Duopoly. Firm Behavior in the Industrial Group Duopoly: Uniformity and Symmetry
A better understanding of the patterns of behavior of a firm in an oligopolistic market allows the analysis of a duopoly, i.e. 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, consequently, the profit that the firm will receive, depend 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 like home analysis of a pending chess game, where the player is looking for the strongest responses 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 the duopoly was proposed by the French economist Augustin Cournot in 1838 in the book “An investigation of the mathematical principles of the theory of wealth”.
The Cournot model allows us to analyze the behavior of a duopolist firm on the assumption that it knows the volume of output that its only competitor has already chosen for itself. The task of the firm is to determine the size of its own production, in accordance with the decision of the competitor as a given.
The figure shows what the firm's command would be under such conditions. In order not to complicate the graph, we made two additional simplifications. First, they accepted that both duopolists are exactly the same, no different firms. Second, we assumed that the marginal cost of both firms is constant: the MC curve is strictly horizontal. The latter assumption, as 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, on the MC curve, only the middle part is considered, which lies near the technological optimum and really looks like a horizontal straight line.
The analysis of the behavior of the duopolist in the Cournot model was staged. First, let one of the oligopolists (firm No. 1) know for sure that the second competitor does not plan to produce any products at all. In this case, firm No. 1 will effectively become a monopoly. The demand curve for its products (D 0 ) coincides with the demand curve for the entire industry. Accordingly, the marginal revenue curve will take a certain position (MR 0 ). Using the usual rule of equality of marginal revenue and marginal cost MS = MR, firm No. 1 will set the optimal volume of production for itself (in the case shown in the graph - 50 units) and the level of yen (R 1 ).
Well, what happens if the next time firm No. 1 becomes aware that its competitor himself intends to produce 50 units. products at a price P 1 ? At first glance it may seem that by doing so he will exhaust the entire volume of demand and force firm No. 1 to abandon production. Having carefully examined the graph, however, we will see that this is not the case. If firm #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 firm No. 2. But if firm No. 1 sets a lower 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 drops 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, sorting through different possible price levels, we will also obtain different levels of market demand for the products of firm No. 1. In other words, a new demand curve will form for the products of firm No. 1 (on our chart - D 1) and, accordingly, a new marginal curve income ( MR 1 )> Using the rule again MS =MR, it is possible to determine a new optimal production volume (in our case, it will be 25 units - see Fig. 9.2).
Already at this stage of the analysis, the Cournot model allows us to draw important economic conclusions.
1. Under oligopoly, the amount of arbitrariness is greater than the level that would be established under pure monopoly, but less than it would be under perfect competition:
Q m A smaller output of products under oligopoly than under perfect competition, in fact, does not require proof: this is the case in any market of imperfect competition. So, in our example, oligopolists will release 75 units. products. And with perfect competition, output would be greater. Recall that under perfect competition, the demand and marginal revenue curves are the same. (D
=
MR),
therefore, the equilibrium point according to the rule MS
=
MR should be established at the intersection of curves D and MC, which, as can be seen on the graph, will cause the release of 100 units. But the fact that the oligopolistic output will exceed the monopoly output is also understandable. Indeed, in addition to the volume of production that the monopolist would have limited output (50 units), the output of the second producer (25 units) has also been added. 2.Prices in an oligopoly are lower than monopoly prices, but higher than competitive prices: R m >P olig >
P c
(9-2) The economic mechanism leading to the establishment of the described level of yens is also clear. By limiting production and inflating the yen, the monopoly leaves a part of the market demand unsatisfied. This remainder serves as a market for the second duopolist (as well as the third, fourth and further competitors, if we move from a duopoly model to a multi-company oligopoly), allowing him to produce additional output, if, of course, he reduces the yen below the monopoly level (on the chart - from R 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 duopolys will be below the profits that a single firm in the same market would receive* monopolist. P m >p olig >0
(9-3) We will again refrain from commenting on the general tendency of imperfectly competitive markets to make economic profits. The fact that their level is lower than that of monopolies is easiest to prove from the opposite As you know, the MC = MR rule ensures profit maximization. At the very beginning of the analysis of the Cournot model, we made sure that if only one monopolist firm operated on the market (the situation in which it is known about the second duopolist that he does not plan to release products is, in fact, tantamount to a monopoly), guided by this rule, it would establish a certain volume production and price levels. For any other volume of output (and price level), the profit will be less. But after all, the intervention of the second duopolist, the start of production by this second firm, just leads to the deviation of production volumes and prices from the optimum. Consequently, the total profit of the two duopolists will not be as great as that which a pure MONOPOLIST would be able to get. The general conclusion, which is also of great practical importance for the manager, is also obvious: under an oligopoly, there is not one, but many demand curves for the firm's products, namely, each level of output of one of the oligopolists corresponds to a special demand curve for the products of the other oligopolists. Recall how events developed in the model: knowing that the second firm did not plan to produce, the first one behaved like a monopolist and had a demand curve D 0 . As soon as firm No. 2 changed its mind and released 50 units. products, for firm No. 1 there is a new demand curve O,. It is obvious that the reasoning that we carried out in relation to the release by the second firm of 0 and 50 units. products, can be repeated for a variety of 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
MR 2
and MO. In other words, for any oligopolist, the volume of the market is not a constant value, but directly depends on the decisions of competitors. To better understand all the consequences of this pattern, let's turn to the figure. Let's pay attention to the unusual axes used on it. The horizontal scale is for one firm, and the vertical for another. In such axes, the size of the output of firm No. 1 can be depicted as a response curve to the volume of production of firm No.
2.
Similarly, firm #2's output can be represented as a function of firm #1's output: Q(1) = f
Q(2),
Q(2)
= φ Q(1) where Q(1) - the size of the production of firm No. 1; Q(2) - the size of the production of firm No. 2. With this formulation of the problem, we are actually trying to understand what will happen from the simultaneous efforts of two firms to adjust their output to the output of another firm. Let's see if both firms can establish mutually acceptable production volumes. We took all the data for the chart 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 on the release of 12.5 units. (dot BUT). But if firm No. 1 really releases 12.5 units. products, then, as can be seen in the graph, firm No. 2, in accordance with its reaction curve, should release not 75, but 42.5 units. (dot AT). But such a level of output by a competitor will force firm No. 1 to produce not 12.5 units, as it was going to, but 29 units. products (point O, etc. It is easy to see that the level of production that the firm sets on the basis of the existing size of the competitor's production, 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 changes the plans of firm No. 2 again. 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 - the point O). 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 release 33.3 units is indeed optimal. Each firm produces the volume of output that maximizes its profits for a given output of the competitor. It is not profitable for any of the firms to change the volume of production, therefore, the equilibrium is stable. It is called the Cournot equilibrium in theory. Under Cournot equilibrium
is understood as such a combination of outputs of each firm, in which none of them has incentives to change their decision: the profit of each firm is maximum, provided that the competitor maintains this output. or in another way, at the Cournot equilibrium point, the output volume 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 an 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. The mathematical theory of games, however, shows that the Cournot equilibrium is achieved under some assumptions about the logic of the behavior of duopolists, but not under others. At the same time, the understandability (predictability) of the actions of the partner-competitor and his readiness for cooperative behavior in relation to the rival is of decisive importance 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 duopoly model was proposed by the French economist Cournot in 1838. The Cournot model analyzes the behavior of a duopolist firm on the assumption that it knows the volume of output that its only competitor has already chosen for itself. The task of the firm is to determine its own size of production. Additional simplifications are made in the model: both duopolists are exactly the same, the marginal costs of both firms are constant (the MC curve is strictly horizontal). Let us assume that firm 1 knows that the competitor is not going to produce anything. Firm 1 is practically a monopoly. The demand curve for its products (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 cost MC=MR, firm 1 will set the optimal volume of production for itself (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 sorting 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. By using the MC=MR rule, a new optimal production volume can be determined. Short term. The graph reflects the process of choosing the optimal volume of production 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 curves of marginal income and marginal costs (MC=MR). The projection of this point on 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 firm, but also becomes the point of industry-wide market equilibrium under monopoly conditions. With a monopoly, the degree of market imperfection reaches a maximum. O 1) strong underproduction of goods compared to the competitive level (QM< 2) a significant overpricing in comparison with 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 point of view of the monopolist) maximum. However, it is worth noting that the monopoly charges the highest possible price for it, 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 decision of the monopolist to change the scale of production depends only on the ratio of market demand curves and long-run average costs. The monopolist himself determines how many products in the industry to produce => he can vary the supply in order to maximize profits. P Second graph: market demand changes (buyers buy more) => new curves form => new price=> huge profits => a company moves into the long run if it can set a price higher than the average long run costs. 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 duopoly model was proposed by the French economist Cournot in 1838. The Cournot model analyzes the behavior of a duopolist firm on the assumption that it knows the volume of output that its only competitor has already chosen for itself. The task of the firm is to determine its own size of production. Additional simplifications are made in the model: both duopolists are exactly the same, the marginal costs of both firms are constant (the MC curve is strictly horizontal). Let us assume that firm 1 knows that the competitor is not going to produce anything. Firm 1 is practically a monopoly. The demand curve for its products (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 cost MC=MR, firm 1 will set the optimal volume of production for itself (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 sorting 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. By using the MC=MR rule, a new optimal production volume can be determined. Question No. 34: "The behavior of the monopoly firm in the short and long run" A monopoly, like a perfectly competitive firm, may face the challenge of minimizing losses in the short run. A similar situation may arise, in particular, with a sharp decline in demand for its products. Even with the optimal size of its output, the monopolist will receive revenue in excess of direct costs (VC), but not enough to cover gross costs (TC = FC + VC). Stopping production, he will bear fixed costs(FC). In the absence of revenue, they will amount to 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 larger the gross margin, the smaller the total loss will be. The principle according to which the firm will choose the volume of output, the former - the equality of marginal revenue and marginal cost (MR = MC). The value of the average cost of issuing Q' will be equal to ATC'. Accordingly, the total costs, ATC'*Q' (the area of the rectangle with sides ATC' and Q' in the lower graph and the height equal to TC' in the upper one), will be greater than the revenue TR'. However, this revenue will exceed variable costs (VC) and will provide the maximum contribution margin (TR'-VC'). The difference between the values of TC' and TR' will be the minimum loss of the monopolist in the short run for all possible outputs. The monopolist's loss is minimized when the slope of the gross revenue curve () is equal to the slope of the gross and variable costs(), which confirms the equality of the values of MR and MC. In the long run, a monopoly firm that has previously minimized losses will leave the industry as economically inefficient. This is a relatively rare case. As a rule, a monopoly that receives economic profit in the short run retains it in the long run, optimizing output based on the equality of marginal revenue and long-run marginal cost. The duopoly model was proposed by Antoine Auguste Cournot in 1838. D wopolia – market structure when there are two firms in the market, the relationship of which are two firms in the industry and the market price. Peculiarity- the revenue (=profit) that the firm will receive depends not only on its decision, but also on the decision of the competing firm, which is also interested in maximizing its profit. Cournot model analyzes the behavior of a duopolist firm on the assumption that it knows the volume of output that its only competitor has already chosen for itself. The task of the firm is to determine its own size of production, in accordance with the decision of the competitor as a given. Additional simplifications: the duopolists are the same, the marginal costs of both firms are constant: the MC curve is strictly horizontal. Suppose firm 1 knows that a competitor is not going to produce anything at all. In this case firm #1 is effectively a monopoly. The demand curve for its products (D 0) will therefore coincide with the demand curve for the entire industry. Accordingly, the marginal revenue curve will take a certain position (MR0). Well, what happens if firm No. 1 becomes aware that its competitor intends to produce 50 units. products? If firm No. 1 sets a price P1 for its products, then there really will be no demand for it: those 50 units that the market is ready to accept at this price have already been supplied by firm No. 2. But if firm No. 1 sets a price P2, then the total demand market will be 75 units. (see industry demand curve D0). Since firm #2 offers only 50 units, firm #1 will have 25 units left. (75-50=25). If the price is lowered to P3, then, repeating similar reasoning, it can be established that the market demand for the products of firm No. 1 will be 50 units. (100-50 = 50). It is easy to see that by going through different possible price levels, we will get and different levels market needs for the products of firm No. 1. In other words, a new demand curve will form for the products of firm No. 1 (on our chart - D.) and, accordingly, a new marginal revenue curve (MR.). Using the rule MC = MR again, we can determine the new optimal production volume (in our case, it will be 25 units). 9. Why does the loss of price flexibility in the case of oligopolization of the market have a big impact on the economy? Highlighted text may not be needed
.
When a firm wants to move into a position that gives maximum profit, it will be forced to lower the price of products, thereby expanding sales. Competitors may not do anything in response, but may consider their interests to be infringed. After all, the expansion of sales by this firm means a decrease in the demand curve for their products. Therefore, they can lower prices themselves and thereby expand sales. The position of the break point of the demand curve becomes unpredictable. Changing prices and output in an uncoordinated oligopoly therefore becomes a risky business. It is very easy to cause a price war. The only reliable tactic is the principle "Do not make sudden movements." It is better to make all changes in small steps, with a constant eye on the reaction of competitors. Thus, an uncoordinated oligopolistic market is characterized by price inflexibility. There is another possible reason for price inflexibility. If the marginal cost (MC) curve crosses the marginal revenue line along its vertical section, then a shift in the MC curve above or below its original position will not entail a change in the optimal combination of price and output. That is, the price ceases to respond to changes in costs. Indeed, until the point of intersection of marginal cost with the line of marginal revenue does not go beyond the vertical segment of the latter, it will be projected onto the same point on the demand curve. In the case of an uncoordinated oligopoly, price self-regulation of the market, if not completely destroyed, is blocked: prices have become inactive, they no longer respond flexibly to changes in supply and demand, except for the most dramatic changes in these parameters. In the conditions of an uncoordinated oligopoly, serious distortions of prices and production volumes in comparison with the objective demands of the market become possible. There are also destructive price wars of giant corporations, when these imbalances break out and the oligopolists move on to open competitive battles. Examples of such wars were especially common in the early stages of formation big business- at the end of the 19th - the first half of the 20th century. 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. Decision 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 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. Decision. 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 be different if each of the trays were located at a distance of 40m from the ends of the beach? Let be p 1 and p 2 ≈ shop prices BUT and AT, q 1 and q 2 ≈ corresponding quantities of goods sold. Score AT 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 AT. 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 AT. 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 a 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 AT 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 solution. 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.
"
35. Behavior of a monopoly firm in the short and long term.
This is especially evident in the fact that the typical consequences of imperfect competition affect this market with particular force.
First graph: market demand does not change, then the monopolist goes into the long run if the price is above the average long run cost.
With the volume of output Q', the equality MR = MC is observed, which means the choice of the optimal size of production and minimization of the inevitable loss. With it, the gross revenue TR will be Р'*Q' (the area of a rectangle with sides Р' and Q' in the lower graph and a height equal to TR' in the upper one).
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. Equality MR=MC as a condition for choosing the optimal size of production takes the form MR=LMC.
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