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University of Toronto Mississauga
Yasin Janjua

Eco205 Chapter 12 – Imperfect Competition 18th January 2013 Oligopoly A market with few firms but more than one Overview: Pricing Of Homogeneous Goods Competitive Outcome It is difficult to predict exactly the possible outcomes for prices when there are few firms; prices depend on how aggressively firms compete, which in turn depends on which strategic variables firms choose, how much information firms have about rivals, and how often firms interact with each other in the market The Bertrand model — identical firms choose prices simultaneously in their one meeting in the market, has Nash equilibrium. This figure assumes that marginal cost (and average cost) is constant for all output levels. Even though there may be only two firms in the market, in this equilibrium they behave as if they were perfectly competitive, setting price equal to marginal cost and earning zero profit. Perfect Cartel Outcome At the other extreme, firms as a group may act as a cartel, recognizing that they can affect price and coordinate their decisions. Indeed, they may be able to act as a perfect cartel, achieving the highest possible profits, namely, the profit a monopoly would earn in the market. One way to maintain a cartel is to bind firms with explicit pricing rules. Such explicit pricing rules are often prohibited by antitrust law. Firms do not need to resort to explicit pricing rules if they interact on the market repeatedly. They can collude tacitly. Other Possibilities The Bertrand and cartel models determine the outer limits between which actual prices in an imperfectly competitive market are set. This band of outcomes may be very wide, and such is the wealth of models available that there may be a model for nearly every point within the band. Cournot Model Cournot model - An oligopoly model in which firms simultaneously choose quantities Nash Equilibrium in the Cournot Model For a pair of quantities, qA and qB, to be a Nash equilibrium, qA must be a best response to qB and vice versa. We have to start by computing the best-response function for firm A. Its best-response function tells us the value of qA that maximizes A’s profit given for each possible choice qB by firm B. Nash equilibrium requires each firm to play its best response to the other. The only point where both are playing best responses is the intersection between their best-response functions. No other point would be stable because one firm or the other or both would have an incentive to deviate Comparisons and Antitrust Considerations The equilibrium price and industry profit in the Cournot model is above the perfectly competitive level and below the monopoly level; industry output is below the perfectly competitive level and above the monopoly level. The firms manage not to compete away all the profits as in perfect competition. But the firms do not do as well as a monopoly would, either The industry does not attain the monopoly profit in the Cournot model because firms do not take into account the fact that an increase in their output lowers price and thus lowers the other firm’s revenue. Firms ‘‘overproduce’’ in this sense. According to this model, firms would have an incentive to form a cartel with explicit rules limiting output. Another way to increase profits would be for the firms to merge, essentially turning a Cournot model with two firms into a monopoly model with one firm. Consumers benefit from the higher output and lower prices in the Cournot model compared to monopoly. Government authorities, through the antitrust laws, often prohibit conspiracies to form cartels and mergers that would increase concentration in the industry. Assuming the government authorities act in the interest of consumers, the Cournot model provides some justification for these laws Generalizations As the number of firms grows large, it can be shown that the Nash equilibrium approaches the competitive case, with price approaching marginal cost Bertrand Model Bertrand model - An oligopoly model in which firms simultaneously choose prices To state the model formally, suppose there are two firms in the market, A and B. They produce a homogeneous product at a constant marginal cost (and constant average cost), c. Note that this is a generalization of our assumption in the Cournot model that production was costless. Firms choose prices PA and PB simultaneously in a single period of competition. Firms’ outputs are perfect substitutes, so all sales go to the firm with the lowest price, and sales are split evenly if PA = PB. We will generalize the demand curve beyond the particular linear one that we assumed in the Cournot model to be any downward-sloping demand curve. We will look for the Nash equilibrium of the Bertrand model. It turns out that the marginal analysis (MR = MC) we used to derive the best-response functions in the Cournot model will not work here since the profit functions are not smooth. Starting from equal prices, if one firm lowers its price by the smallest amount, its sales and profit would essentially double instantly. Nash Equilibrium in the Bertrand Model The only Nash equilibrium in the Bertrand game is for both firms to charge marginal cost: PA = PB = c. In saying that this is the only Nash equilibrium, we are really making two statements that both need to be verified: (1) that this outcome is a Nash equilibrium, and (2) that there is no other Nash equilibrium. To verify that this outcome is a Nash equilibrium, we need to show that both firms are playing a best response to each other - that neither firm has an incentive to deviate to some other strategy. In equilibrium, firms charge a price equal to marginal cost, which in turn is equal to average cost. But a price equal to average cost means firms earn zero profit in equilibrium. It will make no sales and therefore no profit, not strictly more than in equilibrium. If it deviates to a lower price, it will make sales but will earn a negative margin on each unit sold since price will be below marginal cost. So the firm will earn negative profit, less than in equilibrium. Because there is no possible profitable deviation for the firm, we have succeeded in verifying that both firms’ charging marginal cost is a Nash equilibrium. To verify that this outcome is the only Nash equilibrium, there are a number of cases to consider. It cannot be a Nash equilibrium for both firms to price above marginal cost. If the prices were unequal, the higher-pricing firm, which would get no demand and thus would earn no profit, would make positive sales and profit by lowering its price to undercut the other. If the above-marginal-cost prices were equal, either firm would have an incentive to deviate. By undercutting the price ever so slightly, price would hardly fall but sales would essentially double because the firm would no longer need to split sales with the other. Nash equilibrium cannot involve a price less than marginal cost either because the low-price firm would earn negative profit or could gain by deviating to a higher price. For example, it could deviate by raising price to marginal cost, which, since it also equals average cost, would guarantee the firm zero profit Bertrand Paradox Price is set to marginal cost, and firms earn zero profit. This is the same as perfect competition that’s why its called a paradox. It is paradoxical that competition would be so tough with as few as two firms in the market. The Bertrand Paradox could also be avoided by making other assumptions, including the assumption that the marginal cost is higher for one firm than another, the assumption that products are slightly differentiated rather than being perfect substitutes, or the assumption that firms engage in repeated interaction rather than one round of competition. Capacity Choice and Cournot Equilibrium Capacity constraint - A limit to the quantity a firm can produce given the firm’s capital and other available inputs. The firm can satisfy this increased demand because it has no capacity constraints, giving firms a big incentive to undercut. If the undercutting firm could not serve all the demand at its lower price because of capacity constraints, that would leave some residual demand for the higher-priced firm, and would decrease the incentive to undercut Firms cannot sell more in the second stage than the capacity built in the first stage. If the cost of building capacity is sufficiently high, it turns out that the subgame-perfect equilibrium of this sequen- tial game leads to the same outcome as the Nash equilibrium of the Cournot model. The principal lesson of the two-stage capacity/price game is that, even with Bertrand price competition, decisions made prior to this final (price-setting) stage of a game can have an important impact on market behavior Comparing the Bertrand and Cournot Results The Bertrand model predicts competitive outcomes in a duopoly situation, whereas the Cournot model predicts prices above marginal cost and positive profits; that is, an outcome somewhere between competition and monopoly. These results suggest that actual behavior in duopoly markets may exhibit a wide variety of outcomes depending on he precise way in which competition occurs the equilibrium outcomes from the two games resemble that from the Prisoners’ Dilemma. The Nash equilibrium in all three games is not the best outcome for the players. Players could do better if they could cooperate on an outcome with lower outputs in Cournot, higher prices in Bertrand, or being Silent in the Prisoners’ Dilemma. But cooperation is not stable because players have an individual incentive to deviate. In equilibrium of both the Cournot and Bertrand games, firms in a sense compete too hard for their own good (to the benefit of consumers) Product Differentiation Market Definition We assume that the market is composed of a few slightly differentiated products that can be usefully grouped together because they are more substitutable for each other than for goods outside the group Bertrand Model with Differentiated Products One way to model differentiated products is to specify demand curves that are functions of the product’s own price and also of the price of the other good. Example given on page 456 With differentiated products, the profit functions are smooth, so one can use marginal analysis to compute the best-response functions, similar to the analysis of the Cournot model. The best-response functions show the profit-maximizing price for a firm given a price charged by its competitor. The best-response functions tend to be upward-sloping: an increase in, for example, B’s price increases A’s demand, which would lead A to respond by raising its price. This contrasts with the Cournot case, where the best- response functions were downward sloping Product Selection Product characteristics—including color, size, functionality, quality of materials, etc.—are strategic choices for the firms just as are price and quantity. Consider a two-stage game in which firms choose product characteristics in the first stage and price in the second There are two offsetting effects at work in the first-stage product-characteristics game. One effect is that firms prefer to locate near the greatest concentration of consumers because that is where demand is greatest. For example, if consumers’ favorite colors are beige and metallic gray automakers will tend to produce beige and metallic-gray cars. This effect leads firms to locate near each other, that is, to produce very similar products. There is an offsetting strategic effect. Firms realize that if their products are close substitutes, they will compete aggressively in the second-stage price game. Locating further apart softens competition, leading to higher prices. An increase in product differentiation between the two firms shifts their best-response functions out and leads to a Nash equilibrium with higher prices for both. If firms’ products become too specialized, they risk the entry of another firm that might locate in the product space between them. Search Costs Prices may differ across goods if products are d
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