Duopoly. Firm behavior in a duopoly. Cournot model Behavior of a monopoly firm in the short and long run

Cournot's Assumptions:

Firms produce homogeneous goods

Firms know the market demand curve

Firms make decisions about the volume of production simultaneously, independently and independently of each other.

When deciding on the volume of production, firms consider the production volume of their competitor to be known and complete.

CURNOUGH EQUILIBRIUM - is achieved in the market when, in a duopoly, each firm, acting independently, chooses such an optimal volume of production that the other firm expects from it. The Cournot equilibrium occurs as the intersection point of the response curves of two firms.

9. Cournot model: the behavior of a duopolist firm in the short and long run.

§ Cournot Antoine Augustin (1801-1877), French economist, mathematician and philosopher, predecessor mathematical school bourgeois political economy. In his "Investigations into the Mathematical Principles of the Theory of Wealth" (1838), he attempted to investigate economic phenomena using mathematical methods. He was the first to propose the formula D = F(P), where D is demand, P is price, according to which demand is a function of price.

The Cournot model assumes that there are only two firms in the market, and each firm assumes that the competitor's price and output remain unchanged, and then makes its own decision. Each of the two sellers assumes that its competitor will always keep its output stable. The model assumes that sellers do not find out about their mistakes. In fact, these sellers' assumptions about the competitor's reaction will obviously change when they learn about their previous mistakes.

Cournot model

Rice. Cournot duopoly model

Let us assume that duopolist 1 starts production first, which at first turns out to be a monopolist. Its output (Fig.) is q1, which at the price P allows it to extract the maximum profit, because in this case MR = = MC = 0. With a given volume of output, the elasticity of market demand is equal to one, and total revenue will reach a maximum. Then duopolist 2 starts production. In his view, the output will shift to the right by Oq1 and will be aligned with the line Aq1. He perceives segment AD" of the market demand curve DD as a curve of residual demand, which corresponds to his marginal revenue curve MR2. The output of duopolist 2 will be equal to half of the demand unsatisfied by duopolist 1, i.e. segment q1D", and the value of its output is equal to q1q2, which will give opportunity to maximize profits. This issue will be a quarter of the total market demand at zero price, OD "(1/2 x 1/2 = 1/4).

In the second step, duopolist 1, assuming duopolist 2's output remains stable, decides to cover half of the still unsatisfied demand. Assuming that duopolist 2 covers a quarter of the market demand, the output of duopolist 1 at the second step will be (1/2)x(1- 1/4), i.e. 3/8 of the total market demand, etc. With each successive step, the output of duopolist 1 will decrease, while the output of duopolist 2 will increase. Such a process will end in balancing their output, and then the duopoly will reach the state of Cournot equilibrium.

Many economists considered the Cournot model to be naive for the following reasons. The model assumes that duopolists do not draw any conclusions from the fallacy of their assumptions about the reaction of competitors. The model is closed, i.e. the number of firms is limited and does not change in the process of moving towards equilibrium. The model says nothing about the possible duration of this movement. Finally, the assumption of zero transaction costs seems unrealistic. Equilibrium in the Cournot model can be represented by response curves showing the profit-maximizing outputs that one firm will produce given the competitor's outputs.

On fig. 34.2, the response curve I represents the profit-maximizing output of the first firm as a function of the output of the second. Response curve II represents the profit-maximizing output of the second firm as a function of the output of the first.

Rice. 34.2. response curves

Response curves can be used to show how equilibrium is established. If we follow the arrows drawn from one curve to the other, starting with output q1 = 12,000, then this will lead to the realization of the Cournot equilibrium at point E, at which each firm produces 8000 products. At point E, two response curves intersect.

Duopoly (from Latin duo - two and Greek pōlēs - seller)

a term used in bourgeois political economy to refer to the market structure of a branch of the economy in developed capitalist countries, in which there are only two suppliers of a certain product and there are no monopolistic agreements between them on prices, markets, production quotas, etc. The concept of market 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 of the early 20th century. The second form is the modern mass production market, which is also dominated by two companies. Between them there is usually a tacit agreement 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 in the initial period of production of a new product and a "trial of strength" of two suppliers, or as a state of fierce competition in 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, on the other hand, consider debt a kind of monopoly (which is true).

The economic and mathematical study of dialectics began as early as the 19th century. A. Cournot, J. Bertrand (France) and F. Edgeworth (Great Britain). In the 30s. 20th century G. Shtakkelberg (Germany) characterized certain types of diocese that depend on the behavior of duopolists. The modern theory of marketing was formed under the influence of the theories of monopolistic competition by E. Chamberlin (USA), imperfect competition by J. Robinson (Great Britain), and the work 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 in assets, differences in the types of D. and market institutions, the level of information about the market, etc.).

Lit.: Chamberlin E. Kh., Theory of monopolistic competition, trans. from English, M., 1959; Zhams E., History of economic thought of the twentieth century, trans. from French, Moscow, 1959; Seligman B., The 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 good or service and many buyers. In practice, the profits that can be made from this form of imperfect competition are usually less than... Glossary of business terms

A type of industry market where 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 received if two ... ... Financial vocabulary

- (duopoly) A market in which there are only two sellers, each of which must take into account the possible responses 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, markets, quotas, etc. This situation was theoretically ... ... Wikipedia

duopoly- The situation in the market, where there are only two manufacturers offering one product. [JSC RAO "UES of Russia" STO 17330282.27.010.001 2008] duopoly A market mechanism in which two sellers of the same product operate (this rather abstract ... ... Technical Translator's Handbook

- (from Latin duo two and Greek poleo I sell) an economic term that denotes an economic structure in which there are only two suppliers of a certain product that are not interconnected by a monopolistic agreement on prices, markets, quotas, etc ... Big Encyclopedic Dictionary

Duopoly- a market mechanism in which two sellers of one product operate (this rather abstract case is often used, due to its visibility, when modeling market processes). D.'s analysis, bearing the name of O. Cournot and proposed by him in ... ... Economic and Mathematical Dictionary

duopoly- Exclusive control of the supply of products to a particular market and service by two suppliers who dominate that market and thus determine the prices and scope of supplies ... Geography Dictionary

Duopoly- (from lat. duo two + gr. poleo sell; eng. duopoly) a situation in which there are two manufacturers on the commodity market offering identical products (goods) ... Encyclopedia of Law

AND; well. [from lat. duo two] A market dominated by two sellers of a particular product or service that are not bound by agreements on prices, markets, etc. * * * duopoly (from Latin duo two and Greek pōléō I sell), an 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, markets, quotas, etc. This situation was theoretically ... ... Big Economic Dictionary

Books

• Microeconomics for advanced. 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, ...

Duopoly A market structure in which two sellers, protected from additional sellers, are the only producers of a standardized product that has no close substitutes.

Duopoly models provide an illustration of how an individual seller's proposals for a rival's response affect equilibrium output. The Cournot duopoly model assumes that each of the two sellers assumes: that its competitor will keep its output unchanged, at the current level.

The Cournot model is based on two main assumptions about the behavior of a firm in a duopoly: first, each firm is aimed at maximizing its profit; and secondly, each of the firms assumes that if its own output changes, the other firm will maintain its output at a substantial level. Under these conditions, achieving equilibrium in the market will look like in the following way. Let's assume that there are only two sellers ("A" and "B") of an identical product in the region. Entry to the market of this product is not possible for other sellers. Assume that both sellers can produce this product at the same cost. Let us assume that firm A starts production first, owns the entire market, and assumes that there will be no rivals in the market. In this case, firm A behaves like a monopoly, and therefore both its volume and price are monopoly. Immediately after Firm A begins production, Firm B appears. Other firms are not expected. Firm "B" assumes that firm "A" will not change the achieved volume of production and sales. Firm "B" will increase the market supply, which will cause a decrease in the price of this product. Firm B will increase its output every period, and Firm A will decrease its output every month. The final equilibrium output of each firm will reach 1/3 of the competitive output. The total market output is equal to 2/3 of the equilibrium competitive output for a given demand for the good. Consequently, the process of achieving equilibrium in the market is as follows: one of the enterprises chooses the volume of output that maximizes its own profit, then the second enterprise, assuming that the level of output remains unchanged, determines its own profit-maximizing sales volume. This market adjustment process goes through several "action and response" stages until firms reach equilibrium. This is the Cournot equilibrium for a duopoly.

Cournot equilibrium- this is a non-cooperative equilibrium: each firm makes decisions that give the greatest possible profit from the given actions of its competitors. Equilibrium in the Cournot model can be represented through response curves. The response curve shows the maximizing output that will be produced by one firm given the output of another rival firm.

The Cournot model establishes a direct relationship between the performance of industries, as measured by the difference between price and industry-weighted average marginal cost (MC), and the level of market concentration, as measured by the Herfind-la-Hirschman index:

where: H is the Herfindahl Hirschman index, an indicator that determines the degree of market concentration . (2.22)

where. S1 is the market share of the firm providing the largest volume of supplies; S2 is the market share of the next largest supplier firm, etc.

Therefore, the underlying Cournot model predicts a tendency for price to fall towards marginal cost as the number of sellers increases (i.e., in an industry with less concentration, prices are more likely to be closer to what would have been the result of competition). Addition of conjectural changes ranks oligopolistic pricing schemes from competitive to monopoly.

The main problem in defining the pricing situation in an oligopolistic market is to better understand the determinants of assumptions about the behavior of firms in specific conditions. Game theory is recognized as the main tool for solving this problem.

In the Cournot duopoly, the marginal cost of each firm is constant and equal to 10. Market demand is determined by the ratio Q = 100 - p.

a) Determine the best response functions for each of the firms.

b) What is the output of each firm?

Compare the aggregate output of a Cournot duopoly with that of a cartel.

Give a graphic illustration: designate the Cournot-Nash point, the points at which the firm has monopoly output and competitive output.

Solution

where: Q = q1 + q2

P = a - (q1 + q2)

Duopolist profits:

P \u003d TR - TS \u003d P * Q - C * Q

P \u003d (a–bQ) * Q - C * Q \u003d aQ - bQ 2 -CQ

P1 \u003d aq 1 - q 1 2 - q 1 q 2 - cq 1,

P2 \u003d aq 2 - q 2 2 - q 1 q 2 - cq 2.

Profit maximization condition:

1) (aq 1 - q 1 2 - q 1 q 2 - cq 1) I = 0 2) (aq 2 - q 2 2 - q 1 q 2 - cq 2) I = 0

a - 2q 1 - q 2 - c \u003d 0 a - 2q 2 - q 2 - c \u003d 0

a \u003d 2q 1 + q 2 + c a \u003d 2q 2 + q 1 + c

q 1 \u003d (a - c) / 2 - 1/2 q 2 q 2 \u003d (a - c) / 2 - 1/2 q 1

Find the equilibrium volumes according to Cournot:

q 1 * \u003d (a - c) / 2 - 1/2 * ((a - c) / 2 - 1/2 q 1)

¾ q 1 \u003d (a - c) / 4

q 1 * \u003d (a - c) / 3 \u003d (100 - 10) / 3 \u003d 30 units of production

P \u003d a - 2 (a - c) / 3 \u003d (a + 2c) / 3 \u003d (100 + 2 * 10) / 3 \u003d 40

cartel collusion:

TR \u003d P * Q \u003d Q * (100 - Q) \u003d 100Q-Q 2

MR = 100 - 2Q = MC

P=100-45=55, hence q= 45/2 = 22.5 units.

Problem 3 (Cournot and Stackelberg duopolies)

Two firms produce the same product. For both firms, marginal costs are constant, for firm 1 they are equal to TC 1 = 20+2Q per piece, and for firm 2 they are equal to TC 2 =10+3Q per piece. There is a reverse demand function for bread p \u003d 100 - Q, where Q \u003d q 1 + q 2.

a) Find the firm 1 response function.

b) Find firm 2's response function.

c) Find the output of each firm in the Cournot equilibrium.

d) Find the output of each firm in the Stackelberg equilibrium, considering firm 1 as the leader and firm 2 as the follower. Count your profits.

Solution.

P 1 \u003d TR 1 - TS 1 \u003d Pq 1 - 20 -2q 1 \u003d 100 q 1 - q 1 2 - q 1 q 2 - 20 -2q 1,

P 2 \u003d TR 2 - cq 2 \u003d Pq 1 - 10 -3q 1 \u003d 100 q 2 - q 2 2 - q 1 q 2 - 10 -3q 2.

Profit maximization:

100 - 2q 1 - q 2 - 2 = 0,

q 1 * \u003d (98 - q 2) / 2 \u003d 33 units.

100 - 2q 2 - q 1 - 3 = 0

q 2 * \u003d (97 - q 1) / 2 \u003d 32 units.

Price Р = 100 – (32+33) = 35 arb. units

Profit 1f 100 * 33 - 33 2 - 33 * 32 - 20 - 2 * 33 \u003d 1069 conventional units.

Profit 2f 100 * 32 - 32 2 - 33 * 32 - 10 - 3 * 32 \u003d 1014 conventional units.

Stackelberg equilibrium

P \u003d 100 q 1 - q 1 2 - q 1 * (97 - q 1) / 2 - 20 -2q 1 \u003d 49.5 q 1 - q 1 2 / 2 - 20

49.5 - q 1 \u003d 0

Leader: q 1 \u003d 49.5 units.

Follower: q 2 \u003d (97 - q 1) / 2 \u003d (97 - 49.5) / 2 \u003d 23.75 units.

P \u003d 100 - (49.5 + 23.75) \u003d 26.75 units.

P1 \u003d Pq 1 - 20 -2q 1 \u003d 26.75 * 49.5 - 20 - 2 * 49.5 \u003d 1205.125 conventional units.

P2 \u003d Pq 2 - 10 -3q 2 \u003d 26.75 * 23.75 - 10 - 3 * 23.75 \u003d 554.0625 conventional units.

Problem 4. Let's assume that on a beach stretched along a straight line with a length of 100, at a distance of 60 m and 40 m from its left and right ends, there are 2 kiosks - A and B, from which juice is sold. Buyers are located evenly: at a distance of 1 m from each other; and each buys 1 glass of juice during a given period of time. The costs of juice production are zero, and the costs of its "transportation" "by the buyer from the tray to his place under the beach umbrella are 0.5 rubles per 1 m of the way. Determine the price at which 1 glass of juice will be sold in kiosks A and B, and the number of tablespoons of juice sold from each of them for a given period.

b) How would the results obtained change if each of the trays were located at a distance of 40 m from the ends of the beach?

Let be p 1 and p 2 ≈ shop prices BUT And IN, q 1 and q 2 ≈ corresponding quantities of goods sold.

Shop IN can set the price p 2 > p 2 , but in order to q 2 exceeded 0, its price cannot exceed the price of the store i>A more than the amount of transport costs for the delivery of goods from BUT in IN. In fact, it will maintain its price at a level somewhat lower than [ p 1 - t(l - a - b)], the cost of purchasing goods in BUT and deliver it to IN. Thus, he will receive an exclusive opportunity to serve the right segment b, as well as consumers of segment y, the length of which depends on the price difference p 1 and p 2 .

Figure 3. Hotelling Linear City Model

Likewise, if q 1 > 0, store BUT will serve the left segment of the market but and segment X on the right, with the length X with increasing p 1 - p 2 will decrease. The boundary of the market service areas for each of the two stores will be the point of indifference ( E in Fig.) of buyers between them, taking into account transportation costs, determined by the equality

p 1 + tx = p 2 + ty. (1)

Other: value relationship X And at is determined by the given identity

a + x + y + b = l. (2)

Substituting the values ​​of y and x (alternately) from (2) into (1), we obtain

x = 1/2[l √ a √ b √ (p 2 - p 1)/t], (3)

y = 1/2[l √ a √ b √ (p 1 - p 2)/t].

Then the stores arrived BUT And IN will

p 1 = p 1 q 1 = p 1 (a+x) = 1/2(l + a - b)p 1 - (p 1 2 /2t) + (p 1 p 2 /2t), (4)

p 2 = p 2 q 2 = p 2 (b+y) = 1/2(l - a + b)p 2 - (p 2 2 /2t) + (p 1 p 2 /2t).

Each store sets its own price so that at the existing price level in the other store, its profit will be maximum. Differentiating profit functions (4) with respect to p 1 and, accordingly, p 2 and equating the derivatives to zero, we obtain

dp1/d p 1 = 1/2(l + a - b) √ (p 1 /t) + (p 2 /2t), (5)

dp2/d p 2 = 1/2(l - a + b) √ (p 2 /t) + (p 1 /2t)

p* 1 = t[l + (a-b)/3] = 0.5* (100 + (60-40)/3) = 53.33 rubles, (6)

p* 2 = t[l + (b-a)/3] = 0.5* (100 + (40-60)/3) = 46.67 rubles,

q* 1 = a+x = 1/2[l + (a-b)/3] = ½* = 53.33, (7)

q* 2 = b+y = 1/2[l + (b-a)/3] = ½* =46.67.

With equal removals

p* 1 = t[l + (a-b)/3] = 0.5* (100 + (40-40)/3) = 50 rubles, (6)

p* 2 = t[l + (b-a) / 3] \u003d 0.5 * (100 + (40-40) / 3) \u003d 50 rubles,

q* 1 = a+x = 1/2[l + (a-b)/3] = ½* =50, (7)

q* 2 = b+y = 1/2[l + (b-a)/3] = ½* =50.

Answer For a kiosk at a distance of 60 meters, the price is 53.33 rubles. and number 53.33; and for a kiosk at a distance of 40 meters, the price is 46.67 rubles. and number 46.67.

In the second case, the price will be 50 rubles. and 50 clients for each of the kiosks.

Task 5. A profit-maximizing monopolist produces a product X with costs of the form TC=0.25Q 2 +5Q and can sell the product in two market segments characterized by the following demand curves: P=20-q and P=20-2q

A) What quantities and at what price will the monopolist sell in each of the market segments if he is allowed to practice price discrimination? Find the change in the total profit of the monopolist in the transition to a policy of price discrimination.

Give a graphic illustration to all points of the decision.

When calculating, round off to the first decimal place.

Revenue in market 1 TR 1 = P 1 *Q 1 = (20-q 1)*q 1 =20q 1 -q 2 1 MR=TR’ = 20-2q 1

Revenue in market 2 TR 2 = P 2 *Q 2 = (20-2q 2)*q 2 =20q 2 -2q 2 2 MR=TR’ = 20-4q 2

MR=MC - profit maximization condition

Optimal prices in market segments

P 1 = 20 - 12 = 8 units; P 2 \u003d 20 - 2 × 6 \u003d 8 units.

Thus, the profit of the monopoly was

P \u003d 8 * 12 + 8 * 6-0.25 * 18 * 18-5 * 18 \u003d -27 units.

Perhaps you this morning
Not enough pretzels.
I doubt it won't be enough.
But there is still a possibility.
The old confectioner died. But
His disappearance is unlikely
Someone will notice, except relatives
And maybe one old woman
From our cafe "Vec Riga". 1 (1969)

Maurice Chaklais

Key Concepts

• Monopolistic competition
• demand line DD (jnutatia mutandis)
• Industrial group
• demand line dd (ceteris paribus)
• Condition of uniformity
• Excess power
• Symmetry condition

Pure competition and pure monopoly are ideal forms. They help to understand the essence of the structure of diverse market relations, but in their extreme (absolute) forms they almost never occur in real life. This chapter deals with monopolistic competition, a market structure that we encounter on a daily basis.

The term and model of monopolistic competition was 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) that are 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.

monopolycompetition is a market structure in which many firms sell a heterogeneous product in the same market.

According to Chamberlin, a monopolistically competitive industry is formed by a set of sellers offering a set of products that are close substitutes. Each seller seeks to maximize profit by changing the quality of his product and the quantity offered for sale. Although product differentiation practically difficult to measure, it is generally accepted that it is in it that the essence of monopolistic competition lies.

• 1 Old Riga (Latvian).

10.1. "Industrial group": uniformity and symmetry

Changing every moment
I'm a doppelgänger around the world! I am a double to all around!
Leonid Aronzon (19391970) Translation by R. McKane

Consider monopolistic competition as one of the four main market structures on the basis of the set of structural variables already known to us, given in chapters 7-9 (Table 10.1).

Table 10.1
Structural variables of monopolistic competition

The nature of a manufacturing group offering close substitutes can be determined by examining how manufacturing decisions separate manufacturer influence behavior others manufacturers of the "industrial group".

IndustrialGroup- this is a large number of product manufacturers that can quite successfully, although not fully, replace each other.

Each firm in a situation of monopolistic competition is similar to the others, that is, representative. Chamberlin's hypothesis about the nature of monopolistic competition rests on the conditions uniformity And symmetry. one

Condition of uniformity is that the supply and demand curves of each producer in the group are identical. As applied to the production of beer, for example, this assumption suggests that the costs of producing a bottle of Baltika beer are essentially the same as those of Stepan Razin, and the demand conditions are practically the same.

Conditionuniformity (uniformity): Chamberlin's idea that the cost and demand curves of each member of an industry or group are identical.

• 1 These terms do not appear in Chamberlin's writings and probably originated during the discussion regarding the problem of monopolistic competition. Formally, they are presented in the work: Stigler G J. Five Lectures on Economic Problems. London, 1949.

Both types of beer have their own "niche" in the market and have more or less loyal followers. At the same time, the consumers of Baltika and Stepan Razin do not have any fundamentally different characteristics. In a competitive market, no manufacturer has a monopoly on the "best product". If a new kind of product emerges that is more popular than others, other manufacturers can 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 differentiated to some extent, 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 his 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 retaliatory measures.

Figuratively speaking, the Chamberlin firm can be compared to one of the many fishing boats with several fishermen with fishing rods. If one fisherman finds a more tempting bait for fish, then his share in the total catch will increase markedly. But since the situation is symmetrical, other fishermen can follow suit. But if everyone starts using the best bait, then the bait of the first fisherman will no longer be particularly attractive to the fish, and his share in the total catch will decrease again.

10.2. Short-term and long-term equilibrium

Juice of mutual friendship, forgiveness of insults
Mei $ ov 5 Tinas mvq EXX^u Nap0I; like old times>
laAiv eq shrhl? Us, beautiful Hellas happy people,
Flo? hgLso kt aiuuusotsL B pour cheerful meekness into our hearts!
Tivi lraothera Kepaaov tov vow
Km ttiv ayopav 4 niv aya 9 cov Rashshm with an apple, mega onion, tops,
EtzlHoelUsi, to Meyapcov CKopoScov, Cucumbers, pomegranates, evil garlic,
ZvKUCOv jipaxov , m Xw , pouov , Small shirts for slaves.
DoiLouch xAaviCKiovcov niKpcov Let us see the Boeotians again/
Km Boicoxcov ye cpepovtaa iSeiv with partridges| with crack kwami, with a goose, with a sheep,
Km Kepi tautq nnaq aOpoouq Let the Kopay eels be brought in baskets,
Och/ covouvtaq tirraSeovsh im> homonym,
Morihso, TeKhea, GKhaikett, aUoiq We tear from hands and bargain. Cling to the trays
Tevemq poXKhosh kata MeXav 9 vov Famous gourmets: Morih, Telei
HKeiv wrepov gs t 4 v ayopav , and Glaucet. Finally, Melanthius is coming:
Taq 5 e yaeyara59t ... He comes to the market later than everyone, Alas!
Aristophanes (446385 BC) All sold out...

Translation by Adrian Piotrovsky The essence of monopolistic competition manifests itself within four parameters: (1) product differentiation; (2) uniformity; (3) symmetry; and (4) a relatively large number of manufacturers.

• Product differentiation implies that each manufacturer has limited control above the price, i.e. forms descendingschuyu demand curve. The manufacturer has the ability to "pull" some buyers to him, carrying out a certain reduction in prices and changing the quality of products. On the other hand, a firm can raise the price of its products somewhat without losing the bulk of buyers (regular customers who, for one reason or another, prefer this particular manufacturer).
• Uniformity provides a basis for analyzing the behavior of a "representative" group member, assuming that each producer will behave in the same way as other members of the group, i.e., will offer the same amount of output for sale at the same price. If one producer expects to benefit from lowering his price, he will obviously do so, but then other members of the group will want to get a similar benefit and also reduce prices.
• Symmetry and 4) a large number of manufacturers imply that the individual producer acts as if his own price behavior is extended to a larger group. At the same time, the total result of making similar decisions by all members of the group becomes significant and noticeable.

Feature of the market of monopolistic competition 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 the prices of their products.

• 1 In chapter 2 (paragraph 2.1) we have already met the terms "ceteris paribus" - "ceteris paribus" and "mutatis mutandis" - "mutatis mutandis".

At equally high prices, each representative producer controls a relatively small and equal market share. The simultaneous reduction in prices by all sellers leads to the fact that each firm increases its sales by an equal amount. For example, at the point BUT each producer will receive a price of 0.6 r. per unit of goods and will sell 45 units; at the point IN each company will earn you 0.5 rubles. per unit of goods and will sell 50 units.

Curve DD like a demand line industries 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 (prices of other firms are fixed).

An individual producer will not charge the same price as his competitors if he believes that some other the price can bring him a higher profit. If the manufacturer thinks that other firms will continue to adhere to the already existing price (say, 0.6 r. per piece), then he, having set the price of 0.6 r. per piece, will sell 45 pcs. However, the manufacturer can set both a higher and a lower price (say, 0.7 or 0.5 rubles per piece), and sell, respectively, either 35 units. (dot BUT"), or 55 units. (dot BUT") goods.

Curvedd more elastic than a curveDD . It is more sensitive to price changes, provided that the other members of the group do not change their prices. Decreasing the individual price from 0.6 to 0.5 rubles. per piece of goods provides not only an additional 5 units. sales similarly to other members of the group (as shown by the curve DD), but on top of that, an additional 5 units that our producer will receive from the losses of the other members of the group.

At higher than R 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 because if our firm raises its price, competitors are likely to keep their prices at the same level, and if one firm lowers its price, other firms will be forced to follow suit in order not to lose their customers.

short term balance. Suppose that the initial equilibrium of the production group is determined by the point A 0 in Fig. 10.2, but at a total price P Q and release q0 . Separate manufacturer, acting within the demand line dd0 , with appropriate marginal income(mr Q) is able to increase his own profit by lowering the price of his products to the level P t and producing q " launch units (with tg "ts). This corresponds to a new equilibrium point BUT".

But if the example of one manufacturers follow other and 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 AND j . Curve dd will begin to move down and to the left, as prices of substitute goods(which are suggested by all other members of the group) also decreased. Each member will get a new demand line dd, passing through point A, and 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 the same price for the whole 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 of monopolistic competition resembles a model of equilibrium under monopoly conditions, in which the firm's demand curve slopes downward, and tg<Р,а price exceeds marginal cost.

However, on the other hand, the situation also resembles the equilibrium of pure competition at the 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 balance. In the short run, a representative firm can earn a certain economic profit (mc > 0) if the price exceeds the total average cost (P>ATS) at equilibrium output q*. However, since the market is competitive, economic gains (or losses) cannot exist in long-term period. This is because, as in a purely competitive industry, in 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 leave the industry - entry and exit of firms in this model are practically unlimited.

When a new firm enters the industry, the market share of the representative firm decreases, resulting in a corresponding shift to the left of the lines DD And dd. The individual firm is forced to cut prices, which further pushes 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 equal to zero (mc = 0). The representative firm maximizes its profit when tg = ts, but the position of the curve dd is such that this maximization is carried out at mc = 0 (zero economic profit).

Rice. 10.3. Long run balance

For greater clarity, we compare the equilibrium competitive firm in the short term and long term on the same chart (Fig. 10.4). On fig. 10.4, but the situation is depicted short-term equilibrium of a monopolistically competitive firm. Since the firm is the only producer of its own brand and has a downward-sloping demand curve, the final price in the short run (PSR) exceeds average costs (ATS) and the firm makes a positive profit (shaded box). However, these profits attract new manufacturers with competing brands to the industry. As a result, the firm's market share shrinks and its demand curve shifts downward. Therefore, at 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. The equilibrium of a monopolistically competitive firm in the periods: a) short-term and b) long-term

This situation differs from the pure competition model in two respects. Firstly, in accordance with the profit maximization condition, the price exceeds the marginal cost (P > MS). Secondly, the contact cannot be at the minimum point of the L GS, i.e., at the point M in Figure 10.3.

10.3. The effectiveness of monopolistic competition

There is no limit to greedy striving... There is no end to unsuccessful labor... There is no end and no joyless path... God, be merciful to me, a sinner...
L. A. May (18221862)

Based on the study of long-term equilibrium, it can be concluded 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 Figure 10.3) are similar to the pure monopoly model; Secondly, zero profit condition leads to excess power i.e. each firm operates below the minimum value ATS.

Excesspower: a condition that characterizes the long-run equilibrium under monopolistic competition, in which the firm operates at a level of output less than the optimal level at which the minimum total average cost could be achieved.

The existence of excess capacity implies that the cost of producing a unit of a product under monopolistic competition is higher than if the product were homogeneous.

Does overcapacity mean that the model of monopolistic competition is "inefficient"? On the one hand, monopolistic competition leads to economic losses: a certain aggregate amount of output can be provided at a lower cost.

Welfare losses that result from prices exceeding marginal cost are not easy to identify. Despite the loss of "dead weight" (the shaded triangle in Figure 10.3), Chamberlin expresses his conviction that monopolistic competition is more perfect. market structure than pure competition. The presence of excess capacity or loss of efficiency is the kind of price that consumers bear for differentiation goods and for that availability sources of supply provided by monopolistic competition.

Suppose now that the producer has increased its output by one unit above the equilibrium value (Figure 10.5). Curve dd will move down: the output of all other producers has increased, and prices have decreased. Thus, more closely related substitute products became available to buyers at lower prices. This decrease in price can be measured using the shaded area. L.

Rice. 10.5. Welfare effects from increased output when P* > mc

The result of a price decrease consists of two opposite effects: a positive effect or welfare gain (denoted by the letter G) and a negative effect or welfare loss (denoted by the letter G). L). Based on this, we conclude that an increase in output is economically justified if G > L, i.e. up to the point where G = L. If this criterion is valid, then the efficient price must always exceed marginal cost, and monopolistic competition cannot be compatible with economic efficiency under pure competition. Section 10.5 presents an algebraic example in which the monopolistic competition equilibrium condition is considered in more detail.

10.4. Competitive markets for product attributes

The market is full of paintings
All with swans and rainbows.
And Vanka is an avant-garde artist
All cubes squares.
Vanka - avant-garde
Everything aims with a sniper's squint.
He knows the neoclasses
Savings book appetites
a foolish businessman,
Antichrist of a new type. (1971)

A. A. Voznesensky

The monopolistic competition model does not consider how manufacturers differentiate their products. However, many product differences can be quantified. Although the products are varied, most of their main characteristics are quite comparable. Thus, the total price of a product can be broken down into several components: one price per feature.

The firm may try to improve its position through the implementation of product differentiation - to add or allocate new qualities of the product and assign 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 Kelvin Lankaster. 2 The Lancaster model has already been discussed in Chapter 4 (Section 4.10). The construction of the model proceeds from 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 by combining goods and services in a certain way.

The Lancaster model is shown in fig. 10.6. Let's pretend that Z% and Z 2 along the ordinate and abscissa axes are two characteristics of the quality of the products of the monopolistically competitive group. Thus, the product of each firm forms attribute 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 customer will buy a single product only if his indifference curve (, because q° is accepted by the donor; the slope of this curve is b

Curve DD intersects the y-axis at a point BUT 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:

2Q DD: p = 200 2 q 200 -

dd: p=q.

Equilibrium condition.Curve PositionDD fixed in the short run: there is no industry entry or exit. Moving along a curve DD involves 2 effects on the price of a representative firm's product: the output of the firm itself (b= 1) and the output of its competitors [(PI) but=

Curve Positiondd is changing with the output of the group:

• if q° = 25, then the expression dd is written like this: R*= 175 q;
• if q° = 50 then dd expressed as: p = 150 q etc.

Increase output of the group shifts the demand curve of each member of the group down.

R 200

Rice. 10.7. Algebraic illustration of short run equilibrium

Curve Position tg depends on the curve dd, which means from q°. At the same time, the angle of inclination tg twice the angle dd. In our example:

tg = 2q.

Let the curve ts expressed in linear form, for example:

ts = 25 + 0.5q.

Each manufacturer maximizes its profit (tg= ts), and the output is the same for all group members (q = q°). Equate ts And tg.

25 + 0,53 q.

We get: q* = 50. So, the equilibrium of the system is carried out at q* 50 ir*= = 100, as shown in Fig. 10.7.

At q° = q* = 50 curve dd representative firm looks like: 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 the curves DD (R= 200 2 q) Anddd(p = = 1509).

The short-run curve thus obtained is also the long-run equilibrium curve if the fixed costs are 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 \u003d 25 + 0.25 g,

ate = + 25 + 0,25<7.

If q = 50, ate = 100 = p.

Economic surplus and efficiency. On fig. 10.5 Welfare effects from an increase in output were measured using figures GhL.

Wherein G represented the "gain" from expanding output, a L - the corresponding welfare "loss" 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.

Equilibrium output is efficient if G ~ L, if Kommersant= (n\)a. This condition is achieved when b = 1, i = 101 and a = 0.01.

Control tasks

Review questions

1. Which of the structural variables are of particular importance in the model of monopolistic competition?
2. Explain why the property of symmetry is necessary to form the concept of a representative firm.
3. Comment on the meaning of the demand lines mutatis mutandis and ceteris paribus in the model of monopolistic competition.
4. Explain the firm's response to a decrease in demand in the short run.
5. What is the equilibrium between price and output of a firm in the short run? What happens if too many new firms enter the industry?
6. What are the conditions for long-run equilibrium in a monopolistic competition market?
7. How do you understand the concept of excess capacity?
8. Suppose that all firms in a monopolistically competitive industry have united into one large monopoly. Would this firm produce the same number of different types of goods? Would it produce only one type of product? Explain.
   A task
9. Each of the 20 firms in the monopolistic competition industry has a curve dd, given by the equation: R= 10 0.001(2 What will be the curve dd for each firm after 5 new firms enter the industry?

Chapter 11 Oligopoly

Ferret married a rat
And the rat took the ferret.
And made a ferret to Alice
Present in four stalls.
And life flowed amazingly
She and he shine
For every glass of beer
They ask for a million.
(1995)
Nikolai Tryapkin

Key Concepts

• Equilibrium
• Duopoly
• Expected price
• Broken demand curve
• Oligopoly
• Price leadership
• Reaction function

Duopoly:

• Cournot
• Bertrand
• Stackelberg
• Collusion

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 cause as much discussion and controversy as oligopoly. In real life, typically monopolistic industries are automotive, metallurgy, aluminum, chemical, etc.

The fundamental difference between an oligopoly and monopolistic and pure competition is that with an oligopoly in the industry there is only several rivals, therefore, each firm must 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 the oligopoly as one of the four main market structures on the basis of the structural variables given in the four previous chapters (Table 11.1).

We already know that in the model of perfect competition, products are homogeneous, and in monopolistic competition, they are heterogeneous (differentiated). In the oligopolistic model, products can be either homogeneous or heterogeneous.

table11.1
Structural variables of an oligopoly

Opportunities to enter the industry also vary widely - from completely blocked entry to fairly free (depending on the characteristics of the strategic behavior of oligopolists).

In the perfect competition model firms pursue an optimal policy of behavior: when the market is in equilibrium, they have no reason to change the price or output. When supply and demand are equal, the firm sells everything it produces and maximizes its profit.

In the monopoly model the firm-monopolist is in equilibrium under the condition MR = MS. In this case, the monopolist maximizes its profit and also pursues the optimal policy (from the point of view of the monopoly).

In the oligopoly model the firm also tends to implement the best policy given 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 oligopolistic firm behaves best given the behavior of its competitors.

First of all, consider the conditions for the emergence of an oligopoly.

11.1. Economies of scale and oligopoly

Each carved
For a huge piece:
There's jam and meringue
And rough white cream.
Everyone thinks: here we go
And, having sated, I will fall asleep,
And your sweet dream
I will not share with anyone.

N. V. Baytov

Let's compare the oligopoly with another major player in the market economy - the natural monopoly. A typical oligopolistic firm, one of the world's top 500 national and multinational corporations, is typically much larger in capital and geographic scope than a typical natural monopoly.

It seems obvious that a firm that alone dominates the market must be larger than one that shares the market with few competitors. But precisely the size of the market, and not the absolute size of the firm, determines, iswhether the market is monopoly or oligopolistic.

For example, petroleum products can be transported at a much lower cost (relative to unit price) than electricity or water; The oil industry is also oligopolistic. On the other hand, local electricity networks are almost always represented by one seller and are a natural monopoly. The market for oil products is generally global, while the market for electricity is local.

Rice. 11.1. The difference between a natural monopoly (a) and an oligopoly (b). Economies of scale determine firm size, while market demand determines the number of firms

On fig. 11.1 let's compare the market conditions leading to the formation of a natural monopoly and an oligopoly. In Fig.11.1, but, market demand curve (D) crosses the long-run average cost curve (LAC) the only producer to the left of the minimum point. The only company in the industry that has a total average cost L GS, and output Q , at a price R g, can discourage potential competitors from entering the market. However, the natural monopolist will maximize profits based on the conditions PBX 0(at MS a =MR), limiting you start volume Q 0 , and setting the price R t, as discussed in chapter 9.

Unlike a natural monopoly, an oligopoly is the "natural" result of a situation in which one firm experiences uneconomics of scale by trying to dominate the market alone. At the same time, the minimum size of an efficient firm is large enough that such a firm is a price-setter.

On 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 attempted to serve the entire market, then a price would have to be set to cover the costs. R or higher.

The second firm, 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 all the required volume (Ј Qo) at the price of zero profit (P 0). However, the number of firms in the industry (n =Q^/" LQ^) is too small for price competition to lead to 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 to Q^, by setting the cartel price at the level R t. Entry into an industry can be difficult, although not completely blocked: economies of scale do not prevent entry into an industry, but can set an upper limit on the number of producers.

The typical oligopoly produces a wide range of goods, selling goods that are co-products in production (gasoline and petrochemicals), complements in consumption (televisions 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 manufacture, sell, and advertise in many markets at the same time.

11.2. Classical duopoly theories

God sent me a wonderful dream:
Flowing to meet each other.

Nature has changed
Everything breathes double life:

I look - from dusk to dawn,
Two suns reflect the waters

In a single moment to the sky:
Two hearts beat in the chest of nature -

Two suns rise radiant
And the blood flows like a double key

In fiery amber porphyry.
Through the veins of God's creation,

And over the resurrected earth
And the doubled world lives -

The couple shone in the sky.
In one moment, two moments. (1827)

S. P. Shevyrev (18061864)

The analysis of an oligopolistic market structure is traditionally accepted to begin with the simplest models of a duopoly, i.e., a market in which two firms operate.

11.2.1. Cournot theory

If it's good together here,
It's good to be alone here. (1994)

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 happens if a second seller enters a monopoly market, previously operated by a single monopoly firm? Can the emerging duopoly(industry with two sellers) achieve stable output at certain prices and outputs? If so, is it possible to add a third seller to the industry, then a fourth, and so on, until the monopoly turns into competition?

• 1 CournotA. Recherches sur les principles mathftmatique de la theorie des richesses. Paris, 1938.

Cournot considered the market homogeneous product with two sellers (Fig. 11.2). As in pure competition, in a homogeneous oligopoly both sellers must establish single price: otherwise, only a seller offering a lower price can find a buyer.

Suppose the market price R(and hence the average income AK) is a linear function of the total output:

P= a b{ q,+ q2 ), (11.1)

where ^ + q2 = Q - release of the first and second seller; the marginal cost curve for each seller is horizontal: MS= k (k - constant).

In the Cournot model, each duopolist assumes that the rival will not change its output in response to his actions (the rival's output is a fixed value). one

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 firm's point of view 1. On fig. 1 1.2, and seller 1 estimates his own average income function (ARt =D,) like:

P=(a bq*) bq v (11.2)

• 1 This is, of course, a very weak form of interdependence, but, as we shall see, even this will eventually lead to the fact that the behavior of each firm influences the behavior of its rival.

assuming that the output of seller 2 is equal to q\. The idea is that firm 2 got the first q* 2 units of market demand, leaving Firm 1 to work on the remainder of the market.

Because (butbq* 2) - the value is constant, the marginal income of the seller 1 is equal to: "

AR
MR l P+J^q i = (abq* 2)~bq i bq i = (abq* 2)2bq i . (11.3)

At MR = MS= to firm 1 will offer q* output units. Equilibrium market price P* of output

P * a bq \ bq \ (11.4)

Situation from the firm's point of view 2. While firm 1 decides on 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 revenue of seller 2 is equal to:

AR
MR 2= P + Iq~ 2?2"(" SCH) 2bqr (11.6)

On 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 only come into equilibrium if each duopolist produces as much as his competitor expects of him (if q* x = q° v q\= q* 2 , UP° =P*).

Back to the premise that the market was originally monopoly, i.e. q* = O in fig. 11.2, but. Acting as a monopolist, seller 1 sets the output at which MR{ \u003d MS \u003d k. Then, taking into account formula (11.3), we have:

a2bq lk. (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 Firm 1's total revenue exceeds its total costs. (TR{ >GS (), i.e. the market will demonstrate its attractiveness.

VCl kq l ( l /2 b )( ak /2 P )

1 Firstly, formerly the relationship between price and marginal revenue (MR R+ *dp) we have already considered repeatedly. 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 is 7, < (1 / Ab) (a2 ak). 1

Cournot simplified the analysis by assuming that the fixed costs of both sellers are zero. At any price above marginal cost, seller 2 tends 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 structured so that R°< Р*: Expecting Seller 1 to maintain monopoly issuance at q{ = (ak) / 2 b (Formula 11.8), Seller 2 defines his marginal revenue function as:

MR2 (a + k) 2 bq2 ,

setting the volume of output based on the condition MR = 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 former monopolist (seller 1), the market price will inevitably fall. Seller 1's expectations of a monopoly price have come into conflict with reality, and its output must be adapted to the new situation.

In the Cournot model, adjusting output to unexpected changes in market demand (so that other sellers do not produce their own given release) determines reaction function each seller.

FunctionreactionsCournot[q*, = R,(q t)] - a curve showing how much output one duopolist (/) will supply to the market for each given volume of output supplied by another duopolist (y).

The seller's reaction function 1 is derived from the profit maximization rule MR{ = MO.

(butbq2 ) 2 bq x = k.

Let's define q{ :

q r (1/2) (a k bq2 ).

In this way, under duopoly conditions, the reaction function has the form:

1 This result is obtained in the following way. The economic profit for seller 1 is expressed as follows: Rpq{ (VC + FC) t > FCy Replacing the monopoly parameters with q i And R, get chim Pq t = (1 / 2a+k) [(butk) / 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. Hence it follows that Pq t US, > FC V if FC{ < (a2 ak) / 4 b.

9 *(a* ty). (11.10)

At D 2= 0, = (1 / 2 b) { a k) there was a situation of monopoly production.

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 receives a new profit maximization volume according to the response function that is derived from the solution MR2 = MS.

Firm 1 reaction function: At kg Equilibrium KurnoNash (C N)

Firm response function 2: q* 2 gtaj)

Rice. 11.3. Cournot duopoly model "a) duopoly reaction functions and Cournot's "solution"; b) output and prices under monopoly, competition and duopoly

Release rules for q2 are: (butbq t) 1 bq2 = k, where q2 = (1 / 2) (butk 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 seller 1's output.

ruleduopoliesCournot: if seller 1 decreases his output by one unit, then seller 2 will increase his output by half a unit (and vice versa).

This process of adjusting one seller's output to another seller's output is expected to bring total output and the resulting price into stable equilibrium. 1 The graphical solution of the Cournot duopoly is shown in fig. 11.3, but.

ak qi = Hb~"

At2 b) (butk bq 2) And q2(1 / 2b) (a k bq x) we have:
ak 3 ak 1 ak

H + Z 2

2 q"~"2 b

2* + < b =2 T ; «"

Equilibrium outputs of duopolists:

_ a k _, a k

The equilibrium releases of duopolists are the coordinates of the Cournot-Nash equilibrium point (point C N).

In this way, total equilibrium output in a duopoly is:

a*=(?* 1 +?* 2)=^~. (item 12)

As shown in fig. 11.3, b,equilibrium duopoly Cournot price(R) less than the monopoly price (P t), but more than the price of marginal cost, i.e., the competitive price (R.). one

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 solution of the equilibrium can be transferred from the duopoly model to the model of the proper oligopoly.

We summarize the main parameters of the Cournot model in Table. 11.2.

If you ask the question what will happen if the duopoly enters the market the third seller (the duopoly will turn into a "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 where the industry's marginal revenue equals (total) marginal cost. Condition MR = MS leads to that but 2 bq = k, or q = (but k) / 2 b = q{ + q2 , And

P_ = a b

2 b

a + k

If output (and hence profit) is divided equally between the two firms, then q{ = q2 = = (ak) / 4 b. We put this output in the firm's response 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 the output of one seller corresponds to a monopoly, then the second seller will produce more than his cartel quota, thereby reducing the price below the monopoly level.

Under Cournot equilibrium, the duopoly price R is determined by substituting industry output into the function of average industry revenue:

f,2 a2 k. 3 k + a which is less than R, and more marginal cost, while a >k.

table 11.2
Main equilibrium parameters of the Cournot model 1

From this it is easy to conclude that with an increase in the number of firms (P) in the industry, the output of each individual firm will decrease, and the total output of the industry will increase:

a k n

Q. "*¦- X ^TT(" is)

Therefore, it can be argued that the Cournot model predicts the approximation of total output to the volume of production of a perfectly competitive industry with a sufficiently large number of its subjects. 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).

11.2.2. Stackelberg theory

Divided into First and Second,
Sometimes we don't think ahead
What is the first -
Unknown way to create
Second -
Just pave the way
That the First live in one impulse,
Well, the Seconds ... Their appearance is businesslike. (1968)
V. A. Lakhno

In 1934, the German economist Heinrich von Stackelberg attempted to refine the Cournot duopoly model. The novelty of the model was that in it, duopolists could engage in 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

1. When calculating the parameters of the table. 11.2 we proceeded from the fact that the market demand curve has the form: P = a +bQ, and the profit is: l =PQ PC.
2. StackelbergH. Von. Marktform and Gleichgewicht. Vienna, 1934.

If the follower of the Stackelberg model adheres to the assumptions of the Cournot model - follows his own response curve and makes a decision on the release, assuming that the opponent's release 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 suggests the possibility of the existence of four combinations of two types of behavior (Table 11.3)

Table 11.3
Possible combinations of behavior in the Stackelberg model

In the first two cases, the behavior of duopolists is stable: one firm is a leader, the other is a follower.

In the third case, we have a typical Cournot model (as a special case of the Stackelberg model).

In the fourth case, the unleashing of a price war is inevitable, which will continue until one of the duopolists renounces its claim to leadership, or the rivals collude.

Consider situation 1 (2), since it is this situation 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 the 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
i, = - P121 4)

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 function of the linear demand function both leaders:

.aka.k.s. "
P = a "b(2b + ^b) = k t 11" 22)

We have 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, for buyers, this would be the best option. But for oligopolists it is unacceptable - this is the worst result for them (it is better to collude 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 better describes reality depends on the industry. For an industry of approximately the same size firms, the Cournot model is probably more appropriate. In industries dominated by one large firm, the Stackelberg model may be more realistic.

table 11.4

	Main	equilibrium parameters of the Stackelberg model
	Release		Profit			Marketprice
leader	lastvatel	industries	leader	lastvatel	industries
		3(ak) Ab		(ak?166	3(ak) 2 166	(a+3k)BUT

11.3. The price problem of oligopoly: the Bertrand model

The butcher was always humble before Shakespeare And he took off his hat, but he did not have respect for him In his soul, Shakespeare, without a doubt, Was an ignoramus in the mystery of market prices.
Thomas B. Aldrich (18361907)

In 1883, the French scientist J. Bertrand (1822-1900) criticized the Cournot duopoly model, stating that price, not output, is the firm's main strategic variable. According to Bertrand, each firm sets its own price based on the assumption that the opponent's price will remain fixed, i.e., not the output, but the price set by the firm is a constant parameter for the duopolist.

As in the Cournot model, the position of the duopolists in the Bertrand model is symmetrical: selling below a competitor will be the strategy of choice for both firms. Obviously, therefore, 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).

On fig. 11.4 shows the response function of the Bertrand model.

FunctionreactionsBertrand[ P* i = R(P t)] - a curve showing at what price a 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 each of their products depends on its own price and the price of a rival. Duopolists choose prices simultaneously, but each takes the opponent's price as given. Firm response curve 1 [ R^ PJ] shows firm 1's profit maximizing function as a function of the price set by firm 2. Firm 2's response curve has the same meaning. Firms can cut prices up 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 Table. 11.211.5 together to compare the outcomes of the Cournot, Bertrand and Stackelberg duopoly strategies. To these we add another duopoly strategy: the strategy of collusion to create a joint monopoly (Table 11.6).

Rice. 11.4. Reaction functions of the Bertrand model

Table 11.5
Basic equilibrium parameters of the Bertrand model

Table 11.6
Comparison of duopoly models

As this table shows, the most profitable strategy for duopolists would be to create a joint monopoly through collusion, since the total profit resulting from this strategy is the highest. In second place (in terms of obtaining the maximum total profit) is the Cournot model, in third place is the Stackelberg model. In the Bertrand model, oligopolists do not receive positive economic profits (as in a situation of pure competition).

11.4. Broken demand model

I was looking for an answer
To a question.
As soon as I found it
- the answer became a question. (1982)

S. Misakovsky

In 1939, Harvard economist Paul Sweezy offered the following explanation. apparent price inflexibility in industries with few sellers. Rivals react differently to price changes upwards and downwards. If the firm BUT raise the price of its products IN gains new customers that firm A will lose from the price increase. If, on the other hand, the firm BUT lower the price of its products IN will lose some of its customers.

Every firm strives to avoid losses. If the reason for the loss of profits of the firm IN was the reduction in the price of goods by the firm BUT, it is natural to expect from the firm IN similar to a price cut. From the firm's point of view BUT this means that when the price of its product rises, it must expect to lose some of its customers in favor of rivals (therefore, the firm's demand curve BUT elastic with price increases). But if the firm BUT will lower the price of its products, it should not count on poaching customers from competitors, since they will also be forced to lower prices (the firm's demand curve BUT inelastic as price falls). 1 The Suisey hypothesis is expressed using the following premises:

• In an oligopolistic industry, each firm expects competitors to react to changes in the price of their products.
• Firms do not collude about output volumes and price levels.
• Each firm will try to maximize its short-run profit by increasing output if marginal revenue exceeds marginal cost and decreasing output if marginal cost exceeds marginal revenue.

The logical consequence of these premises is broken demand model of an oligopoly, shown in fig. 11.5. Let the firm A produce the volume of output o per unit of time at the equilibrium market price R. At the point (Р 0 , Q^) two curves intersect: the line D0 is a demand curve of the type ceteris paribus. It reflects the immutability of competitors' prices. with an increase company prices BUT. Line D x is a demand curve of the type mutatis mutandis. It reflects the property of price changes by rivals following downgrade prices for their products by the firm BUT.

• 1 Sweezy P. Demand Conditions under Oligopoly // Journal of Political Economy, 1939. June . PP. 568573.

Demand curve ceteris paribus D 0 is more elastic than the demand curve mutatis mutandis Dv As a result, the overall demand curve of the oligopoly (abc) has a broken look.

ft

About QoQi ~ ?

Rice. 11.5. Broken oligopoly demand curve

What should an oligopolist do with such a demand line to maximize his profit? The answer is known: equalize marginal revenue with marginal cost (MR = MS). However, the shape of the marginal revenue curve (adef) even more peculiar: it is not only broken, but also with a gap (which is explained by the presence of different slopes of the curve abc).

Break in the curve MR allows the firm to significantly change costs (from MC-Q before MS X without changing the profit-maximizing output level.

However, in general, the fate of this seemingly original and interesting concept is not very happy. Empirical testing of the oligopoly demand curve model casts doubt on the fact of its break. In addition, there were reproaches that the model does not explain the initial occurrence of the “reversal 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 authors' conservatism.

Let's not rush. In any case, the broken demand model can be useful for explaining situations in new oligopolistic industries, when rivals still do not know each other well, or in the case of newcomers joining the industry, about whom little is also known.

11.5. Rivalry and collusion

When a healer and a priest Strengthen their alliance with the judge, then labor is not in vain: They will cleanse you in no time for the sake of money, kill you and give you a drink.
Francisco A. Figueroa (17911862)

The strategy of oligopolists, for all its diversity, has two poles: rivalry and collusion. If the 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 sectoral market.

Equilibrium of the industry in collusion. When oligopolists collude, they may agree on prices, market shares, advertising costs, and so on.

The formal agreement of oligopolists is called cartel. A cartel is able to maximize profits if it operates as a monopoly, that is, if the members of the cartel operate as one firm. A similar situation is shown in Fig. 11.6.

The general market demand curve corresponds to the market curve MR. Curve MS cartel is the horizontal sum of the curves MS its members. Profits are maximized at issuance Q* and price R* at MS =MR.

However, having agreed on a cartel price, cartel members can compete with each other using non-price competition for getting a bigger share of sales Q*.

Rice. 11.6. profit maximizing cartel

If, on the other hand, the members of the cartel agree among themselves on the division of the market, then each of them will receive an appropriate quota.

Silent collusion: price leadership. Since many countries have anti-cartel laws in the name of combating monopolization, firms can enter into silent conversation. 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 dominantacceptance. If the price leader is a firm whose behavior deserves the trust of other members of the oligopoly, then this situation is called pricebarometer firm leadership All other firms in the industry are called Konkarental environment.

At price leadership of the dominant company The leader maximizes profit based on the equality of his own marginal cost and marginal revenue.

On fig. 11.7, but the market demand and supply curves 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 fraction of market demand minus the competitor's 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 but). 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
a) „w / b)

S competitive environment

S competitive environment

RA

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 profit of the leader will reach a maximum when the marginal cost of its production is equal to the marginal revenue. This state corresponds to the release point of the leader (q L) and the price he set (P L). The competitive environment will take this price as given and will produce QF products. The total output of the industry will be 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. Contributing factors include the following:

• there are very few firms in the industry, and all of them are well known to each other; firms do not hide cost parameters and production methods from each other;
• firms have similar production methods and average costs;
• firms produce similar products; there is a dominant firm in the industry; barriers to entry into the industry are significant; the market is stable; the state does not pursue an active anti-collusion policy.

Collision destruction. In a collusive situation, there is always a temptation to break quota agreements or lower prices.

Imagine a cartel consisting of five identical firms (Fig. 11.8, but). Let the equilibrium price be 10 den. units, and the equilibrium volume is 1000 units. with a quota of each firm of 200 units.

Rice. 11.8. Firm's propensity to increase production above quota or to lower the cartel price

Now let's look at Fig. 11.8, b. It illustrates the situation of one of the cartel members, the firm BUT. Cartel price of 10 den. units equals the same marginal revenue for a sole proprietorship. This will create a desire for firm members to produce more than their quota. The firm will maximize its profit by selling 600 units. goods at MS = R =MR, taking away a part of the market from other cartel members, but leaving the total output of the industry unchanged.

On the other hand, the firm BUT may be tempted to lower the selling price of their products below the cartel price. With a fairly elastic demand curve (AR in fig. 11.8, b) the firm can reduce the price of a unit of production to 8 den. units when selling 400 units. products.

Naturally, other members of the cartel may take countermeasures in response to these violations of collusion, which is fraught with the risk of unleashing a price war.

11.6. Game theory and its application in advertising

Poetry? It's a hobby.
I breed pigeons.
And Mr Smith is embroidering with garus.
It's not work. You don't sweat.
You don't get money.
I'd take on a soap commercial.

Basil Bunting (19001984)

As attractive as the result of a collusion may be for its participants, it is 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 similar to the prisoner's dilemma can be analyzed on the basis of the mathematical game theory developed by J. von Neumann and O. Morgenstern back in the 1940s. one

Table 11.7
The prisoner's dilemma

A prisonerY

Confession Silence

Confession

Prisoner X

Silence

• 1 See: Neumann J., Morgenstern O. Theory of Games and Economic Behavior. 3d cd. Prince tone. 1953.

This concept can be used, for example, in the advertising strategy of an oligopoly. In an oligopoly, product differentiation and sales rivalry can lead to an excessive increase in advertising spending. The firm is able to optimize these costs based on game theory.

In table. 11.8 shows the consequences of the implementation 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 capture a part of the firm's market. IN and increase its revenue by 40 million, having received 20 million in net profit. This transfer of profit from the firm IN to the firm BUT happens if the company's advertising budget IN will remain unchanged. Similarly, if the firm IN increase its advertising spending by $20 million over the firm's spending BUT, then the firm IN will receive 40 million additional revenue and 20 million rubles. additional profit. one

table 11.8 shows that the simultaneous increase by two firms of their budgets by 20 million rubles. will result in lower profits. The maximum cumulative profit will be made if both firms maintain their current advertising budgets.

Table 11.8
Monopoly Non-Price Competition: Profit from an Advertising Strategy

Maintaining the current	Increasing the budget
		budget	and for 20 million rubles.
	Saving the 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.
	for 20 million rubles	B = 120 million R.	B = 80 million R.

The worst case scenario would be for each firm to independently form the advertising budget (in the absence of collusion).

1 The price elasticity of a firm's advertising activity can be defined as c m= = (dQ ,/&4,) (A J Q), and the cross elasticity of advertising as r | iA = (EO / d(U). Therefore, the percentage change in the firm's income i as a result of a 1% change in its advertising budget (at constant prices) is:

dAJA, ~ dA, "p&"qSa h^"aA, ^ L *

dAJ /AJ

where in "*" dA t /A,

Control tasks

Review questions

1. What are the similarities and differences between monopolistic competition and oligopoly?
2. What factors facilitate the creation of a cartel, and what contribute to its collapse?
3. Which positions of the model with a broken demand curve have been criticized?
4. What is the main disadvantage of the Courpeau, Bertrand and Stackelberg models?
5. What are the similarities between the collusion problem and the prisoner's dilemma?
6. Does the equilibrium in the Cournot model satisfy the definition of Nash equilibrium?
7. What is a dominant strategy and why is the equilibrium in dominant strategies stable?
   Problemsfordiscussions
8. In the five chapters of Part II, you've been introduced to basic (and non-basic) market structures. Discuss which of them have become widespread in the economy of modern Russia, and which are rare. Were there any market structures in the Soviet economy?
   A task
9. Oligopoly mean income function: R= 100 2 (Q , + Q). cost function
   each firm is equal to: С = 100 + 10 Q , i = 1,2 (where MCt = 10). To find:

• a) the marginal revenue function for each firm in the Cournot model (assumed
  expectation that the other seller will not change the output);
• b) the quantitative response function for each firm;
• c) equilibrium price and output for the Cournot model;
• d) compare the profit of each firm and compare it with the profit if
  firms colluded.