Cournot duopoly model. Cournot quantity duopoly model Efficiency of monopolistic competition
The simplest oligopolistic situation is when there are only two competing firms in the market. The main feature of duopoly models is that the revenue and profit that a firm receives depends not only on its decisions, but also on the decisions of a competing firm interested in maximizing its profits. The first model of duopoly was proposed by the French economist Cournot in 1838.
The Cournot model analyzes the behavior of a duopoly firm based on the assumption that it knows the volume of output that its only competitor has already chosen for itself. The firm's task is to determine its own production size. Additional simplifications are made in the model: both duopolists are exactly the same, the marginal costs of both firms are constant (the MC curve runs strictly horizontal).
Let's assume that firm 1 knows that its competitor is not going to release anything. Firm 1 is practically a monopoly. The demand curve for its product (D 0) coincides with the demand curve for the entire industry. Marginal revenue curve MR 0 . According to the rule of equality of marginal revenue and marginal costs MC=MR, firm 1 will set its optimal production volume (50 units). Firm 2 intends to produce 50 units of products. If firm 1 sets a price P 1 for its products, then there will be no demand for it. This price has already been set by firm 2. But if firm 1 sets the price P 2, then the total market demand will be 75 units. Since firm 2 offers 50 units, firm 1 will have 25 units left. If the price is lowered to P 3, then the market demand for the products of firm 1 will be 50 units. By going through different possible price levels, one can obtain different market needs for the products of firm 1, i.e. for the products of firm 1, a new demand curve D 1 and a new marginal revenue curve MR 1 will be formed. Using the MC=MR rule, you can determine the new optimal production volume.
Question No. 34: “Behavior of a monopolist firm in the short and long term”
Before a monopoly, as well as before a perfectly competitive firm, in short term The goal may be to minimize losses. A similar situation may arise, in particular, if there is a sharp decrease in demand for its products. Even with the optimal size of its output, the monopolist will receive revenue that exceeds direct costs (VC), but is insufficient to cover gross costs (TC = FC + VC). Having stopped production, he will bear fixed costs(FC). In the absence of revenue, they will constitute the total losses of the monopolist. To minimize the loss, he needs to continue production, covering part of the loss with the difference between revenue and variable costs (marginal profit). The higher the gross margin, the lower the overall loss will be. The principle according to which the firm will choose the volume of output is the same as the equality of marginal revenue and marginal cost(MR=MS). 
With the output volume Q', the equality MR=MC is observed, which means choosing the optimal production size and minimizing the inevitable loss. With it, the value of gross revenue TR will be P’*Q’ (the area of a rectangle with sides P’ and Q’ on the bottom graph and a height equal to TR’ on the top).
The average cost of producing Q' will be equal to ATC'. Accordingly, the total costs, ATC’*Q’ (the area of a rectangle with sides ATC’ and Q’ on the bottom graph and the height equal to TC’ on the top), will be greater than the revenue TR’. However, this revenue will exceed variable costs (VC) and provide maximum marginal profit (TR’-VC’).
The difference between the values of TC' and TR' will be the minimum amount of the monopolist's loss in the short term for all possible production volumes.
The monopolist's loss is minimized when the slope of the gross revenue curve () is equal to the slope of gross and variable costs (), which confirms the equality of the values of MR and MC.
IN long term a monopolist firm that previously minimized losses will leave the industry as economically ineffective. This is a relatively rare case. As a rule, a monopoly that receives economic profit in the short term maintains it in the long term, optimizing output based on the equality of marginal revenue and long-term marginal costs. 
The profit maximization model of a monopolist in the long run is similar to the model of its behavior in the short run. The only difference is that all resources and costs are variable, and the monopolist can optimize the use of all factors of production, taking into account economies of scale. The equality MR=MC as a condition for choosing the optimal production size takes the form MR=LMC.
Duopoly (from Latin duo - two and Greek pōlēs - seller)
a term used in bourgeois political economy to designate the market structure of an economic sector in developed capitalist countries, in which there are only two suppliers a certain product and there are no monopolistic agreements between them on prices, sales markets, production quotas, etc. The concept of D. reflects various forms of market organization. The first form is a market dominated by two large commercial and industrial companies, between which there is a secret agreement that ensures maximum profit through unequal exchange. This situation is typical for the beginning of the 20th century. The second form is the market modern industries mass production, which is also dominated by two companies. There is usually a tacit agreement between them on monopoly prices and non-price competition. The third form is a market in which there are two suppliers, but there are no monopolistic agreements between them. This is possible in two situations: either as a temporary state of the market during the initial period of production of a new product and a “test of strength” of two suppliers, or as a state of fierce competition during the transition from simpler to more developed forms of monopoly. This form is used by some bourgeois economists for apologetic purposes to prove the possibility of a permanent absence of monopoly in conditions of highly concentrated production. The majority of modern bourgeois economists consider debt to be a type of monopoly (which is true). Economic and mathematical research into mathematics began back in the 19th century. A. Cournot, J. Bertrand (France) and F. Edgeworth (Great Britain). In the 30s 20th century G. Stackelberg (Germany) gave a description of certain types of D., depending on the behavior of duopolists. Modern theory D. developed under the influence of theories monopolistic competition E. Chamberlin (USA), Not perfect competition J. Robinson (Great Britain), the works of R. Triffin (USA) and began to take into account the more complex nature of real market conditions(interdependence between industries, shifts in supply and assets, differences in types of transactions and market institutions, level of information about the market, etc.). Lit.: Chamberlin E. H., Theory of Monopolistic Competition, trans. from English, M., 1959; Zhams E., History of economic thought of the twentieth century, trans. from French, M., 1959; Seligman B., Main currents of modern economic thought, trans. from English, M., 1968; Neumann J., Morgenstern O., The theory of games and economic behavior, Princeton, 1944. Yu. A. Vasilchuk.
Great Soviet Encyclopedia. - M.: Soviet Encyclopedia. 1969-1978 .
See what “Duopoly” is in other dictionaries:
- (doupoly) A market in which there are only two producers or sellers of a given product or service and many buyers. In practice, the profits that can be realized from this form of imperfect competition are usually less than... Dictionary of business terms
Type industry market, but there are only two sellers and many buyers. It is believed that the profits that can be obtained as a result of such imperfect competition are less than those that would be obtained if two... ... Financial Dictionary
- (duopoly) A market in which there are only two sellers, each of whom must take into account the possible retaliation of the other. In a Cournot duopoly, each seller assumes that the competitor will maintain the same volume... ... Economic dictionary
- (from Latin: two and Greek: I sell) a situation in which there are only two sellers of a certain product, not interconnected by a monopolistic agreement on prices, sales markets, quotas, etc. This situation was theoretically ... ... Wikipedia
duopoly- The situation in the market where there are only two manufacturers offering one product. [OAO RAO "UES of Russia" STO 17330282.27.010.001 2008] duopoly A market mechanism in which there are two sellers of the same product (this is quite abstract... ... Technical Translator's Guide
- (from the Latin duo two and the Greek poleo I sell) an economic term that denotes an economic structure in which there are only two suppliers of a certain product, not interconnected by a monopolistic agreement on prices, markets, quotas, etc.... Big Encyclopedic Dictionary
Duopoly- a market mechanism in which two sellers of the same product operate (this rather abstract case is often used, due to its clarity, when modeling market processes). Analysis by D., named after O. Cournot and proposed by him in... ... Economic and mathematical dictionary
duopoly- Exclusive control of the supply of products to a specific market and service by two suppliers who dominate this market and thereby determine prices and the scale of supply... Dictionary of Geography
Duopoly- (from Latin duo two + gr. poleo sell; English duopoly) a situation in which on the product market there are two manufacturers offering identical products (goods) ... Encyclopedia of Law
AND; and. [from lat. duo two] Economy A market dominated by two sellers of a certain product or service that are not interconnected by agreements on prices, sales markets, etc. * * * duopoly (from Latin duo two and Greek pōléō sell), economic term, ... ... encyclopedic Dictionary
DUOPOLY- (from Latin: two and Greek: I sell) a situation in which there are only two sellers of a certain product, not interconnected by a monopolistic agreement on prices, sales markets, quotas, etc. This situation was theoretically ... ... Large economic dictionary
Books
- Microeconomics for advanced students. Problems and solutions, A. P. Kireev, P. A. Kireev. The collection contains tasks on the main sections of microeconomics: consumer theory, producer theory, market theory (free competition, monopoly), general economic equilibrium,...
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ABSTRACT
BEHAVIOR OF A FIRM UNDER DUOPOLY
Duopoly (from Latin: two and Greek: I sell) is a situation in which there are only two sellers of a certain product, not interconnected by a monopolistic agreement on prices, sales markets, quotas, etc. This situation has been theoretically considered A. Cournot in the work “A Study of the Mathematical Principles of the Theory of Wealth” (1838). Cournot's theory comes from competition and is based on the fact that buyers announce prices and sellers adjust their output to these prices. Each duopolist estimates the demand function for the product and then sets the quantity to be sold, assuming that the competitor's output remains unchanged. According to Cournot, a duopoly occupies an intermediate position in terms of output between a complete monopoly and free competition: compared to a monopoly, the output here is slightly larger, and compared to pure competition, it is smaller.
Initial conditions and main task of the model
There are two similar firms in the market (duopoly situation), each of which owns a source of mineral water, which it can develop at the same cost. For simplicity, they are assumed to be zero. Mineral water firms sell on the market. Market demand is known and has the form of a linear function:
The total production volume of the two firms is:
The behavior of a company in a duopoly. Cournot model
Each firm strives to maximize profits based on the constant volume of its competitor's output, regardless of what volume it chooses (in other words, the competitor's output is taken as a given value). For example, if firm 1 believes that firm 2's possible output is zero (i.e. it is the only manufacturer and the demand for its product coincides with market demand), then it produces one volume at the optimum point. If the possible output of firm 2 is greater, then firm 1 will adjust its output based on residual demand (market demand minus demand for firm 2’s products), i.e. will produce slightly less at the optimum point. Finally, if firm 1 believes that its competitor supplies 100% of market demand, its optimal output will be zero.
Thus, firm 1's optimal output will change depending on how it thinks firm 2's output will grow.
The main task of the model is to determine at what volume of output both firms reach equilibrium.
The simplest oligopolistic situation is when there are only two competing firms in the market. The main feature of duopoly models is that the revenue and profit that a firm receives depends not only on its decisions, but also on the decisions of a competing firm interested in maximizing its profits. The first model of duopoly was proposed by the French economist Cournot in 1838.
The Cournot model analyzes the behavior of a duopoly firm based on the assumption that it knows the volume of output that its only competitor has already chosen for itself. The firm's task is to determine its own production size. Additional simplifications are made in the model: both duopolists are exactly the same, the marginal costs of both firms are constant (the MC curve runs strictly horizontal). duopoly seller goods equilibrium
The simplest oligopolistic situation is when there are only two competing firms in the market.
The main feature of duopoly models is that the revenue and profit that a firm receives depends not only on its decisions, but also on the decisions of a competing firm interested in maximizing its profits. The first model of duopoly was proposed by the French economist Cournot in 1838.
The Cournot model analyzes the behavior of a duopoly firm based on the assumption that it knows the volume of output that its only competitor has already chosen for itself. The firm's task is to determine its own production size. Additional simplifications are made in the model: both duopolists are exactly the same, the marginal costs of both firms are constant (the MC curve runs strictly horizontal).
Let's assume that firm 1 knows that its competitor is not going to release anything. Firm 1 is practically a monopoly. The demand curve for its product (D0) coincides with the demand curve for the entire industry. Marginal revenue curve MR0. According to the rule of equality of marginal revenue and marginal costs MC=MR, firm 1 will set its optimal production volume (50 units). Firm 2 intends to produce 50 units of products. If firm 1 sets price P1 for its products, then there will be no demand for it. This price has already been set by firm 2. But if firm 1 sets the price P2, then the total market demand will be 75 units. Since firm 2 offers 50 units, firm 1 will have 25 units left. If the price is lowered to P3, then the market demand for the products of firm 1 will be 50 units. By going through different possible price levels, one can obtain different market needs for the products of firm 1, i.e. for the products of firm 1, a new demand curve D1 and a new marginal revenue curve MR1 will be formed. Using the MC=MR rule, you can determine the new optimal production volume
Bibliography
1. Blaug M. Theory of duopoly // Economic thought in retrospect = Economic Theory in Retrospect. - M.: Delo, 1994. - P. 296-297. -- XVII, 627 p. -- ISBN 5-86461-151-4
2. Duopoly / Vasilchuk Yu. A. // Debtor - Eucalyptus. - M.: Soviet Encyclopedia, 1972. - (Great Soviet Encyclopedia: [in 30 volumes] / chief editor A. M. Prokhorov; 1969-1978, vol. 8)
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A better understanding of the patterns of firm behavior in an oligopolistic market allows us to analyze duopoly, i.e. the simplest oligopolistic situation, when there are only two competing firms on the market. The main feature of duopoly models is that the revenue and, therefore, the profit that the firm will receive depends not only on its decisions, but also on the decisions of the competing firm, which is also interested in maximizing its profits. The decision-making process in a duopolistic market is reminiscent of home analysis of a delayed chess game, with a player looking for the strongest answers to his opponent's possible moves.
There are many models of oligopoly, and none of them can be considered universal. Nevertheless, they explain the general logic of the behavior of firms in this market. The first and still relevant model of duopoly was proposed by the French economist Augustin Cournot in 1838 in the book “A Study of the Mathematical Principles of the Theory of Wealth.”
The Cournot model allows us to analyze the behavior of a duopoly firm based on the assumption that it knows the volume of output that its only competitor has already chosen for itself. The firm's task is to determine the size of its own production, taking into account the competitor's decision as a given.
The figure shows what the firm's command would be under such conditions. To keep the graph simple, we've made two additional simplifications. Firstly, they accepted that both duopolists are completely identical, indistinguishable firms. Secondly, we assumed that the marginal costs of both firms are constant: the MC curve runs strictly horizontal. The latter assumption, as was shown in the chapter on costs, is not so unrealistic. Rather, it can be said that it limits the analysis to the normal level of capacity utilization. That is, only the middle part is considered on the MC curve, which lies near the technological optimum and really looks like a horizontal straight line.
The analysis of duopolist behavior in the Cournot model was step-by-step. Let first one of the oligopolists (firm No. 1) know for sure that the second competitor does not plan to produce any product at all. In this case, firm No. 1 will actually become a monopoly. The demand curve for its product (D 0 ) will coincide with the demand curve of the entire industry. Accordingly, the marginal revenue curve will take a certain position (M.R. 0 ). Using the usual rule of equality of marginal revenue and marginal cost MS = M.R., Firm No. 1 will set its optimal production volume (in the case shown in the graph - 50 units) and the level of yen (R 1 ).
Well, what will happen if next time firm No. 1 becomes aware that its competitor himself intends to produce 50 units. products at a price of R 1? At first glance it may seem that thereby he will exhaust the entire volume of demand and force firm No. 1 to abandon production. Having carefully examined the chart, however, we will be convinced that this is not so. If firm No. 1 also sets the price R 1 , then there really will be no demand for its products: those 50 units that the market is ready to accept at this price have already been supplied by company No. 2. But if firm No. 1 sets a lower price P 2, then the total market demand will increase (in our example it will be 75 units - see industry demand curve D 0). Since firm No. 2 offers only 50 units, then the share of firm No. 1 will leave 25 units. (75 - 50 = 25). If the price is lowered to R 3 then, repeating similar reasoning, we can establish that the market demand for the products of firm No. 1 will be 50 units. (100 - 50 = 50).
It is easy to understand that, by going through different possible price levels, we will obtain different levels of market demand for the products of firm No. 1. In other words, a new demand curve will be formed for the products of firm No. 1 (in our graph - D 1) and, accordingly, a new marginal curve income ( M.R. 1 )> Using the rule again MS =M.R., you can determine the new optimal production volume (in our case it will be 25 units - see Fig. 9.2).
Already at this stage of analysis, the Cournot model allows one to draw important economic conclusions.
1. In an oligopoly, the volume of arbitrariness is greater than the level that would be established under a pure monopoly, but less than what would be established under perfect competition:
Qm A smaller output of products under an oligopoly than under perfect competition does not, in fact, require proof: the situation is similar in any imperfectly competitive market. So, in our example, the oligopolists will release 75 units. products. And with perfect competition, output would be greater. Recall that in perfect competition the demand and marginal revenue curves coincide (D
=
M.R.),
therefore, the equilibrium point according to the rule MS
=
M.R. should be established at the intersection of curves D and MC, which, as can be seen in the graph, will lead to the release of 100 units. But it is also clear that oligopolistic output will exceed monopoly output. After all, to the volume of production to which the monopolist would limit the output (50 units), the output of the second manufacturer (25 units) was also added. 2.Prices in an oligopoly are lower than monopolistic prices, but higher than competitive prices: R m >P olig >
P c
(9-2) The economic mechanism that led to the establishment of the described level of yen is also clear. By limiting production and inflating the yen, the monopoly leaves part of the market demand unsatisfied. This remainder serves as a sales market for the second duopolist (as well as the third, fourth and further competitors, if we move from the duopolistic model to a multi-firm oligopoly), allowing him to release additional products, if, of course, he reduces the yen below the monopoly level (in the graph - from P 1 to R 2
).
At the same time, its yen will be higher than the competitive price level (P 3). the total profits of both duopolies will be below those profits that a single firm would receive in the same market* monopolist. P m >p olig >0
(9-3) We will again refrain from commenting on the general tendency of imperfectly competitive markets to generate economic profit. And the fact that their level is lower than that of monopolies is easiest to prove from the opposite As is known, the MC = MR rule ensures profit maximization. At the very beginning of the analysis of the Cournot model, we were convinced that if only one monopolist firm acted in the market (a situation in which it is known about the second duopolist that it does not plan to produce products is actually equivalent to a monopoly), it, guided by this rule, would establish a certain volume production and price level. At any other output volume (and price level), the profit will be less. But the intervention of the second duopolist, the start of production by this second firm, precisely leads to a deviation of production volumes and prices from the optimum. Consequently, the total profit of two duopolists will not be as great as that which a pure MONOPOLIST would be able to obtain The general conclusion, which also has enormous practical significance for a manager, is obvious: in an oligopoly, there is not one, but many demand curves for the company’s products, namely, each level of output of one of the oligopolists corresponds to a special demand curve for the products of the remaining oligopolists. Let us recall how events developed in the model: knowing that the second firm did not plan production, the first behaved as a monopolist and had a demand curve D 0 . As soon as firm No. 2 changed its decision and produced 50 units. products, for firm No. 1 a new demand curve O, has developed. It is obvious that the reasoning that we carried out in relation to the production of 0 and 50 units by the second company. products can be repeated in relation to the most different levels of production of this company. Each new choice of a given firm will generate a new demand curve for its competitor's product. The graph, in particular, shows the demand curve for the products of firm No. 1 (see D 2), which will arise when firm No.
2
exactly 75 units. products. In this case, the optimal production volume for firm No. 1 itself will be 12.5 units. products (intersection
M.R. 2
And MO. In other words, for any oligopolist the market volume is not a constant value, but directly depends on the decisions of competitors. To better understand all the consequences of this pattern, let us turn to the figure. Let's pay attention to the unusual axes used on it. The production volumes of one company are plotted horizontally, and the production volumes of another company are plotted vertically. On such axes, the size of production by firm No. 1 can be depicted as a response curve to the volume of production of firm No.
2.
Similarly, the output of firm No. 2 can be represented as a function of the output of firm No. 1: Q(1) = φ
Q(2),
Q(2)
= φ Q(1) where Q(1) - production size of firm No. 1; Q(2) is the production size of firm No. 2. With this formulation of the problem, we are actually trying to understand what will come of the simultaneous efforts of two firms to adjust their production volume to the production volume of the other firm. Let's see if both firms can establish mutually acceptable production volumes. We took all the data for the graph from the previous example. So, if it is known about firm No. 2 that it is going to produce 75 units. products, then firm No. 1 will decide to produce 12.5 units. (dot A). But if firm No. 1 actually produces 12.5 units. products, then, as can be seen in the graph, firm No. 2, in accordance with its reaction curve, should produce not 75, but 42.5 units. (dot IN). But such a level of production by a competitor will force firm No. 1 to produce not 12.5 units, as it had planned, but 29 units. products (point O, etc. It is easy to notice that the level of production that a company sets based on the current size of production of a competitor, each time turns out to be such that it forces the latter to reconsider this level. This causes a new adjustment in the volume of production of firm No. 1, which in turn again changes the plans of firm No. 2. That is, the situation is unstable, non-equilibrium. However, there is also a point of stable equilibrium - this is the point of intersection of the reaction curves of both firms (on the graph - point ABOUT). In our example, firm No. 1 produces 33.3 units. based on the fact that the competitor will release the same amount. And for latest issue 33.3 units really is optimal. Each firm produces the volume of output that maximizes its profits given the competitor's output. It is not profitable for any of the firms to change the volume of production, therefore, the equilibrium is stable. In theory, it was called the Cournot equilibrium. Under Cournot equilibrium
is understood as such a combination of output volumes of each firm in which none of them has incentives to change its decision: the profit of each firm is maximum, provided that the competitor maintains this output volume. or in other words, at the Cournot equilibrium point, the volume of output expected by competitors of any of the firms coincides with the actual one and at the same time is optimal. The existence of Cournot equilibrium indicates that oligopoly as a type of market can be stable, that it does not necessarily lead to a series of continuous, painful redistribution of the market by oligopolists. Mathematical game theory, however, shows that the Cournot equilibrium is achieved under some assumptions about the logic of behavior of duopolists, but not under others. In this case, the understandability (predictability) of the actions of the competing partner and his readiness for cooperative behavior in relation to the opponent are crucial for achieving balance. Perhaps this morning you Maurice Chaclays Pure competition and pure monopoly are perfect forms. They help to understand the essence of the structure of diverse market relations, but in their extreme (absolute) forms they are almost never found in real life. This chapter examines monopolistic competition, a market structure we encounter every day. The term and model of monopolistic competition were introduced into scientific circulation in 1933 by E. Chamberlin. In a broad sense, all types of market structure (including oligopoly, which will be discussed in Chapter 11), located between pure monopoly and pure competition, can be interpreted as monopolistic competition. And the very name “monopolistic competition” was given because it contains elements of both of the above-mentioned ideal market structures. Monopolisticcompetition is a market structure in which many firms sell a heterogeneous product in one market. According to Chamberlin, a monopolistically competitive industry consists of many sellers offering a set of products that are close substitutes. Every seller strives to maximize profits by varying the quality of his product and the quantity offered for sale. Although product differentiation practically difficult to measure, it is generally accepted that this is where the essence of monopolistic competition lies. Changing every moment Let's consider monopolistic competition as one of the four main market structures based on the set of structural variables already known to us, given in Chapters 7-9 (Table 10.1). Table 10.1 Essence production group offering close substitutes can be determined by examining how production decisions separate producers influence behavior others manufacturers of the “industrial group”. Industrialgroup- this is a large number of product manufacturers who can quite successfully, although not fully, replace each other. Each firm in a situation of monopolistic competition is similar to others, i.e., representative. Chamberlin's hypothesis regarding the nature of monopolistic competition rests on the conditions uniformity And symmetry. 1 Uniformity condition is that the demand and supply curves of each producer in the group are identical. In relation to the production of beer, for example, this assumption suggests that the costs of producing a bottle of Baltika beer, in essence, do not differ from the production of Stepan Razin, and the demand conditions are almost the same. Conditionuniformity (uniformity):
Chamberlin's idea that the cost and demand curves of each member of an industry or group are identical. Both beers have their own “niche” in the market and have more or less loyal followers. At the same time, consumers of Baltika and Stepan Razin do not have any fundamentally different characteristics. In a competitive market, no one producer has a monopoly on best product" If a new type of product appears that is more popular than others, other manufacturers may modify the characteristics of their products, copying the best features of the most popular one without imitating it 100%. The equilibrium system is formed by a whole range of goods, the characteristics of which are to some extent differentiated, and these goods are liked or disliked differently by different consumers. Symmetry condition means that the action of one producer (in the form of a change in the price of its product) affects all other members of the group. Conditionsymmetry:
Chamberlin's idea that the action of one producer forces other members of a monopolistically competitive group to take certain countermeasures. Figuratively speaking, the Chamberlin firm can be compared to one of many fishing boats with several fishermen with fishing rods. If one fisherman finds bait that is more tempting for fish, then his share of the total catch will increase significantly. But since the situation is symmetrical, other fishermen can follow his example. But if everyone starts using the best bait, then the first fisherman’s bait will no longer be particularly attractive to the fish and his share of the total catch will decrease again. The juice of mutual friendship, the forgiveness of insults Translation by Adrian Piotrovsky The essence of monopolistic competition is manifested within four parameters: (1) product differentiation; (2) uniformity; (3) symmetry and (4) comparatively a large number of manufacturers. Features of the monopolistic competition market is that each firm faces two different demand curves: DD
And dd
(Fig. 10.1). d(ceteris paribus) I D(mutatis mut andis) 0 35 40 Qo = 45 50 55 Rice. 10.1
. Two demand curves under monopolistic competition LinedemandDD
(mutatismutandis) 1
demonstrates a situation in which all firms uniformly
change prices for their products. At equally high prices, each representative producer controls a relatively small and equal share of the market. A simultaneous reduction in prices by all sellers leads to the fact that each firm increases its sales by equal value. For example, at the point A each manufacturer will receive a price of 0.6 rubles. per unit of goods and will sell 45 units; at the point IN Each company will give you 0.5 rubles. per unit of goods and will sell 50 units. Curve DD
similar to the demand line industry purely competitive model and differs only in that it shows the share of each individual producer in total market demand. For example, dot IN for 100 manufacturers corresponds to a market volume of 5000 units. Linedemanddd
(ceterisparibus)
demonstrates a situation in which only one
the firm changes its price (the prices of other firms are fixed). An individual producer will not set the same price as his competitors if he believes that a certain other the price can bring him higher profits. If the manufacturer thinks that other firms will continue to adhere to the existing price (say, 0.6 rubles per piece), then he, too, by setting the price of 0.6 rubles. per piece, will sell 45 pcs. However, the manufacturer can set either a higher or lower price (say, 0.7 or 0.5 rubles per unit), and sell either 35 units, respectively. (dot A"), or 55 units. (dot A") goods. Curvedd
more elastic than curveDD
.
It is more sensitive to price changes, provided that other members of the group do not change their prices. Reducing the individual price from 0.6 to 0.5 rubles. per piece of goods provides not only an additional 5 units. sales similar to other members of the group (as shown by the curve DD),
but on top of that there is also an additional 5 units that our manufacturer will receive from the losses of the remaining members of the group. At higher than P 0, price, line dd
lies to the left, and at a price lower than P 0, to the right of the demand line DD.
This is explained by the fact that if our company increases the price, competitors will most likely keep their prices at the same level, and if one company lowers the price, other companies will be forced to follow this example in order not to lose their customers. Short-term equilibrium. Let us assume that the initial equilibrium of the production group is determined by point A 0 in Fig. 10.2, A at total price P Q
and release q0
. Separate producer acting within the demand line dd0
,
with appropriate marginal income(mr Q) is able to increase its own profits by lowering the price of its products to the level P t
and producing q
"
output units (at tg "ts). This corresponds to a new equilibrium point A". But if manufacturers follow the example of one other and will also reduce the price of their products to the level R, then the equilibrium of the system will move along the curve DD
to point I j. Curve dd
will begin to shift down and to the left, as prices of goods and substitutes(which are suggested by all other group members) also decreased. Each member will receive a new demand line dd,
passing through point A, and will revise the conditions for making a profit accordingly. The process will continue until the group reaches the position shown in Fig. 10.2, b. Point E corresponds to a single price for the entire group R*, and each participant sells q
*
units of production. Rice. 10.2. Equilibrium in the short run Once this position is reached, each producer receives a demand line dd*
and is not inclined to change either the price of its products or the volume of output. On the one hand, this short run equilibrium monopolistic competition resembles the equilibrium model under monopoly conditions, in which the firm’s demand curve has a downward slope, and tg<Р,а
price exceeds marginal cost. However, on the other hand, the situation also resembles equilibrium pure competition at market equilibrium price (R*), over which the individual producer has no control. The only difference from pure competition is that the firm's demand curve is not perfectly elastic. Long-term equilibrium. In the short run, a representative firm can receive a certain economic profit (tc > 0) if the price exceeds total average costs (P>ATS) at equilibrium output q*.
However, since the market is competitive, economic profit (or loss) cannot exist in long term period. This is explained by the fact that, as in purely competitive industry, under monopolistic competition, the existence of economic profits or losses creates incentives for new firms to enter the industry or for some of those already present to exit the industry - Entry and exit of firms in this model are practically unlimited. When a new firm enters an industry, the market share of the representative firm decreases, which leads to a corresponding shift to the left of the lines DD
And dd.
An individual firm is forced to reduce prices, which further shifts the curve down dd.
The process continues until the curve dd
will not reach the total average cost curve A TS(dot E in Fig. 10.3), in which economic profit is zero (tc = 0). A representative firm maximizes its profits at tg = ts, but the position of the curve dd
such that this maximization is carried out at tc = 0 (zero economic profit). Rice. 10.3. Long-run equilibrium For greater clarity, let us compare the equilibrium of a competitive firm in the short-term and long-term periods on one graph (Fig. 10.4). In Fig. 10.4, A the situation is depicted short term equilibrium of a monopolistically competitive firm. Since the firm is the only producer of its brand of goods and is dealing with a downward sloping demand curve, the final short-term price (PSR)
exceeds average costs (PBX) and the firm earns a positive profit (shaded rectangle). However, these profits attract new manufacturers into the industry with competing brands of goods. As a result, the firm's market share declines and its demand curve shifts downward. Therefore, in equilibrium in the long run (Fig. 10.4, b) price equals average cost, and each firm earns zero economic profit despite having monopoly power. Rice. 10.4. Equilibrium of a monopolistically competitive firm in periods: a) short-term and b) long-term This situation differs from the pure competition model in two respects. Firstly, in accordance with the condition of profit maximization, the price exceeds marginal costs (P > MS). Secondly, the contact cannot be at the point of minimum L GS, i.e. at the point M in Fig. 10.3. There is no limit to greedy striving... There is no outcome to unsuccessful work... There is no end and joyless path... God, be merciful to me, a sinner... Based on the study of long-term equilibrium, we can conclude that the optimality condition characteristic of the pure competition model is violated under monopolistic competition. This is explained by the following considerations. Firstly, because price exceeds marginal cost (P > MS), welfare losses (shaded area in Fig. 10.3) are similar to the pure monopoly model; Secondly, the zero profit condition leads to excess power, i.e. each firm operates below the minimum value ATS. Excessivepower:
a condition characterizing long-term equilibrium under conditions of monopolistic competition, in which the firm operates at a volume of output that is less than optimal, at which the minimum total average costs could be achieved. The existence of excess capacity implies that the cost per unit of production under monopolistic competition is higher than if the product were homogeneous. Does excess mean production capacity“inefficiency” of the monopolistic competition model? On the one hand, monopolistic competition leads to economic losses: a certain total output can be achieved at lower costs. The welfare losses that result from prices exceeding marginal costs are not easy to identify. Despite the loss of “dead weight” (shaded triangle in Fig. 10.3), Chamberlin expresses the conviction that monopolistic competition is more perfect market structure than pure competition. The presence of excess power or loss of efficiency is a kind of payment that consumers bear for differentiation goods and for that availability sources of supply provided by monopolistic competition. Let us now assume that the producer increased its output by one unit above the equilibrium value (Fig. 10.5). Curve dd
will move down: the output of all other producers increased, and prices decreased. Thus, a larger number of close substitute goods became available to buyers at a higher price. low prices. This reduction in price can be measured using the shaded area L.
Rice. 10.5. Welfare effects from increasing output when P * > tc The result of a price decrease consists of two opposing effects: a positive effect, or welfare gain (indicated by the letter G), and a negative effect, or welfare loss (indicated by the letter L).
Based on this, we conclude that an increase in output is economically justified if G
>
L,
i.e. to the point at which G
= L.
If this criterion is valid, then the efficient price must always exceed the marginal cost and monopolistic competition cannot be compatible with economic efficiency under conditions of pure competition. Section 10.5 presents an algebraic example in which the equilibrium condition of monopolistic competition is considered in more detail. The market is full of paintings, A. A. Voznesensky The monopolistic competition model does not consider how producers differentiate their products. However, many product differences can be measured quantitatively. Although the products are varied, most of their basic characteristics are quite comparable. Thus, the total price of a product can be broken down into several components: one price for each feature. A firm may try to improve its position by implementing product differentiation - adding or highlighting new product qualities and charging a higher price for its product. This concept was first proposed by Lester Tesler, 1 and its ideas in relation to the model of monopolistic competition by Calvin Lan Custer. 2 The Lancaster model has already been discussed in Chapter 4 (section 4.10). The model is based on the fact that the consumer derives utility from the characteristics rather than from the goods themselves, and is able to buy the most preferred set of characteristics, combining goods and services in a certain way. Lancaster's model is shown in Fig. 10.6. Let's pretend that Z%
and Z 2 along the ordinate and abscissa axes represent two characteristics of the quality of products of a monopolistically competitive group. Thus, the product of each firm forms attributive combination and is located on a separate ray emanating from the origin of coordinates: thus, four different products correspond to points A, B, C andD.
The graph illustrates a set of preferences: a buyer will purchase a single product only if his indifference curve (, because q°
accepted as standard; the angle of inclination of this curve is equal to b Curve DD
intersects the ordinate axis at the point A and has a slope - [(P 1)a + b], because q
= q° =
Q/
n
(Where Q
-
release of the entire group). Let the parameter values be equal: A = 200, a = 0,01, n = 101, b
=
1. Then the equations of demand curves can be expressed as follows: 2 Q DD:
p = 200 2
q
200 - dd: p=q.
Equilibrium condition.Curve PositionDD
in the short term it is fixed: there is no industry input or output. Moving along a curve DD
assumes the impact of 2 effects on the price of the product of a representative firm: the output of the firm itself (b= 1) and the release of its competitors [(PI) A= Curve Positiondd
is changing with group output volume: Increase the group's output shifts the demand curve of each member of the group downward. Rice. 10.7. Algebraic illustration of short-run equilibrium Curve position tg depends on the curve dd,
which means from q°.
In this case, the angle of inclination tg twice the inclination angle dd.
In our example: tg = 2q.
Let the curve ts expressed in linear form, for example: ts = 25 + 0.5q.
Each producer maximizes his profit (tg= ts), and the output is the same for all group members (q =
q°).
Let's equate ts And tg. 25 + 0,53
q.
We get: q* =
50. So, the system is in equilibrium at q*
50 ir*= = 100, as shown in Fig. 10.7. At q°
= q*
= 50 curve dd
representative company has the form: R= 150 q,
and the curve tg= 150 2
q.
At tg= ts we have: 150 2
q*
= 25 + 0,5<7*, или q*
50. Price/?* = 100 corresponds to the intersection of curves DD
(R= 200 2
q) Anddd(p =
= 1509). The short-term curve obtained in this way is also the long-term equilibrium curve if fixed costs are equal to 3125 den. units Since the curve ts is linear (ts= 25 + 0,5
q),
corresponding curves avc
And ate
can be represented as follows: avc
= 25 + 0.25 g, ate
= + 25 + 0,25<7. If q
= 50, ate
= 100 = p.
Economic surplus and efficiency. In Fig. 10.5 Welfare effects from increased output were measured using figures GhL.
Wherein G
represented the “gain” from expanding output, a L
-
the corresponding welfare "losses" caused by the downward shift of the curves dd.
Within the linear model used above, G
And L
can be represented as follows: G= (R
ts) dq = (p mr)dq= (bq)dq. L
= [(n
1) aq]
dq.
The equilibrium output is efficient if G ~
L,
If Kommersant= (p\)a. This condition is achieved when b
= 1, i = 101 and a = 0.01. Ferret married a rat Duopoly: Price leadership Oligopoly is a market structure in which a small number of sellers are opposed by many buyers. Perhaps few problems in microeconomic theory generate as much debate and disagreement as oligopoly. In real life, typical monopolistic industries are automobile, metallurgy, aluminum, chemical, etc. The fundamental difference between oligopoly and monopolistic and pure competition is that in an oligopoly there is only several rivals and therefore each company is obliged to take into account the reaction of other participants to its actions. The actions of any oligopolist in the industry have a direct impact on each of the rivals, i.e. firms in the industry are interdependent. Consider oligopoly as one of the four main market structures based on the structural variables given in the four previous chapters (Table 11.1). We already know that in the model of perfect competition the products are homogeneous, but in monopolistic competition they are heterogeneous (differentiated). In an oligopolistic model, products can be either homogeneous or heterogeneous. Table11.1
Opportunities for entering the industry also vary widely - from completely blocked entry to fairly free entry (depending on the characteristics of the strategic behavior of oligopolists). In the model of perfect competition firms pursue an optimal policy of behavior: when the market is in equilibrium, they have no reason to change the price or volume of output. When supply and demand are equal, the firm sells everything it produces and maximizes its profit. In the monopoly model The monopolist firm is in equilibrium under the condition M.R.
= MS. In this case, the monopolist maximizes its profit and also pursues optimal policy (from the point of view of the monopoly). In the oligopoly model The firm also tends to pursue optimal policies based on the actions of its rivals and assumes that other firms in the industry will do the same. This concept was first formulated by J. Nash (in 1951). EquilibriumNash:
Each oligopolist firm behaves in the best possible way given the behavior of its competitors. First of all, let's look at the conditions for the emergence of oligopoly. Everyone cut out for themselves N. V. Baytov Let's compare oligopoly with another major player in a market economy - a natural monopoly. A typical oligopolistic firm, one of the 500 largest national and multinational corporations in the world, is usually much larger in capital and geographic scope than a typical natural monopoly. It seems obvious that a firm that single-handedly dominates a market must be larger than one that shares the market with a few competitors. But exactly The size of the market, and not the absolute size of the company, determines and revealswhether the market is monopolistic or oligopolistic. For example, petroleum products can be transported at significantly lower costs (relative to the unit price of the product) than electricity or water; The oil industry is also oligopolistic. On the other hand, local power grids are almost always represented by a single seller and are a natural monopoly. The market for petroleum products is typically global, while the market for electricity is local. Rice. 11.1. Difference between natural monopoly (a) and oligopoly (b). Economies of scale determine the size of the firm, while market demand determines the number of firms In Fig. 11.1 compare market conditions leading to the formation of a natural monopoly and oligopoly. In Fig. 11.1, A, market demand curve (D)
intersects the long-run average cost curve (L.A.C.)
the only manufacturer to the left of the minimum point. The only enterprise in the industry with total average costs L GS, and output Q, at a price R g, can discourage potential competitors from entering the market. However, a natural monopolist will maximize profits based on conditions ATS 0(at MS a =M.R.),
by limiting the output to volume Q 0 and setting the price R t, what was discussed in chapter 9. Unlike a natural monopoly, an oligopoly is the “natural” result of a situation in which one firm experiences diseconomies of scale in attempting to dominate a market alone. At the same time, the minimum size of an efficient firm is quite large, so such a firm is a price setter. In Fig. 11.1.6 the market demand curve intersects the firm’s long-term average cost curve to the right of its horizontal section. If a firm with a short-run cost curve ATS X tried to serve the entire market, it would have to set a price to cover costs R or higher. The second company, building a smaller enterprise (for example, with costs ATS 0), gets the opportunity to become a potential monopolist by setting a price R Since the minimum production capacity to enter the industry is Q 0 , only a small number of firms are sufficient to produce the entire required volume (Ј Qo) at a price of zero profit (P 0). At the same time, the number of firms in the industry (n =Q^/"
L.Q.^)
turns out to be too small for price competition to lead to the establishment of the lowest price R. Competition among a small number of firms makes price fixing more attractive. A group of firms operating in an oligopolistic industry is able to limit output by Q^,
by setting the cartel price at R t. Entry into an industry can be difficult, although not completely blocked: economies of scale do not prevent entry into the industry, but can set an upper limit on the number of producers. A typical oligopoly produces a wide range of goods, selling goods that are by-products in production (gasoline and petrochemicals), by-products in consumption (TVs and VCRs) or similar products intended for different consumers (small, family and luxury cars). Product differentiation increases the difficulty of entry for those few sellers who must produce, sell, and advertise in many markets simultaneously. God sent me a wonderful dream: Nature has changed I look - from sunset to sunrise, In a single moment on the horizon: Two suns rise radiant In fiery amber porphyries. And over the resurrected earth The couple shone across the sky. S. P. Shevyrev (18061864) It is traditional to begin the analysis of an oligopolistic market structure with the simplest models of duopoly, i.e., a market in which two firms operate. If it's good here together, Rimma Chernavina The first theory of oligopoly was developed by a French economist and mathematician Antoine Augustin Cournot(18011877) in 1838 1 Cournot asked the question: what will happen if a second seller enters a monopolistic market in which a single monopoly firm previously operated? Can the emerging duopoly(industry with two sellers) achieve stable output at certain prices and production volumes? If so, is it possible to add a third seller to the industry, then a fourth, etc., until the monopoly turns into competition? Cournot looked at the market homogeneous product with two sellers (Fig. 11.2). As in conditions of pure competition, in a homogeneous oligopoly both sellers must establish single price: otherwise, a buyer can only be found by a seller offering a lower price. Let us assume that the market price R(and therefore the average income AK) is a linear function of total output: P=
a
b{
q,+
q2
),
(11.1) where ^ + q2
=
Q
- release of the first and second seller; Moreover, the marginal cost curve of each seller is horizontal: MS= k (k
-
constant). In the Cournot model, each duopolist assumes that in response to its actions the rival will not change its output (the rival’s production volume is a fixed value). 1 Rice. 11.2. Cournot model: a) output and expected price of seller 1 (former monopolist) and b) seller 2 (firm entering the market) Situation from the company's point of view 1. In Fig. 1
1.2, and seller 1 estimates his own average income function (AR t
= D ,) as: P=(a
bq*)
bq v
(11.2) assuming that seller 2's output is equal to q\.
The idea is that firm 2 gets the first q* 2
units of market demand, giving firm 1 the rest of the market to operate. Because (Abq* 2)
- the value is constant, the marginal income of seller 1 is equal to: " AR At M.R.
= MS= To
firm 1 will offer q*
units of release. Equilibrium market price P* of output
P
*
a
bq
\
bq
\
(11.4)
The situation from the company's point of view 2. While firm 1 is making a decision regarding its output (q\
product, and, based on this, determines its own demand function (average income AR2
=
D2
):
P = (a
bq\)
bq2
.
(11.5)
In this case, the marginal income of seller 2 is equal to: AR In Fig. 11.2, b shows that firm 2 produces q° 2 at the market price P°, if firm 1 produces the volume of output that seller 2 expects from it, i.e. q\.
In the Cournot model, price and output come into equilibrium only if each duopolist produces as much as his competitor expects from him (if q*
x
=
q°
v
q\=
q* 2 ,
uP°
=P*). Let's return to the premise that the market was originally a monopoly, i.e. q*
= O in Fig. 11.2,
A. Acting as a monopolist, seller 1 sets output at which M.R.{
= MS = k. Then, taking into account formula (11.3), we have: a2bq l k.
(11.7)
q l =(ak)/2b
(11.8)
P
a
b
[(
a
k
)/2
b
]
~ a + A;(And 9) Seller 2 will enter the market if the total income of firm 1 exceeds its total costs (TR{
>GS (), i.e. the market will demonstrate its attractiveness. VC l
kq l
(
l
/2
b
)(
ak
/2
P
)
1 Firstly, previously the relationship between price and marginal revenue (M.R.
R+ *dp) we have already considered more than once. Secondly, We know that dP/
dq t
dP/
dq2
b,
uTR l Pq r (^a + k)[(ak)/2b] = (l/2)(a 2 /2k"), seller 2 will have an incentive to enter the market if R 7, <
(1 / Ab) (a2
ak). 1
Cournot simplified the analysis by assuming that both sellers' fixed costs were zero. At any price above marginal cost, seller 2 has a tendency to enter the market. But the entry of seller 2 into the market contradicts the expectations of the former monopolist (seller 1). Figure 11.2 is constructed so that R°< Р*:
Expecting seller 1 to support monopoly output at q{
= (ak) / 2
b
(formula 11.8), seller 2 will determine his marginal revenue function as: M.R.2
(a +
k) 2
bq2
,
setting the volume of output based on the condition M.R.
= MS*= k,
or (a +k) 2
bq2
= To. 2
bq2
= a or q2
= a /Ab.
When the output of seller 2 is added to the output of the previous monopolist (seller 1), the market price will inevitably fall. Seller 1's expectations of a monopoly price are in conflict with reality, and his output must be adjusted to the new situation. In the Cournot model, the adjustment of output to unexpected changes in market demand (due to which other sellers do not produce their given issue) determines reaction function each seller. FunctionreactionsCournot[q*,= R,(q t)]
- a curve showing what volume of products will be supplied to the market by one duopolist (/) for each given volume of products supplied by another duopolist (y). The reaction function of seller 1 is derived from the profit maximization rule M.R.{
= MO. (Abq2
)
2
bq x
= k.
Let's define q{
:
q r
(1/2)
(a
k
bq2
).
Thus, under duopoly conditions, the reaction function has the form: 1 This result was obtained as follows. Economic profit for seller 1 is expressed as follows: RPq{
(V.C. +
F.C.)
t >
FCy
Replacing the monopoly parameters with qi
And R, we'll get Pq t
= (1 / 2a +k) [(Ak) / 2
b]
a2
/ 4
b
ak
/ 4
b
+
ak
/ 2
b
k2
/ 2
b
= (a2
+
ak
2
k2
) / 4
b.
VC i
kq l
(1 / 2
b) (a
k)
k
= (2
ak
2
k2
) / 4
b.
It follows that Pq t
US, > FC V
If F.C.{
< (a2
ak) / 4
b.
9
*(a*
ty).
(11.10) At D 2= 0, =
(1 / 2
b) {
a
k)
a situation of monopoly release arose. However, the entry of seller 2 into the market leads to a decrease in the output of seller 1 by V 2 units from each unit of output produced by seller 2, i.e. D9 1 /D? 2 (1/2)(*)1/2. When seller 1 changes its output, seller 2 obtains a new profit-maximizing quantity according to the reaction function that is derived from the solution M.R.2
= MS. Firm 1 reaction function: U
kg
Equilibrium CournotNash (C
N)
Firm 2 reaction function: q* 2
gtaj) Rice. 11.3. Cournot duopoly model "a) duopoly reaction functions and Cournot “solution”; b) output and prices under conditions of monopoly, competition and duopoly Release rules for q2
are: (Abq t)
1
bq2
= k,
where q2
=
(1 / 2) (Ak
bq x).
Because Aq2
/
D(b)
=* 1/2, then the second seller will increase his output by 1/2 unit for each unit of decrease in the output of seller 1. RuleduopoliesCournot:
if seller 1 reduces its output by one, then seller 2 will increase its output by half a unit (and vice versa). This process of adjusting one seller's output to another seller's change in output is expected to bring total output and the resulting price to a stable equilibrium. 1 The graphical solution of the Cournot duopoly is shown in Fig. 11.3, A. ak q i = Hb~" At2
b) (Ak bq 2) And q 2(1 / 2b) (a k bq x) we have: H + I 2 2
q"~"2
b 2* + < b =2 T ; «" Equilibrium outputs of duopolists: _ a
k
_, a
k The equilibrium outputs of duopolists are the coordinates of the Cournot-Nash equilibrium point (point C
N).
Thus, The total equilibrium output under duopoly is equal to: a*=(?* 1 +?* 2)=^~. (clause 12) As shown in Fig. 11.3, b,equilibrium duopoly Cournot price(R) less than the monopoly price (R t), but more than the price of marginal costs, i.e., competitive price (R.). 1 An important achievement of A. Cournot is that he revealed the very problem of duopoly. He also showed that a number of assumptions that determine the equilibrium solution can be transferred from the duopoly model to the oligopoly model itself. Let us summarize the main parameters of the Cournot model in table. 11.2. If you ask the question what will happen if the duopoly market enters third seller (duopoly will turn into “triopoly”), then, using the reasoning given above, we get the following result: 3(a
k)
1 If sellers 1 and 2 collude, the monopoly price will require limited output at which the industry's marginal revenue equals (total) marginal cost. Condition M.R.
= MS leads to the fact that A 2
bq
= k,
or q
= (A k) / 2
b
=
q{
+
q2
,
And P_ =
a
b 2
b a +
k If output (and therefore profit) is divided equally between two firms, then q{
=
q2
=
= (ak) / 4
b.
Let's place this output in the firm's reaction function and make sure that monopoly output does not correspond to the Cournot equilibrium: a, =b(akbu,) =- (akb) = - ">
. 41
2
*¦>" 2b
Ab" 8b
4b If one seller's output corresponds to a monopoly, then the second seller produces more than its cartel quota, thereby reducing the price below the monopoly level. In Cournot equilibrium, the duopoly price R is determined by substituting industry output into the average industry revenue function: f,2
a2
k. 3
k +
a
which is less than R, and more marginal costs until a >k.
Table 11.2 From this it is easy to conclude that with the increase in the number of firms (P) in the industry, the output of each individual firm will decrease, and the overall output of the industry will increase: a
k
n Q. "*¦- X ^TT("
is)
Therefore, it can be argued that the Cournot model predicts that total output will approach the output of a perfectly competitive industry when the number of its subjects is sufficiently large. The same thing happens with the price: .
a
k.,
n.
P =
a
bQ =
a
b
(-G)(-G). which after simplification gives: n+\ n+\ With growth P magnitude [a/ (n+\)] decreases infinitely, a [
kn/ (n+1)] approaching k,
i.e. to marginal cost (MS). Divided into First and Second, In 1934, the German economist Heinrich von Stackelberg attempted to improve the Cournot duopoly model. The novelty of the model was that in it duopolists can adhere to two different types of behavior: (a) strive to be leader or (b) stay follower This marked the beginning of a model based on price leadership. 2 If a follower of the Stackelberg model adheres to the assumptions of the Cournot model - follows his own response curve and makes a decision on release, assuming the opponent's output is given, then the leader knows the follower's response curve and takes it into account when developing his own strategy, acting like a monopolist. Thus, the Stackelberg model assumes the possibility of the existence of four combinations of two types of behavior (Table 11.3) Table 11.3 In the first two cases, the behavior of duopolists is stable: one firm is the leader, the other is the follower. In the third case, we have a typical Cournot model (as a special case of the Stackelberg model). In the fourth case, the outbreak of a price war is inevitable, which will continue until one of the duopolists renounces its claim to leadership, or the rivals enter into a conspiracy. Let us consider situation 1 (2), since it is precisely this that represents the Stackelberg model in a state of stable equilibrium. The leader's profit function is equal to the product of the price of his products (formula 11.2) multiplied by output: ni
=
p^1 ~kQi
=
(a~
H>_6< 7 i)? i _ k(iv
In this formula q2
represents the reaction function of the second firm (Formula 11.10). Substituting its value into our profit formula, we have: "
a
k
bqA a
k J
Equating the derivative of this expression with respect to q l
zero, we have: a
k Then the equilibrium price is: , ^ , 3(ak)a + 3k
,.
l.^
P=abQ=ab
v "
=--
. (11.19) ¦ leader's profit: *.=?;
("go) {
a
k?
¦ follower profit: (a
k) 2 So, The follower's profit is half that of the leader. It remains to consider the last, fourth combination of behavior of the Stackelberg model, in which both firms strive to become leaders. This is quite simple to do: it is enough to substitute the values of the optimal output into the already well-known linear demand function both leaders: .akak s. " We got an interesting result: in the case of a price war, price equals costs, i.e., the economic profit of duopolists is zero, which is incompatible with the oligopoly model. Of course, this would be the best option for buyers. But for oligopolists it is unacceptable - this is the worst result for them (it is better to enter into an agreement with a competitor or at least accept the fate of a follower). Let's summarize. The equilibrium parameters of the Stackelberg model can be summarized as follows (Table 11.4). The Cournot and Stackelberg models are alternative cases of oligopolistic behavior. Which one best describes reality depends on the industry. For an industry consisting of firms of approximately equal size, the Cournot model is probably more appropriate. In industries where one large firm dominates, the Stackelberg model may be more realistic. Table 11.4
Basic equilibrium parameters of the Stackelberg model Release Profit Marketprice leader afterbirthmaker industry leader afterbirthmaker industry 3(ak) Ab (ak?166
3(ak) 2 166 (a + 3k)A The butcher was always humble before Shakespeare and took off his hat, but had no respect for him in his soul: after all, Shakespeare, without a doubt, was ignorant in the mystery of market prices. In 1883, the French scientist J. Bertrand (1822-1900) criticized the Cournot duopoly model, saying that price, not output, was the main strategic variable of the company. According to Bertrand, each firm sets its own price based on the assumption that the rival’s price will remain fixed, i.e., not output, but the price set by the firm is a constant parameter for the duopolist. As in the Cournot model, the position of duopolists in the Bertrand model is symmetrical: selling at a price lower than a competitor will be the choice strategy for both firms. It is obvious, therefore, that the process of price reduction by one and the other firm can continue until the equilibrium price becomes equal to the marginal cost (P* = MS). In Fig. Figure 11.4 shows the reaction function of the Bertrand model. FunctionreactionsBertrand[
P*
i =
R(P t)]
- a curve showing at what price the product will be supplied to the market by one duopolist (/") for each given price of products supplied by another duopolist (y). In this case, two firms sell goods, the demand for the products of each of them depends on its own price and the price of its rival. Duopolists choose prices simultaneously, but each perceives the rival's price as given. Firm 1 reaction curve [
R^
P.J.]
shows the profit-maximizing profit of firm 1 as a function of the price set by firm 2. The reaction curve of firm 2 has the same meaning. Firms can reduce the price to the Bertrand-Nash equilibrium point (B
N),
at which price equals marginal cost and economic profit becomes zero. Let us now summarize the data in the table. 11.211.5 together in order to compare the results of the Cournot, Bertrand and Stackelberg duopoly strategies. To these we add another strategy of duopoly: the strategy of collusion to create a joint monopoly (Table 11.6). Rice. 11.4. Bertrand model reaction functions Table 11.5 Table 11.6 As this table shows, the most profitable strategy for duopolists would be to create a joint monopoly through collusion, since the total profit obtained from this strategy is the highest. In second place (from the point of view of obtaining the maximum total profit) is the Cournot model, in third place is the Stackelberg model. In Bertrand's model, oligopolists do not receive positive economic profits (as in a situation of pure competition). I was looking for an answer S. Misakovsky In 1939, Harvard economist Paul Suisy proposed the following explanation: apparent price inflexibility in industries with few sellers. Rivals react differently to upward and downward price changes. If the company A will raise the price of its products, the company IN receives new customers that firm L will lose from a price increase. If, on the other hand, the company A will lower the price of its products - the company IN will lose some of its customers. Every company strives to avoid losses. If the reason for the loss of profit of the company IN was a reduction in the price of goods by the company A, then it is natural to expect from the company IN similar to a price reduction. From the company's point of view A this means that if the price of its product increases, it should expect to lose some of its customers to rivals (so the firm's demand curve A elastic when price increases). But if the company A will lower the price of its products, it should not rely on poaching customers from competitors, since they will also be forced to lower prices (the firm's demand curve A inelastic when price decreases). 1 The Suizy hypothesis is expressed using the following premises: The logical consequence of these premises is model of broken demand oligopoly, shown in Fig. 11.5. Let firm L produce the volume of output O per unit time at the equilibrium market price R. At point (P 0, Q^) two curves intersect: line D0
is a demand curve of the type ceteris
paribus.
It reflects the property of constant prices of competitors when increasing company prices A. Line D x
is a demand curve of the type mutatis
mutandis.
It reflects the property of rivals changing prices following reduction prices for its products by the company A.
Demand curve ceteris
paribus
D 0 is more elastic than the demand curve mutatis
mutandis
D v
As a result, the overall oligopoly demand curve (abc)
has a broken appearance. ft
About QoQi ~ ? Rice. 11.5. Bent oligopoly demand curve What should an oligopolist do, given such a demand line, to maximize its profits? The answer is known: equalize marginal revenue with marginal costs (M.R.
= MS). However, the shape of the marginal revenue curve (adef)
is even more unique: it is not only broken, but also with a discontinuity (which is explained by the presence of different slopes of the curve abc).
Gap in the curve M.R.
allows the company to significantly change costs (from M.C. Q
before MS X without changing the profit-maximizing level of output. However, in general, the fate of this seemingly original and interesting concept is not very happy. An empirical test of the oligopoly demand curve model cast doubt on the fact of its kink. In addition, there were reproaches that the model does not explain the initial occurrence of the “breaking price” R Why is this price located exactly at this level, and not higher or lower? In 1982, one of the most irreconcilable critics, J. Stigler, expressed the opinion that the broken demand model does not reflect anything at all, and its presence in microeconomics textbooks is explained by the conservatism of the authors. Let's not rush. In any case, the broken demand model can be useful for explaining situations in new oligopolistic industries, when rivals do not yet know each other well, or in the case of newcomers joining the industry, about whom little is also known. When a doctor and a priest strengthen an alliance with a judge, then the work is not in vain: They will cleanse you, kill you, and sing you out in no time for the sake of money. The strategy of oligopolists, with all its diversity, has two poles: rivalry and collusion. If oligopolists collude, they can agree and act as a single monopoly, jointly maximizing industry profits. On the other hand, they may compete with each other for a share of the industry market. Industry equilibrium under collusion. When oligopolists collude, they may agree on prices, market shares, advertising costs, etc. A formal agreement among oligopolists is called cartel. A cartel is able to maximize profits if it acts as a monopoly, that is, if the cartel members act as one firm. A similar situation is shown in Fig. 11.6. The general market demand curve corresponds to the market curve M.R..
Curve MS cartel is the horizontal sum of the curves MS its members. Profit is maximized at output Q*
and price R* at MS =M.R..
However, having agreed on a cartel price, cartel members can compete with each other using non-price competition for receiving a larger share of sales Q*.
Rice. 11.6. Profit-maximizing cartel If, on the other hand, the cartel members agree among themselves to divide the market, then each of them will receive the corresponding quota. Tacit collusion: price leadership. Since many countries have anti-cartel legislation in the name of combating monopolization, firms can enter into silent agreement. One form of tacit collusion is price leadership. The leader may be the largest firm in the industry. This situation is known as price leadership of the dominant companyacceptance. If the price leader is a firm whose behavior deserves the trust of other members of the oligopoly, then this situation is called priceleadership of the companybarometer All other firms in the industry are called horse-drawnrental environment. At price leadership of the dominant enterprise The leader maximizes profit based on the equality of his own marginal costs and marginal revenue. In Fig. 11.7, A The curves of market demand and supply of the competitive environment are shown. Firms in a competitive environment, like firms in perfect competition, take the price (set by the leader) as given. The leader's demand curve is the portion of market demand minus the competitive demand curve. At a price R ( all market demand is satisfied by the competitive environment and the demand for the leader's products is zero (point A). On the contrary, at a price R 2 all market demand is satisfied by the leader, and the demand for products of the competitive environment is zero (point b). MS leader S competitive environment S competitive environment Rice. 11.7. Price leadership of the dominant enterprise: a) division of the market between the leader and the competitive environment; b) determination of price and output The leader's profit will reach its maximum when the marginal cost of its production equals the marginal revenue. This state corresponds to the leader release point (q L)
and the price he set (P L).
The competitive environment will perceive this price as given and will produce Q F
products. The total output in the industry will be equal to Q T.
Factors contributing to collusion. Collusion between firms is more likely when the firms know each other or the leader well and when they trust each other. Among the factors contributing to collusion are the following: Breaking up the conspiracy. In a collusive situation, there is always a temptation to violate quota agreements or reduce prices. Let's imagine a cartel consisting of five identical firms (Fig. 11.8, A). Let the equilibrium price be 10 den. units, and the equilibrium volume is 1000 units. with a quota of 200 units for each company. Rice. 11.8. The tendency of a firm to increase production above quota or to reduce the cartel price Now let's look at Fig. 11.8, b. It illustrates the situation of one of the cartel participants, the company A. Cartel price of 10 den. units equals, moreover, the marginal revenue for an individual firm. This will create a desire for members of the firm to produce more than quota. The firm will maximize its profit by selling 600 units. goods at MS = P =M.R.,
taking away market share from other cartel members but leaving the industry's overall output unchanged. On the other hand, the company A may be tempted to reduce the selling price of its products below the cartel price. Having a fairly elastic demand curve (AR
in Fig. 11.8, b), The firm can reduce the unit price to 8 deniers. units when selling 400 units. products. Naturally, in response to these violations of collusion, other members of the cartel can take countermeasures, which is fraught with the outbreak of a price war. Poetry? This is a hobby. Basil Bunting (1900-1984) No matter how attractive the outcome of a conspiracy may be for its participants, it turns out to be difficult to maintain it - after all, what benefits one firm often harms other firms. The problem of confrontation between colluding oligopolists is reminiscent of prisoner's dilemma. The essence of this dilemma is as follows. Two prisoners are being held in separate cells for a serious crime. However, the prosecution does not have sufficient evidence (the evidence is only enough for a year in prison). Each prisoner was told that if he confessed and the other did not, the first would be released and the second would receive 20 years. If both confess, then each will receive 5 years (Table 11.7). Situations like the prisoner's dilemma can be analyzed on the basis of mathematical game theory, developed by J. von Neumann and O. Morgenstern back in the 1940s. 1 Table 11.7 A prisonerY Confession
Silence Confession Prisoner X Silence In table Figure 11.8 depicts the consequences of two advertising strategies for two sellers. When implementing the current advertising strategy, each company receives 100 million rubles. profits from the sale of durable goods (such as cars). Firm L believes that if it increases its advertising budget by 20 million rubles, it will take over part of the firm's market IN and will increase its revenue by 40 million, receiving 20 million net profit. This transfer of profits from the company IN to the company A will happen if the company's advertising budget IN will remain unchanged. Likewise, if the company IN will increase its advertising costs by 20 million compared to the company's expenses A, then the company IN will receive 40 million additional revenue and 20 million rubles. additional profit. 1 Table 11.8
shows that the simultaneous increase by two companies of their budgets by 20 million rubles. will lead to a decrease in profits. Maximum total profits will be achieved if both firms maintain their current advertising budgets. Table 11.8 Keeping it flowing Increase in budget total budget that for 20 million rubles. Save current A = 100 million R. A = 120 million R. strategy B = 100 million R. B = 60 million R. seller IN Budget increase A = 60 million R. A = 80 million R. pa 20 million rub. V = 120 million R. B = 80 million R. The worst solution would be for each company to independently formulate the advertising budget (in the absence of collusion). 1 The price elasticity of a firm’s advertising activities can be defined as ts m= = (dQ ,/&4,) (A
J
Q),
and the cross elasticity of advertising as r | iA = (EO / d(U). Therefore, the percentage change in firm income i
as a result of a 1% change in its advertising budget (at constant prices) is equal to: dAJA, ~ dA, "p&"qSa h^"aA, ^ L * dA J /A J where in "*" dA t /A,
"
Not enough pretzels.
I doubt it won't be enough.
But there is still a possibility.
The old pastry chef died. But
His disappearance is unlikely
Someone other than your loved ones will notice
And maybe one old lady
From our cafe “Vec Riga”. 1 (1969)Key Concepts
10.1. "Industrial group": uniformity and symmetry
I am a double to everything around me! I am a double to everyone around!
Leonid Aronzon (19391970) Translation by R. McKane
Structural variables of monopolistic competition10.2. Short-term and long-term equilibrium
Mei $ ov 5 Tinas mvq ЕХХ^ш Нап0И; just like before>
laAiv eq shrhl? We, the beautiful Hellas happy people,
Flo? hgLso kt aiuuusotsL Shed cheerful meekness into our hearts!
Tivi lraotera Kepaaov tov vow The entire market is 1IM to the top,
Km ttiv ayopav 4 niv aya 9 cov Rush with apple, onion, tops,
EtslHoelUsi, to Meyapcov CKopoScov, Cucumbers, pomegranates, evil garlic,
ZvKUCOv jipaxov, m Xw, pouov, Small shirts for slaves.
DoiLoyuch xAaviCKiovcov niKpcov Let us see the Boeotians again/
Km Boicoxcov ye cpepovtaa iSeiv with partridges| with quacks, with a goose, with a sheep,
Km Kepi tautq nnaq aOpoouq Let them bring Kopai eels in baskets,
Och/ covouvtaq tirraSeovsh And all around we T0LPIMS| they are homonymous,
Morikhso, TeHea, GHaikett, aUoiq We tear it out of our hands and bargain. Huddle up to the trays
Tevemq poHHosch kata MeXav 9 vov Famous delicacies: Morih, Telei
HKeiv wrepov gsht 4 v ayopav, and Glavket. Finally, Melanphius is coming:
Taq 5 e yaeyara59t... He comes to the market later than everyone else, Alas!
Aristophanes (446385 BC) Sold out...
10.3. Efficiency of monopolistic competition
L. A. May (18221862)
10.4. Competitive markets for product attributes
All with swans and rainbows.
And Vanka is an avant-garde artist
All cubes and squares.
Vanka - avant-garde artist
He aims everything with a sniper's squint.
He knows the neophytes
savings book appetites,
Foolish businessman,
Antichrist of a new type. (1971)
R 200Test tasks
Review questions
TaskChapter 11 Oligopoly
And the rat took the ferret.
And the ferret did it to Alice
Presentation in four stalls.
And life flowed miraculously,
She and he shine:
For every bottle of beer
They are asking for millions.
(1995)
Nikolay TryapkinKey Concepts
Structural variables of oligopoly11.1. Economies of scale and oligopoly
For a huge piece:
There's jam and meringue,
And rough white cream.
Everyone thinks: I’ll eat
And, having had enough, I fall asleep,
And your sweet dream
I won't share it with anyone.
11.2. Theories of classical duopoly
Flows to meet each other.
Everything breathes double life:
Two suns reflect the waters,
Two hearts beat in the chest of nature -
And the blood flows like a double key
Through the veins of God's creation,
And the double world lives -
There are two moments in one moment. (1827)11.2.1. Cournot theory
How good it is to be alone here. (1994)
MR l P+J^q i = (abq* 2)~bq i bq i = (abq* 2)2bq i .
(11.3)
MR 2= P + Iq~ 2?2 "(" SCH) 2bqr
(11.6)
ak 3 ak 1 ak
Basic equilibrium parameters of the Cournot model 1
11.2.2. Stackelberg theory
We sometimes don't think ahead of time,
What's First -
An unknown path to create,
Second -
Just compact the road,
That the First live by one impulse,
Well, the Second... They look businesslike. (1968)
V. A. Lakhno
Possible combinations of behavior in the Stackelberg model
i, = - P121 4)
P = a " b(2b + ^b) = k
t 11" 22)
11.3. The price problem of oligopoly: the Bertrand model
Thomas B. Aldrich (18361907)
Basic equilibrium parameters of the Bertrand model
Comparison of duopoly models
11.4. Broken demand model
To the question.
I barely found it
- the answer became a question. (1982)
11.5. Rivalry and collusion
FranciscoA. Figueroa (17911862)
a) „w / b)
RA
11.6. Game theory and its application in advertising activities
I breed pigeons.
And Mr. Smith embroiders with garus.
This is not a job. You don't sweat.
You don't get money.
I would take on soap advertising.
Prisoners' dilemma
This concept can be used, for example, in the advertising strategy of an oligopoly. In an oligopoly, product differentiation and sales rivalry can cause excessive increases in advertising costs. The company is able to optimize these costs based on game theory.
Non-price competition of a monopoly: profit from advertising strategy
Test tasks
Review questions
ProblemsFordiscussions
Task
each firm is equal to: C = 100 + 10 Q, i
=
1.2 (where MC t
= 10). Find:
the belief that another seller will not change the release);
firms colluded.