THE BERTRAND DUOPOLY MODEL IN MICROECONOMICS.pptx

The Bertrand duopoly model in economics

1. THE BERTRAND DUOPOLY MODEL

2. Definition A market structure where it is assumed that there are two firms, who both assume the other firm will keep prices unchanged. Therefore, each firm has an incentive to cut prices, but this actually leads to a price war. If products are perfect substitutes this assumes the price will be driven down to marginal cost. This is allocatively efficient (P=MC) but firms may not cover their fixed costs.

3. Background information Bertrand competition is a model of competition in which two or more firms produce a homogenous good and compete in prices. Theoretically, this competition in prices, providing the goods are perfect substitutes, ends with the firms selling their goods at marginal costs and thus making zero profits. The result is also called the Bertrand paradox named after the economist Joseph Bertrand (1822–1900). He identified the key error in the Cournot Competition Model of French mathematician Antoine Augustin Cournot and used prices rather than quantities as the strategic variables, thus showing that the equilibrium price is was simply the competitive price.

4. Bertrand Model Environment Treats the price of competitors as fixed , and all firms decide simultaneously what prices to charge. Few firms that sell to consumers. Firms produce differentiated but highly substitutable products at constant marginal cost. Each firm independently sets its price in order to maximise profits meaning price is each firm’s control variable. Barriers to entry exist. Consumers enjoy perfect information. Firms price at marginal cost and make no profit.

5. Bertrand Model Critical Analysis Assumes that firms compete purely on price, ignoring non-price competition such as quantity, promotion, place. Assumes that sales are divided among the competing firm and that the firm, in undercutting its competitor, is able to meet the full demand of the market. Assumes that the pricing game is a shot game, however, in a dynamic competition, repeated price competition can lead to a equilibrium price higher above the Marginal Cost (MC). Assumes products are identical, whereas in reality, most firms produce products that at least, their consumers perceive as different from a rival’s.

6. Bertrand Model Critical Analysis No search and transaction costs. Like perfect competition, it assumes consumers have perfect information and if a good is 1% cheaper, then consumers will buy Firms can easily increase output and there are no capacity constraints. If a firm increases the price, the model assumes that all demand will move to the cheaper firm. But, this requires supply to be perfectly elastic and the firm to easily increase output in response to the surge in demand. No co-operation between firms and no attempt to collude and fix higher prices

7. Bertrand Model Reaction Functions & Curves Bertrand’s model focuses on price competition. His analytical tools are reaction function of the duopolists. Reaction functions are derived on the basis of iso-profit curves. An iso-profit curve, for a give level of profit, is drawn on the basis of various combinations of prices charged by the rival firms. He assumed only two firms, A and B and their prices are measured along the horizontal and vertical axes, respectively. Their iso-profit curves are drawn on the basis of the prices of the two firms. Iso-profit curves of the two firms are concave to their respective prices axis, as shown in Fig. 3 and 4. Iso- profit curves of firm A are convex to its price axis PA (Fig. 3) and those of firm B are convex to PB (Fig. 4).

8. Bertrand Model Reaction Functions & Curves cont. In Figure 4, we have curve A, which shows that A can earn a given profit from the various combinations of its own and its rival’s price. For example, price combinations at points, a, b and c yield the same level of profit indicated by the iso-profit curve A1. If firms B fixes its prices Pb1– firm A has two alternative prices, Pa1 and Pa2, to make the same level of profits. When B reduces its price, A may either raise its price or reduce it. A will reduce its price when he is at point c and raise its price when he is at point a. But there is a limit to which this price adjustment is possible. This point is shown by point b. So there is a unique price for A to maximize its profits. This unique price lies at the lowest point of iso-profit curve. The same analysis applies to all other iso-profit curves, A1 A2 and A3 we get A’s reaction curve. Note that A’s reaction curve has a rightward slant. This is so because, iso-profit curve tends to shift rightward when A gains market from his rival B. Following the same process, B’s reaction curve may be drawn as shown in Fig. 4. PTO for Fig. 4 & 5.

9. Bertrand Model Reaction Functions & Curves cont.

10. Bertrand Model Reaction Functions & Curves cont. The equilibrium of duopolists suggested by Bertrand’s model may be obtained by putting together the reaction curves of the firms A and B as shown in Fig. 5. The reaction curves of A and B intersect at point E where their expectations materialize, point E is therefore equilibrium point. This equilibrium is stable. Fo, if any one of the firms disagrees to this point, it will create a series of actions and reactions between the firms which will lead them back to point E. PTO for Fig. 5.

11. Bertrand Model Reaction Functions & Curves cont.

12. Criticisms of the Bertrand Model Bertrand’s model has been criticized on the same grounds as Cournot’s model. Bertrand’s implicit behavioral assumption that firms never learn from their past experience seems to be unrealistic. If cost is assumed to be zero, price will fluctuate between zero and the upper limit of the price, instead of stabilizing at a point. It assumes firms do not learn from their mistakes. The initial assumption is that the other firm will keep prices constant, but when they see they also cut their price, they may change their behavior. Firms in a duopoly should be able to make high profits. It depends on the degree of barriers to entry. With two firms, there is a possibility of tacit collusion – or at least a quiet industry which avoids a price war. Over time, there is the possibility firms will learn from their behavior and take a risk in keeping prices above marginal cost. It depends on the objectives of firms, for example, is it to profit maximize or increase market share. Bertrand Competition may be more likely if they are seeking to maximize sales.

13. Criticisms of the Bertrand Model cont. Consumers are not just motivated by buying the cheapest good. Their choices will reflect factors, such as brand loyalty, convenience, ease of purchase and quality of the good. Firms will face capacity constraints and may not be able to increase supply to meet the doubling of demand in a short time. Consumers may not have perfect information about the cheapest goods. There may be search and transaction costs of moving to a cheaper product. It is rare goods are homogenous, even with a good like water, firms may have different brand images.

14. THE END