
Exercise (Stackelberg) n Find the equilibrium in a Stackelberg competition. Suppose that the demand function is given by p(X) = 24 - X and the costs per unit by c 1 = 3, c 2 = 2. n Possible or not? : ?
Blockaded entry p x 1 blockaded entry for firm 2
Reaction functions in the case of blockaded entry
Deterring firm 2’s entry p x 1
Reaction functions in the case of deterred entry
Blockaded and deterred entry n Blockaded entry (firm 2): n Deterred entry (firm 2):
Blockade and deterrence firm 1 as a monopolist c 2 c 1 duopoly no supply blockade firm 2 as a monopolist deterrence
Exercise I (entry and deterrence) 1) Suppose a monopolist faces a demand of the form p(X)=10-0.5X. The firm’s unit costs are 2. a) Find the profit-maximizing quantity and price. Is entry blockaded for a potential entrant with unit costs of 8? b) Assume now that the potential entrant’s unit costs decrease to 4. Is entry still blockaded? c) Find the limit output level and price. Should the incumbent deter?
Exercise II (entry and deterrence) 2) In addition, the firms are supposed to face quasi-fixed costs of 1. Hence, the cost functions are given by a) What is the monopolist’s profit-maximizing quantity and price? b) Is entry blockaded for the potential entrant? c) Find the incumbent’s profit-maximizing output level. (Hint: Compare the profits.)
The quantity cartel n The firms seek to maximize joint profits n Optimization conditions
Cartel quantities x 2 x 1 C S CA quantities in a symmetric cartel
The cartel agreement n The optimization condition is given by n Each firm will be tempted to increase its profits by unilaterally expanding its output. n In order to maintain a cartel, the firms need a way to detect and punish cheating, otherwise the temptation to cheat may break the cartel.
Summary n The cartel is unstable if the firms meet only once. Thus, the cartel agreement is not an equilibrium. n Supposing that the number of repetitions is unknown, the cartel agreement can be an equilibrium outcome.
Exercise (cartel quantities) n Consider a cartel in which each firm has identical and constant marginal costs. If the cartel maximizes total industry profits, what does this imply about the division of output between the firms? n Solution: Nothing. Since all firms have the same marginal cost, it doesn’t matter which of them produces the output. Hal R. Varian, Intermediate Microeconomics
The outcomes of our models quantity price a monopoly (M) and cartel (CA) Cournot (C) Stackelberg (S) perfect competition (PC) p M p C p S p PC = c X M X C X S X PC
Cournot – Executive summary I n A duopoly can only be expected if entry is blockaded for other firms. Otherwise industry profits would attract potential competitors. An entry can be blockaded by cost structures or by certain laws or conditions (legal/administrative barriers). n All competing firms have the incentive to lower costs in common. Firms‘ profit and the industry profit increase. Thus, activities in associations which aim at improving cost structures are worthwhile (collective agreements, government technology promotion,...)
Cournot – Executive summary II n All competing firms have the incentive to increase market demand by appropriate marketing activities. Firms‘ profit and the industry profit increase. Thus, activities in associations which aim at increasing market demand are worthwhile (cooperative advertising campaigns,...) n The attempt to become a cost leader before a simultaneous competition is worthwhile. The firm with the lower marginal cost or unit cost respectively faces higher turnovers and profits. Cost leadership even leads to monopolization.
Cournot – Executive summary III n There are two approaches to cost leadership. The direct approach is to lower your own marginal cost. The indirect approach is known as “raising rivals‘ costs“.
Stackelberg – Executive Summary I n Time leadership is worthwhile: in a Stackelberg equilibrium the leader realizes a profit that is higher than the follower‘s and his own in a Cournot equilibrium. Even with a slight cost disadvantage, the leader‘s profit might be higher than the follower‘s. n If a firm is both Stackelberg leader and cost leader, it can consider deterring the follower‘s entry by offering the limit quantity as a strategic entry barrier.
Stackelberg – Executive Summary II n Entry costs make the follower‘s deterrence easier. The amount of its costs at which entry is deterred increases with the entry costs. n Since the Stackelberg leader offers a higher quantity than the follower, he might enlarge his cost advantage by learning curve effects.
Cartel – Executive Summary I n If all firms keep the cartel agreement, then they can increase their profits compared to the Cournot competition. n Nevertheless cartels are unstable. Cheating even makes higher profits possible. When all firms break up the cartel agreement, their profits decrease. Moreover, they might face a worse position than in the Cournot competition.
Cartel – Executive Summary II n Cartels will not continue to exist when potential competitors‘ entries, who are attracted by the cartel profit, are not blockaded. Therefore, the firms have to be able and willing to restrict or deter entry. If there are administrative barriers, investments in maintenance of these barriers are necessary. If the barriers are more structural, then the firms have to try to keep their cost and technology advantage (cooperation in R&D).