The first model of oligopoly was proposed by the French mathematical economist A. O. Kurnot in 1838. His model, in a simplified version, was designed for the functioning of only two firms in the market.

It is assumed that the second order condition is also satisfied SOC (second optimum

condition):

E 2 i,(P,.P 2) ER, 2

(However, a little later we will consider his model for the case of the presence of any number of firms in the market.)

Cournot assumed that both firms produce homogeneous product (mineral water), that they know the market demand curve (linear), that their operating costs are equal to 0 (this means that marginal costs are also zero). Each duopolist assumes that his rival will not change his output in response to his own change in production (the case zero estimated variation). In other words, when determining its output based on the requirements of profit maximization, each party assumes the output of its opponent given. As we see, it is release Cournot considered it a controlled parameter. This approach is quite traditional. At perfect competition the price does not depend on the output of an individual company. Instead, output is the only controllable variable. The monopolist can choose what to control - price or output (but not both parameters at the same time!). The output of the oligopolist depends on the output of its competitors. (This is exactly the approach Cournot chose.) But it also depends on the choice prices competitors influence the behavior of the oligopolist. (As we will see below, another French mathematician, J. Bertrand, followed this path.)

But let's return to the Cournot duopoly model. Let's first look at it on the graph (Fig. 16.1).

Rice. 16.1.

Let the first company start producing first. At the first step, it will turn out to be a monopolist and, in accordance with the condition M.R.= MS(at MS==0) will select release ts x. By the way, this will be half of the market demand

=|(2 (segment 0, l) j. In accordance with the market demand curve, the price will be set R A.

At the second step, the second firm begins to produce, which will consider the output of the first as a given. Line segment AD demand curve P.D.

the second company will calculate curve of the residual (unsatisfied) market demand with its marginal revenue curve ( MR 2). Since marginal cost is still zero, the second firm will choose output equal to the intercept q x q 2 . 1/2 of residual demand q x D and 1/4 of the total volume of market demand at zero price - 0D. Accordingly, for 3/4 of market demand the price will drop to the level R in.

Then it is the first firm's turn again. It takes into account that 1/4 of market demand is covered (cut off) by the second firm. And for her, the residual demand is 3/4 of the market one. It will cover half of it, i.e. 3/8 (instead of 1/2 in the first step).

If we continue our consideration in the same spirit, it will not be difficult to see that at each step the share of the first firm will be steadily declining until it reaches 1/3 of the total market demand. On the contrary, the share of the second company will constantly increase until it also reaches 1/3 of market demand. At this moment it will come Cournot duopoly equilibrium.

By jointly covering 2/3 of market demand at a single price, each duopolist provides maximum of your profit. But this is not the maximum total industry profit that could be achieved if both firms agreed and acted as monopoly. Accordingly, the price would be higher - at the monopoly level ( R A- in our example). For the first time he said that this is possible and that this does not even require an explicit conspiracy E. Chamberlin (Chamberlin duopoly model).

Duopolists, he argued, would not be so naive as to assume that their rival's output would remain unchanged in response to their own actions: "If each seller rationally and intelligently strives to maximize his profits, then he will understand that when only two or a few sellers act , its own actions have a significant impact on competitors. Therefore, it makes no sense to assume that they will leave unanswered the losses that are caused by his actions." Duopolists will quickly understand that it is better to divide the monopoly output in half (i.e., “take” 1/4 of the total market demand). Then both the market price and their profit will be higher.

Returning to our chart, we note that the first steps of both firms will be the same. But at its second step, the first firm, realizing that its rival is reacting to its actions, will reduce its output from 1/2 of market demand not to 3/8, but to 1/4 O D(segment 0 q(). In this case, the price will return to the monopoly level R L. The second firm, in turn, understands that if it tries to expand output beyond “its” quarter of the market, this will lead to a fall in the market price, response actions from the first firm, a further drop in price and its profit. Thus, having become convinced of their interdependence and interest in a high price, duonolists will “freely and voluntarily” choose the option of a joint monopoly, without even resorting to a secret agreement.

The actions of duopolists in the Cournot model can be clearly demonstrated using another graph, which shows response curvesRC (reaction curve) or, otherwise, best response curvesBR (best response)(Fig. 16.2).

Rice.16.2. Isoprofits and response curves of the first(A) and second(b) duopolists in the Cournot model

But in order to construct these curves, it is necessary to use such a concept as isoprofit, already known to us. Let us remember that in in general terms Isoprofits are curves formed by many combinations of two (or more) independent variables profit functions providing the same amount of profit.

In the Cournot model these variables are issues both companies. Thus, each isoprofit of the first firm in the space of outputs of both firms (Fig. 16.2, A) has many combinations q x And q2, providing this company with the same amount of profit. In principle, any number of such isoprofits can be built (isoprofit card). The isoprofit map of the second duopolist is constructed in a similar way (Fig. 16.2, b).

It is possible to derive isoprofit equations for each of the firms. Let the inverse function of market demand have a linear form: P(Q) = a-b Q. And in the case of a Cournot duopoly: P(q x + q 2) = a-b (q( + q 2). Total costs (TS) can be represented as With q x And With q 2 respectively, where With- specific average costs, equal for both firms.

The profit functions of both can be written as follows:

or

If some level of the firm's profit is taken as a constant value: p x And n 2, then equations of the form

and are isoprofit equations.

Let us note that the isoprofits are concave to the axis of the duopolist whose isoprofits are shown on the graph. The isoprofit form shows how the company will react to the actions of its rivals, trying to maintain the achieved level of profit. How closer isoprofit is located towards its axis, the greater the volume of profit it displays. The maximum possible profit the first firm could receive at point A, when the second firm's output would be zero, and its own would be the largest (monopoly). The maximum profit of the second firm could be achieved at the point IN(see Fig. 16.2). This is true if we consider that the closer the isoprofit comes to its axis, the lower the competitor’s output. For any given (selected) output of one firm, it is possible to find the only output of another firm that will provide the latter with maximum profit. Obviously, this must be the point of contact of some of the isoprofits. For example, in chart 16.2, A for a given output of the second firm q 2 this is the point L, determining the optimal output q x the first company. On chart 16.2, b - respectively point M, determining the optimal output of the second firm (q 2), providing it with maximum profit for a given output of the first firm (q()).

The locus of all such points describes reaction curve the corresponding company for any fixed issue of a rival 1.

An expression can be obtained that reflects the reaction of each firm to a given volume of output from its rival. To do this, remember that the maximum profit is achieved when equal M.R. = MS.

M.R. can be obtained by taking the first partial derivative of the expressions

A MS- as derivatives from cq l And cq 2 .

Having solved these equations for q(iq2, we obtain functions that connect the profit-maximizing level of production of the first (second) firm with the production volume of the second (first) firm:

1 Reaction curves are formed by a set of points of the highest profit that one of the duopolists can receive for a given amount of output of the other.

This is the equation of the reaction curves of duopolists.

The intersection point of the response curves of both duopolists, combined in one two-dimensional release space, corresponds to Cournot equilibrium(Fig. 16.3).

Rice. 163. Reaction functions of duopolists and equilibrium in the Cournot model ( CN)

The equilibrium outputs of Cournot duopolists are determined by mutual substitution. After which we have

The equilibrium outputs of duopolists are coordinates of the point Cournot-Nash equilibrium.

^ 2 (a-c)

• ()oschii release of duopolists: y ~H +? = -;-

Since the second derivatives of the profit function are less than zero:

then at the Cournot equilibrium point duopolists really get maximum profit.

Substituting expressions q wq 2 B inverse demand function equation: (P(Q) = a - bQ), we obtain the value of the equilibrium price in the Cournot duopoly market:

Response curves in the Cournot model can be used to visual illustration successive steps of duonolists (Fig. 16.4).

Rice. 16.4.

Let us assume that, as before, the first company starts, which at the first step is a monopolist. She chooses output at half (a-c)

market demand qj = - . For this issue, the second company has

only one optimal answer corresponding to a point on the curve RC 2.

4 (I C

This is the release qk = -- .

Reacting to the second firm's output as given, the first firm will reduce its production to q((corresponds to point IN on the curve RC X). Again the time comes for the second company to respond. It will increase its output to the level q 2(dot F on the curve RC 2)?

1 (A - With ^

Nash ( CN) with output at the level of market demand - .

In case of cartel agreement or tacit reasonable choice

(Chamberlin model) duopolists will choose output according to the market

(a-s L 4

demand - which corresponds to the point M on the chart.

Cournot oligopoly model for the case with any number of producers in the market

The Cournot model can be extended to an industry with any number of identical firms.

The simplest case is when there is only one company (monopolist) operating on the market. At the first step, she will choose the optimal output at the level

Substituting the resulting expression into the inverse demand function: P = a- - bQ, we will arrive at the expression optimal price monopolist:

Comparing monopoly output with duopolists' total output:

Note that monopoly is less. The price, on the contrary, under a monopoly will be higher:

If we work in the opposite direction, it will not be difficult to see that as the number of firms in the market increases, the market structure will increasingly meet the requirements of perfect competition (with P->°°). At the same time, industry output will increase, and the market price will decrease.

Let the industry have P firms Function costs r. firms: GS,(g/,) (with r = 1 ... P). P(q x + ... + q n)- inverse function of market demand (in the general case, nonlinear).

Let's imagine profit mr industry firms:

How to determine equilibrium in a market when everyone's output depends on the actions of others?

Let us imagine that there are such equilibrium outputs of all firms q x ,q 2 ,...,q n .

For any 2nd firm the following condition must be satisfied: Now we write system of inequalities for all companies in the industry:

From this system of inequalities it follows that if all other firms have maintained equilibrium outputs, then there is no point in changing output for the remaining firm, since this would be a clear deterioration in its position.

First order condition that must be satisfied for the i-th firm

(mRj - mcj) :

In the Cournot oligopoly model TC,(q,) = с? q v This means that all firms in the industry have equal and constant marginal costs: ts = s. Let us denote by MS total industry marginal costs: MS = s? P.

Let's sum up the following equations:

and subtract the expression -:

The expression in square brackets is marginal revenue (MR):

So, we have the Cournot equilibrium condition for an industry with P firms.

If the inverse industry demand function is linear: P(Q) = = a - b Q, That MR(Q) = a - 2b Q. Let us substitute them into the previous equation (Cournot equilibrium condition for an industry with P firms):

Having solved the resulting equation for Q*, we have

1 How much q = q* 2 = ... = q* n = - Q, That q = q* 2 = - =q*n= -^7*

P 0 /7 + 1

How more companies in the industry, the closer the factor -- becomes to one. Accordingly, the total output of all producers 1 + n

the market is approaching industry demand, which is almost completely satisfied only with perfect competition.

Returning to the last graph (see Fig. 16.4), we can see the equilibrium point of the perfectly competitive market (PC). If duopolists agreed to a price at the level of marginal (and average) costs, then they would also be able to satisfy all industry demand 2 .

Having received the release of the oligopolistic market for P firms, we can derive the price equation for this market:

With growth P the first term tends to zero, and the second and, therefore, the amount (i.e. price) strive To With - level of average and marginal costs.

Now you can determine what the profit of each company will be equal to:

The total profit in the industry will be

• 1 With perfect competition by definition long term profit both the typical firm and the industry as a whole is equal to zero: i (* = R? Q- With Q = 0. With linear inverse function
• (I - With

tions of demand P = a - b Q we have: to gk= (i - /> Q) Q = 0 => Q, = 0 and Q, = --.

• 2 It should be noted that Cournot had a completely unusual logic for considering market structures - from pure monopoly and duopoly to perfect competition as a limiting case. Typically, market structures are considered in reverse order.

It is easy to see that with the increase in the number of symmetrical firms in the market, the profit of each will quickly decrease. Total profit too, although slower.

• Chamberlin E. N. The Theory of Monopolistic Competition. Cambridge: Harvard University Press, 1933. P. 18.
• The equilibrium in the Cournot model turned out to be a special case of “Nash equilibrium” (J. Nash - Nobel laureate in Economics 1994). A market is said to be in a Nash state if each firm pursues a strategy that is the best response to the strategies pursued by other producers in the industry (see: Nash J. Equilibrim Points in w-Person Games // Proceedings of the National Academy of Sciences USA. 1950 Vol. 36. P. 48-49).
• MR, = TR"(q,) = (P? q,)’ no q,= P" q, + P.

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ABSTRACT

BEHAVIOR OF A FIRM UNDER DUOPOLY

Duopoly (from Latin: two and Greek: sell) - a situation in which there are only two sellers a certain product, not interconnected by a monopolistic agreement on prices, sales markets, quotas, etc. This situation was 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, output here is slightly larger, and compared to pure competition-- less.

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. Curve marginal income 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 on 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 installs more low price P 2, then the total demand of the market will increase (in our example it will be 75 units - see the industry demand curve D 0). Since firm No. 2 offers only 50 units, then the share of firm No. 1 will remain 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.

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”

A monopoly, like a perfectly competitive firm, may be faced with the task of minimizing losses in the short term. 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 the long run, 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.

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.

35. Behavior of a monopolist firm in the short and long term.

Short term. The graph reflects the process of choosing the optimal production volume by a monopolist and the process of establishing market equilibrium in a monopolized industry. The volume of production will be established at the level Q m, corresponding to the point of intersection of the marginal revenue and marginal cost curves (MC=MR). The projection of this point onto the demand curve (point O m) will also set the equilibrium price P m. Point O m reflects not only the price and quantity optimum for the company, but also becomes the point of industry-wide market equilibrium under monopoly conditions.

Under a monopoly, the degree of market imperfection reaches its maximum.

ABOUT This is especially evident in the fact that the typical consequences of imperfect competition affect this market with particular force.

1) severe underproduction of goods compared to the competitive level (QM<

2) a significant increase in prices compared to the value that would have developed under perfect competition (PM>>PO)

This happens because the complete absence of competitors in the market allows the monopolist to limit supply so sharply that the price level rises to an economically justified (from the monopolist’s point of view) maximum.

However, it is worth noting that a monopoly charges the maximum price it can afford, which is both high enough to maximize profits but low enough to induce consumers to purchase the maximizing output.

Long term. A monopolist does not have a supply curve. The monopolist's decision to change the scale of production depends only on the relationship between the market demand curves and long-term average costs. The monopolist himself determines how much product to produce in the industry => he can vary the supply in order to maximize profits.

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First graph: market demand does not change, then the monopolist enters the long-run period if the price is above long-term average costs.

Second graph: market demand changes (customers buy more) => new curves are formed => new price => huge profits => the company moves into the long-term period if there it can set a price higher than the average long-term cost.