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Chapter 5 Imperfect competition. Outline. An introduction to the theory of games Some oligopoly models Monopolistic competition. Collusion between firms.
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Outline. • An introduction to the theory of games • Some oligopoly models • Monopolistic competition
Collusion between firms • Collusion is difficult to achieve on a competitive market. Might seem less difficult to achieve among oligopolists, that is in industries served by only a small number of firms. • However, collusion usually appears extremely difficult to sustain. • Because it is the interest of each firm individually is usually not in the interest of all firms taken as a whole. • Similar to the prisoner’s dilemma
Prisoner’s dilemma • 2 prisoners • If one of the 2 confesses, the confessor will be freed while the other one will spend 20 years in jail. • If both confess, they both get an intermediate sentence (say 5 years). • Payoff matrix: • Dominant strategy = confess
The sustainability of collusion • Consider 2 firms that are the sole providers of mineral water on a given market. • Market demand curve is given by: P = 20 – Q • MC = 0 • Collusion: each firm will offer half of the monopoly output and sell it at the monopoly price. • Monopoly quantity: 20 – 2Q = 0 Q = 10 and P = 10. • If both firms abide by this agreement: • Each will sell 5 units of output • Profit: P = 50 – 0 = 50.
The sustainability of collusion (ctd 1) • Each firm actually has two options: it can abide by the agreement or defect.Assume that defection means cutting the price from 10 to 9. • If one firm abides by the agreement and the other one defects. What happens? • The defector will capture the entire market because of its lower price. He will sell Q = 20 – 9 = 11 and make a profit of 99. • The other firm sells nothing and makes zero profit. • If both firms defect, they will end up splitting the 11 units of output sold at a price of 9 and will make an economic profit of 49.5
The sustainability of collusion (ctd 2) • Payoff matrix: • Dominant strategy = defect • As this example is set up firms do not do much worse when they defect that when they cooperate. • However, if firms find it in their interest to defect once, they are likely to defect again.
Advertising • Oligopolists compete on prices but also by advertising. When a firm advertises its product, its demand increases for 2 reasons. • First people who never used that type of product before learn about it, which leads some of them to buy it. • Second other people who already consumed a different brand of the product will switch brand because of advertising. • US cigarette industry: brand-switching effect of advertisement is very strong.
Advertising (ctd) • Payoff matrix: • Dominant strategy = advertise
Nash equilibrium • In many games, not every player has a dominant strategy. • The dominant strategy for Firm 1 is to advertise. • But Firm 2 has no dominant strategy • is the Nash equilibrium of the game
Nash equilibrium: definition • A Nash equilibrium is a combination of strategies such that each player's strategy is the best he can choose given the strategy chosen by the other player. • At a Nash equilibrium, neither player has any incentive to deviate from his current strategy. • In a prisoner's dilemma, the equilibrium is a Nash equilibrium. • But a Nash equilibrium does not require both players to have a dominant strategy.
The maximin strategy • In the previous example, we have assumed that Firm 2 believes that Firm 1 will act rationally. • However, Firm 2 may not be sure that Firm 1 will act rationally. • When Firm 2 has no dominant strategy and is not sure of what Firm 1 will do, what should it do? • If firm 2 is extremely cautious, it may choose the maximin strategy: it will choose the strategy that maximises the lowest possible value of its own payoff. • In this situation, the maximin strategy is not to advertise.
Repeated play in prisoner's dilemma • Strategy to prevent defection: tit-for-tat • How it works: the first time you interact with somebody, you cooperate. In each subsequent interaction you do what the person did in the previous interaction. • Robert Axelrod (The Evolution of Cooperation, 1984): tit-for-tat performs very well against a large number of alternative strategies • Conditions for tit-for-tat to be successful: • There must be a rather stable set of players each of whom can remember what the others have done in previous interactions. • Players must allocate a sufficiently high value to the future.
Tit-for-tat • These conditions are often met in human populations. Many people interact repeatedly and keep track of what others did in the past. Examples • World War I • Business world • Additional condition:there is not a known fixed number of future interactions. • Does tit-for-tat generate widespread collusion? By no means: cartels tend to be highly unstable. • Problem of selective punishment • Risk of entry
Sequential games • In many games, one player moves first and the other one can choose his strategy with full knowledge of the first player's choice • Example: USA versus Soviet Union during much of the Cold War • Given the assumed payoff, USA may threaten to retaliate, but if the payoffs are as displayed above, this is not credible. • In order to be sure that there won't be any risk of nuclear war, the USA should install a "doomsday" machine
Useless investments: Sears Tower • Consider the example of the Sears Tower in Chicago(the highest building). • A company X considers whether to build a higher building. Its concern is that Sears may react by building an even higher building.
Sears Tower: strategic entry deterrence • Before Sears had originally built its tower: option of building a platform at the top on which it could subsequently build an addition that would make the building taller. • Building the platform costs 10 units but reduces the cost of making the building taller by 20 units. • This platform is an example of strategic entry deterrence
Outline. • Some oligopoly models • Monopolistic competition
The Cournot model • The central assumption of the model is that each firm treats the amount produced by the other firm as a fixed quantity that does not depend on its own production decisions. • Suppose the market demand curve for mineral water is given by: and suppose MC = 0 • The demand curve for firm 1's water is:
The Cournot model (ctd2) • Firm 1's demand curve is the portion of the original demand curve that lies to the right of this vertical axis. So, it is sometimes called the residual demand curve. • The rule for firm 1's profit maximisation is: MR = MC = 0. • Marginal revenue has twice the slope as demand so that:
The reaction functions • The optimal output level is given by: • This is firm 1’s reaction function: • Firm 2’s reaction function is given by:
The Nash equilibrium of the Cournot model • The intersect of both reaction functions is the Nash equilibrium of the Cournot model:
How profitable are Cournot duopolists? • Since their combined output is 2a/3b, the market price will be: • At this price, each will have a total revenue equal tothe economic profit given by:
The Bertrand model • Each firm chooses its price on the assumption that its rival's price remains fixed. • Suppose that the market demand and cost conditions are the same as in the Cournot example. Suppose firm 1 charges an initial price • Then firm 2 faces essentially 3 choices: • It can charge more than firm 1 and sell nothing. • It can charge the same as firm 1 in which case both firms will split the market demand at that price. • It can sell at a marginally lower price than firm 1 and capture the entire market. • This last option is always the most profitable.
The Bertrand model (ctd) • As in the Cournot model the situations of the duopolists are completely symmetric in the Bertrand model. • So, the strategy of selling at a marginally lower pricewill be chosen by both firms. • In this case, there is no stable equilibrium: the price-cutting process will go on until the price reaches the marginal cost =0. • In this case, both duopolists will share the market equally.
The Stackelberg model • What would a firm do if knowing that its rival is a naïve Cournot duopolist? • This firm would choose its own output level by taking into account the effect of that choiceupon the output level of its rival. • Returning to the Cournot model, assume that firm 1 knows that firm 2 will treat firm 1's output as given. • Firm 2's reaction function is: • Knowing this, firm 1 can substitute R2(Q1) for Q2 in the equation for the market demand curve.
The Stackelberg model (ctd 1) • The demand curve addressed to firm 1
The Stackelberg model (ctd 2) • Firm 1 = Stackelberg leader Firm 2 = Stackelberg follower
Comparison of outcomes • A monopoly with the same demand and cost curves as the Cournot duopolist would have produced: • The Cournot duopolists • P = a/3 • Q = 2a/3b. • The Bertrand duopolists • P = MC = 0 • Q = a/b, so that each of them produce a/2b. • This is similar to the perfect competition situation. and
Comparison of outcomes (ctd 1) • The Stackelberg model: • P = a/4 • Q = 3a/4b • P1 = a2/8b and P2 = a2/16b In the Stackelberg model, the leader fares better than the follower.
Contestable markets • William Baumol, John Panzer and Robert Willig, Contestable Markets and the Theory of Industry Structure, 1982. • The idea is that monopolies sometimes behave just like perfectly competitive firms. • This will happen when entry and exit are perfectly free. • Costless entry: there areno sunk costs associated with entry and exit • When sunk costs are high, new firms will not enter the market even if the incumbent is making high profits • When sunk costs are almost zero, new competitors will enter the market with the idea that they will pull out if post-entry business proves non profitable.
Contestable markets (ctd) • The contestable market theory • Cost conditions will determine how many firms will end up serving the market. • But there is no clear relationship between the actual number of competitors in a market and the extent to which prices and quantities are similar to what we would see under perfect competition. • Critics: there are substantial sunk costs involved in all activities
Competition under increasing returns to scale • Suppose that there exists a duopoly in an industry where there are increasing returns to scale. • 2 firms started at an early stage of development • Should we expect that one firm will drive the other one out of the market? • 2 solutions • Merge: problem of antitrust laws. • Price war: none of the 2 firms has any interest in doing that. • without a threat of entry, a live-and-let-live strategy is very likely to be adopted
Competition under increasing returns to scale (ctd) • Suppose now that a firm has a monopoly position and that potential entrants face substantial sunk costs. • Potential entrants may be reluctant to enter the industry and face a potentially ruinous price war with the incumbent • Last solution • Buyers may be willing to approach a potential entrant. • Local authorities usually do that
Outline. • Monopolistic competition
Monopolistic competition • Monopolistic competitionoccurs when: • Many firms serve a market with free entry and exit • But in which the product of each firm is not a perfect substitute to the product of the other firms on the market. • The degree of substitutability between products determines how closely the industry resembles perfect competition
The Chamberlin model • Developed in the 1930s by Edward Chamberlin and Joan Robinson. • Assumption: there exists a clearly defined market composed of many firms producing products that are close but imperfect substitutes for one another. • So, each firm faces a downward-sloping demand curve but behaves as if its price and quantity decisions should not affect the behaviour of the other firms in the industry • Firms are perfectly symmetric so if it makes sense for a firm to alter its price in one direction, it will make sense for the other firms to do the same
The individual firm’s demand curves • Each firm faces 2 demand curves
Perfect competition versus Chamberlinian monopolistic competition • Perfect competition generates allocative efficiency whereas monopolistic competition does not. • The Chamberlin model is more realistic than the perfect competition model on, at least, one point. • Perfect competition: the price is equal to the marginal cost firms are indifferent to the opportunity of filling a new order. • Monopolistic competition: the price is higher than the marginal cost firms will be very keen on filling an additional order. • In both market structures, long-run profits are 0.
Criticisms of the Chamberlin model • The model considers a group of products which are different in some unspecified way but that are likely to appeal to any given buyer. • George Stigler: it is impossible to draw operational boundaries between groups of products in this way. • The Chamberlinian industry group quickly expands to contain all possible consumption goods in the economy. • Complicates the perfect competition model without altering its most important predictions. • Does not depart sufficiently from the perfect competition model • Assumption that each firm has an equal chance to attract any of the buyers in an industry: not always true
The spatial interpretation of monopo-listic competition • One concrete way of thinking about the lack of substitutability is distance. The seminal paper in this literature has been published by HaroldHotelling in the Economic Journal in 1929 • Consider a small island with a big lake in the middle. Business activities are necessarily located at the periphery of the island. Restaurants: meals are produced under increasing returns to scale. • Circumference of the island is 1 mile. Initially: 4 restaurants, evenly spaced. • Min. distance = 0 and Max distance = 1/8 miles. • L customers scattered uniformly around the circle and the cost of travel is t€ per mile.
The initial location of restaurants • Total cost curve of the restaurant is: TC = F + MQ ATC = TC/Q = F/Q + M
The average cost of a meal with 4 restaurants • If TC = 50 + 5Q where Q is the number of meals served each day. • If L = 100 and there are 4 restaurants, each restaurant will serve 100/4 = 25 persons a day. • So, the total cost is TC = 50 + (5x25) = 175€ per day. Average total cost is TC/25 = 7€ per meal. • Clearly this is higher than if there are only 2 restaurants: each serve 50 meals per day with AC = [50+(5x50)]/50 = 6€. • What is the average cost of transportation if there are 4 restaurants? • In this case the farthest someone can live from a restaurant is 1/8 miles so that he round trip is 1/4 miles. • If the travel cost is 24€ per mile the total travel cost will be 6€.
