Nash Equilibrium or Non Cooperative Equilibrium

Nash equilibrium is a concept from Game theory which establishes that a set of strategies followed by economic agents within a game is in equilibrium if, holding the strategies of all other economic agents are constant, no economic agent can obtain a higher pay-off by choosing a different strategy. For example, when firms operate within an oligopoly, once Nash equilibrium has been reached, none of them will want to change their strategy because by doing it, they cannot obtain a higher profit. In other words, a Nash equilibrium is a solution in which no player can improve his/her pay-off given the other’s strategy. In other words, each player’s strategy is a best response against the other player’s strategy, that is given player A’s strategy, player B can do no better, and given B’s strategy, A can do no better. The Nash equilibrium is also sometimes called the non cooperative equilibrium because each party chooses that strategy which is best for itself, without collusion or cooperation and without regard for the welfare of society or any other party. 

In the solution concept of Nash, each player is assumed to know the equilibrium strategies of the other players, and no player has anything to gain by changing only his or her own strategy unilaterally. If each player has chosen a strategy and no player can benefit by changing his or her strategy while the other players keep their unchanged, then the current set of strategy choices and the corresponding pay-offs constitute a Nash equilibrium.

According to the Nash theorem, every game with a finite number of players and a finite number of strategies will have at least one Nash equilibrium. For this to hold, however, there has to be the possibility of some random elements to strategies. A Nash Equilibrium is a set of mixed strategies for finite, non-cooperative games between two or more players whereby no player can improve his or her pay-off by changing their strategy. Each player’s strategy is an ‘optimal’ response based on the anticipated rational strategy of the other players in the game. 

The theory of Nash equilibrium has two components:
(i) the players act in accordance with the theory of rational choice, given their beliefs about the other players’ actions (i.e., the player makes rational decision-making in the absence of cooperation), and
(ii) these beliefs are correct. If every player / participant knows the game he / she is playing and faces incentives that correspond to the preferences of the player whose role he / she is taking, then difference / deviation between the observed outcome and a Nash equilibrium can be blamed on a failure of one or both of these two components. 

If a Nash equilibrium is established by any means whatsoever, no firm (player) has an incentive to exit / move from it by changing its own behavior. It is self-policing. It is self-policing in the sense that there is no need for group behavior to enforce it. Each firm has self-interest to continue (keep up) it because any move that it can make on its own will not improve its profits, given what other firms are currently doing. 

The Nash equilibrium can be illustrated by making some modifications in the pay-off-matrix given in the table. Now we assume that action and counter-action of advertising (Ad) between Firms A and B. It is a regular phenomenon and the pay-off matrix that appears finally is given in table. The only change in the modified pay-off matrix is that neither Firm A nor Firm B increases its ad-expenditure, then pay-offs change from (15, 5) to (25, 5).

Pay-off Matrix of the Game 
B’s Options 
                                                      Increase Ad        Don’t Increase 

A’s Strategy      Increase Ad          A            B            A              B 
                                                  20           10           30             0 
                         Don’t Increase    A            B            A              B 
                                                  10           15           25             5 

From the payoffs matrix, we can see that Firm A has no more dominant strategy. Its optimum decision depends now on what Firm B does. If Firm B increases its advertising-expenditure, Firm A has no option but to increase its advertisement expenditure. And, if Firm A reinforces its advertisement, Firm B will have to follow the suit. On the other hand, if Firm B does not increase its advertising-expenditure, Firm A does the best by increasing its ad-expenditure. Under these condition, the conclusion that both the firms arrive at is to increase advertising expenditure if the other firm does so, and ‘don’t increase’, if the competitor ‘does not increase’. In the ultimate analysis, however, both the firms will decide to increase the ad-expenditure.

The reason is that if none of the firms increases advertisement, Firm A gains more in terms of increase in its sales ($ 25 million only). And, if firm B increases advertisement expenditure, its sales increase by $ 10 million. Therefore, Firm B would do best to increase its ad-expenditure. In that case, Firm A will have no option but to increase its ad-expenditure. Thus, the final conclusion that emerges is that both the firms will go for advertisement war. In that case, each firm finds that it is doing the best given what the rival firm in doing. This is the Nash equilibrium.

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Payoff Matrix in Game Theory

Game theory summarizes in a tabular way the possible choices available to firms in oligopoly. Game theory applied to oligopoly uses a table that indicates the profit of each firm given the choice of strategy chosen by each. All possible strategies are represented in the table, and so all possible outcomes can be considered at once. This table is called a payoff matrix. The profits listed in the payoff matrix represent / exemplify underlying cost and demand information.

Suppose again that there are two firms. For simplicity, suppose that price and costs are all taken as given and that the only decision for these two firms is how much to spend on advertising and both engage in high levels of advertising, neither will enjoy particularly high profits. If neither firm advertises at a high level, each will keep its respective market share, but both will make larger profits. However, if one advertises while the other does not then the firm that advertises will gain market share and get big increase in profits while the other incurs losses. Assume that advertising might increase on holding the firm’s share of the market but it has little effect in expanding total industry sales. Finally, assume that firms reveal their strategies simultaneously and do not change them. Although it is quite simple, this model contains monetary features of the recognized interdependence of oligopolists.

The model is depicted in the payoff matrix in table.

Payoff Matrix

Firm A’s strategy
High Level of Advertising                                   Low Level of Advertising
High Level of Advertising   X gets $ 5,000      A gets $ 2,000
                                         Y gets $ 5,000      B gets $ 2,000

Low Level of Advertising   X gets $ 2,000     A gets $ 10,000
                                         Y gets $ 20,000   B gets $ 10,000

Both firms choose high levels of advertising. They then earn profits $ 5,000 each. If both adopt low levels of advertising, they each enjoy profits $ 10,000. But of one firm advertises much and the other little, the firm with the high level of advertising earns profits of $ 20,000 and the other firm losses $ 2,000.

Now put yourself in the place of the Manager of firm B, the choice of B firm will depend precisely on what you think from A will do. If you think firm A will try to do you in, then you will assume that if you try to get the $ 10,000 profit available by going for a low level of advertising, Firm A will choose a high level of advertising in self-protection. This strategy assumes you of at least $ 5, 000.

Firm A has exactly the same choices, and so if Firm A assumes that firm B is not be trusted. Firm A also chooses a high level if advertising for his self-preservation. Thus, the conservative maximum strategy leads both firms to high levels of advertising. As a result, each gets a $ 5,000 profit.

Only of the firms cooperated can earn the $ 10,000. Profits that is available to each. If firm B assumes that firm A is a profit maximizing firm with managers who behave rationally, then firm B concludes that firm A will adopt a low level of advertising. If firm A makes the same assumption about firm B then each attains profits of $ 10,000.

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Meaning of The Game Theory and Importance of Game Theory

The term ‘game’ represents a conflict between two or more parties. A game is a decision situation with multiple decision makers where each person’s welfare depends on his/her own as well as other individuals’ actions. That is, a game is a decision situation with strategic interactions among all decision makers.

Game theory is a theory of individual rational decisions taken under conditions of less than full information concerning the outcomes of those decisions. This theory examines the interaction of individual decisions given certain assumptions concerning decisions made under risk, the general environment, and the cooperative or non-cooperative behavior of other individuals.

In the words of Richard G. Lipsey and K. Alec Chrystal, “Game theory is an approach to analyzing, rational decision-making behavior in interactive or conflict situation.”

According to N. Gregory Mankiw, “Game theory is the study of how people behave in strategic situations." By ‘strategic’, we mean a situation in which each person, when deciding what actions to take, must consider how others might respond to that action. Game theory is a mathematical technique used to show for example, how oligopoly firms play their game of business.

Importance of Game Theory

Game theory is an analysis that illustrates how choices between two plays affect the outcome of a “game”. Game theory which sounds playful/laughing in its terminology is filled with significance. It has been used by economists to study the interaction of oligopolistic markets, union-management bargaining disputes, countries’ trade policies, international environmental agreements, reputations, conflicts such as games and war and a large number of other situations. Game theory offers insights for politics, warfare, and everyday life as well.
  1. Game theory is commonly used in economics to illustrate interdependent decision-making among oligopoly firms. It illustrates that one firm makes a decision based on the decision expected from the other firm. One key conclusion from the game theory analysis is that firms often make decisions that are “second best” or the “lesser of two evils”. The classic example of such a decision is the prisoners’ dilemma, in which two prisoners both confess to a crime to avoid harsher punishment when not confessing would avoid any punishments.
  2. Thus, game theory has proved to be useful in analyzing suspects of economic behavior such as natural resource depletion and public goods. The theory of cooperative games which allows collaboration between individuals has been used to analyze cartel formation and industrial and labor market collusion.
  3. Game theory is a body of knowledge which is concerned with the study of decision-making in situations where two or more rational opponents are involved under conditions of competition and conflicting interests. It deals with human processes in which an individual decision making unit who can be an individual, a group, a formal or informal organization, or a society, is not in complete control of the other decision making units, the opponents, and is addressed to problems involving conflict, co-operation or both at various levels.
  4. The main objective in the theory of games is to determine the rules of rational behavior in the game situations, in which the outcomes are dependent on the actions of the interdependent players. A game refers to a situation in which two or more players are competing it.
  5. Game theory is quite useful for understanding the behavior of oligopolies. When game theory is applied to oligopoly, the players are firms. Their game is played in the markets, their strategies are their price/output decisions, and the payoffs are their profits. Because the number of firms in an oligopolistic market is small, each firm must act strategically. Each firm knows that its profit depends not only on how much it produces but also on how much the other firms produce. In making its production decision, each firm in an oligopoly should consider how its decision might affect the production decisions of all the other firms.
In summary, a game theory framework can often help us understand the strategic choices available but it does not always help to predict which of many possible outcomes may occur.

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Firm determines the best level of output and price for products | Joint products in fixed proportions of one to one

The firm determines the best level of output and price for products that are jointly produced in fixed proportion.

Joint products result from production processes that naturally yield multiple products. A decision to run the production process automatically produces the entire product group. For example, the processing of sugarcane results in a by-product called bagasse, which is the residue of the cane stalk after the juice has been squeezed out. By-products may be used, or sold or otherwise disposed of. Bagasse, for example, is burned to make steam to generate electricity. By-products that cannot be used or sold create a problem (and a cost) of disposal. The proportion of joint products may be either fixed or variable.

Joint Products in Fixed Proportions of One to One

Since there is only one production process, there is no economically sound to allocate costs to the individual products. The demand curves, however, can be and usually are quite different for the main product and the by-products. Determination of the optimal output and prices involves optimization of the total marginal revenue from all products in relation to marginal cost. We shall explain the procedure with the help of figure.

In the figure, it depicts two cases of the joint products A and B produced in the fixed proportion 1:1. In order to maximize profit, we must find the level of production at which MRT = MC; however, there is a complication; neither product may be sold beyond the quantity where its individual MR < 0. This is because of negative marginal revenue, means we would be losing money on each unit sold. In both panels, MRs = 0 at QM units of joint production.

The step-by-step procedure for determining optimal output and price goes as follows:

Step 1: Develop or obtain the demand function for Product A (DA on the figure) and it is related to marginal revenue (MRA).

Step 2: Develop or obtain the demand function for By-product B (DB on the graphs) and it is related to marginal revenue (MRB).

Step 3: Add MRA and MRB to obtain MRT.

Step 4: Obtain the total cost function and take its derivate to get marginal cost, MC.

Step 5: Observe the value of Q at which MRB = 0 (QM on the graphs).

Step 6: Observe the level of Q at which MRT = MC (QC on the graphs).

Step 7: Compare QC to QM. If QC ≤ QM, then the optimal output and sales level for both products is QC

This condition is illustrated on Panel A. Go to step 9.

Step 8: If QC > QM, as illustrated on Panel B, then the maximum quantity of By-product B that can be sold is QM. To find the optimal quantity of the main product A, find the level at which MRA = MC. This is at Q3 on Panel B. Of course, Q3 units of By-product B will also be produced but the quantity Q3 – QM will be dumped, destroyed or otherwise disposed of, because selling it means losing money on every unit sold. In the past, the cheapest method of disposal has too often been indiscriminate dumping. Legal and environmentally sound disposal methods may incur additional costs. These additional costs can be quite substantial, and thus provide a powerful incentive to find new uses and new markets for the unwanted product.

Step 9: Use the demand functions of A and B to find the prices at which the optimal quantities may be sold. Thus, in both panels, Product A would sell for PA, and By-product B would sell for PB.

Joint Product in Fixed Proportions Other Than a One-to-one Ratio

If the joint products are produced in fixed proportions other than 1:1, we must first remember that the cost function pertains to output of the main product. Therefore, we want to establish a ratio of 1x, where x is the number of units of By-product per unit of the main product. For example, suppose that the demand and cost functions remain the same for Product A and By-product B of the previous example, but the production technology changes so that the production ratio becomes QA:QB = 2:3.

We note that the ratio 2:3 is the same as the ratio 1.0:1.5. Hence QA = Q and QB = 1.5QA. By making appropriate substitutions of 1.5 QA for QB and vice versa, the procedure described above for a 1:1 ratio can be followed.

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Firm produces multiple products X and Y

The firm produces multiple products X and Y. The firm determines the optimum output and price of X and Y product when they are produced in fixed proportion.

The price theory or micro-economic models of determination are based on the assumption that a firm produces a single, homogeneous product. In actual practice, however, production of a single homogeneous product by a firm is an execution rather than a rule. Most of the firms have more than one product in their line of production. Even the most specialized forms produce a commodity in multiple models, styles and sizes, each so much differentiated from the other that each model or size of the product may be considered a different product. Various models of refrigerators, TV sets, ratio and car models are the examples, which are produced by the same company may be treated as different products for at least pricing purpose. 

The various models are so differentiated that consumers view them at different products and in same cases, as perfect substitutes for each other. It is, therefore, not surprising that each model or product has different AR and MR curves and that one product of the firm competes against the other product. The pricing under these conditions is known as multi-product pricing or product – line pricing.

The major problem in pricing multiple products is that each product has a separate demand curve. But, since all of them is produced under the organization by interchangeable production facilities, they have only one inseparable marginal cost curve. If the revenue curves, AR and MR, are separate for each product, cost curves, AC and MC will inseparable. Therefore, the marginal rule of pricing cannot be applied straight a way to fix the price of each product separately. The solution is similar to the one employed to illustrate third degree price discrimination. As a discriminating, monopoly tries to maximize its revenue in all its markets, so does a multi-product firm in respect of each of its products. To illustrate the multiple product pricing, let us suppose that a firm has two different products – X and Y in its line of production.

In the above figure, AR and MR curves for the two goods are shown in two segments. The marginal cost for all the products taken together is shown by the curve MC which is the factory marginal cost curve. Let us suppose that when the MRs for the individuals products are horizontally summed up, the aggregate MR (not given in the figure) passes through point E on the MC curve. If a line parallel to the X-axis is drawn from point E to the Y-axis through the MRs, the intersecting points will show the points where MX and MRs are equal for each product, as shown by the line EMR (Equal Marginal Revenue line). The points of intersection between EMR and MRs determine the output level and price for each product. The output of the two products are given as OQ1 of product X; and Q1Q2 of product B. The respective prices for the two products are P1Q1 for product X and P2Q2 for Y. These price and output combinations maximize the profit from each product and hence the overall profit of the firm.

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Major Pricing Objectives of a Firm

Pricing objectives are usually considered a part of the general strategy for achieving a broadly defined goal. The firm may aim at one or more of the following objectives. There are other objectives of the firm, which can be analyzed as follows:
  1. Profit maximization: According to economic theory, every business unit is guided by profit maximization. Thus, the objective of profit maximization has become the main pricing objectives of a firm. Similarly, profit has also become the measure of the success of the entrepreneur and maximization of profits for the entire product line. Firms set a price, which would enhance the sale of the entire product line rather than yield a profit on one product only.
  2. Target return on investment (ROI): Return on investment (ROI) may be the long-term objective of the firm. Under this, profits and costs objectives are depended on standard volume and the margins added to standard costs and designed to produce the target profit rate in investment.
  3. Stabilize price: Stabilization of price may be the one of the pricing objectives. Stable price helps to forecast production, sales, use of inputs, investment etc. The stable price also attracts consumer’s interest and preferences for the product of the firm which increases profit of the firm.
  4. Determine price according to competitive condition: Adaptation of prices to bit the diverse competitive situations faced by different products. Market competition relatively low price may be set to stimulate market growth and capture a large share thereof.
  5. Welfare of the firm in the long-term: Every business firm aims long term welfare of the firm. Promotion of the long-range welfare of the firm, i.e. discouraging the entry of competitors.
  6. Flexibility: Flexibility to vary prices to meet changes in economic conditions affecting the various consumer industries.

There must be set the price of product according to consumer’s purchasing power and government policy.

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Concept of Incremental Pricing with Incremental Analysis

The real world counterpart to marginal analysis is incremental profit analysis, which deals with the relationship between the changes in revenues and costs associated with managerial decisions. The emphasis on only the costs or revenues that are actually affected by the decision ensures proper economic reasoning in decision analysis. That is, proper use of incremental profit analysis results in accepting any action that increases net profits and in rejecting any action that reduces profits.

The fact that incremental analysis involves only those factors which are affected by a particular decision. It does not mean that the concept is easy to apply. Proper use of incremental analysis requires a wide-ranging examination of the total effect of the decision. For example, a firm’s decision to introduce a new product. Incremental analysis requires that the decision is based on the net effect of changes in revenues and costs. An analysis of the effect on revenues involves an estimate of the net revenues to be received for the product and, additionally, a study of how sales of the new product will affect the firm’s other products. It may be that the new product will affect the firm’s other products. It may be that the new product will, in fact, compete with the firm’s existing products; if so, even though the new product has a high individual revenue potential, the net effect on revenue might not justify the added expense. At the other extreme, although a new product may not be expected to produce much profit on its own, if it is complementary to the firm’s other products; the expected gain in sales of these other products could result in a large incremental increase in total profit.

The direct incremental costs associated with the new product, the firm must consider any impact on the costs of existing products. For example, introduction of a new product might cause production bottlenecks that would raise the cost of other products.

Incremental analysis involved long-run as well as short-run effects. New products may appear to be profitable in an incremental sense in the short-run because the firm has excess capacity in its existing plant and equipment. Over the long-run, however, this commitment to produce the new item may require a substantial investment when the necessary equipment wears out and must be replaced. There may also be high opportunity costs associated with future production if either expansion of other product lines or development of future alternative products is restricted by the decision to produce the new product.

It is important to stress once again that incremental analysis is based on the changes associated with the decision. For short-run analysis, fixed cost (over-head) is irrelevant and must not be included in incremental analysis.

An Illustration of Incremental Analysis

The Business Week article on flexible pricing cited above reports on pricing practices that reflect the use of incremental logic by numerous firms. The value of this approach is also demonstrated by an example of how Buddha Airlines has used incremental analysis in its flight service decisions. Then considering adding a new flight (or dropping an existing one that appears to be doing poorly), Buddha airways engages in a very through incremental analysis along the lines of table. The corporate philosophy is clear: “If revenues exceed out-of-pocket costs, but the flight on.” In other words, continental compares the out-of-pocket, or incremental, costs associated with each proposed flight to the total revenues generated by that flight. An excess of revenues over incremental costs leads to a decision to add the flight on continental’s schedule.

Table: Incremental Analysis as Employed by Yeti Airlines

Problems: Shall Buddha run an extra daily flight from Kathmandu to Pokhara?
Facts: Fully-allocated costs of this flight Rs. 4,500
          Out-of Pocket costs of this flight Rs. 2,000
          Flight should gross Rs. 3,100

Decision: Run the flight. It will as Rs.1,100 to net profit by adding Rs. 3,100 to revenues and only Rs. 2,000 to costs. Overhead and other costs totaling Rs. 2,500 (Rs. 4,500 minus Rs. 2,000) would be incurred whether the flight is run or not. Therefore, fully-allocated or average costs of Rs. 4,500 are not relevant to this business decision. It is the out-of-pocket, or incremental, costs that count.

The out-of-pocket costs figure that Buddha Airways users is obtained by circulating a proposed schedule for the new flight to every operating department concerned and finding out what added expenses will be incurred by each of them. Here, an alternative costs concept is used. If a ground crew is on duty and between works on other flights, the proposed flight is not charged a penny of their salary. Some costs may even be reduced by the additional flight. For example, on a late-night round trip flight between Kathmandu and Pokhara, Yeti Airways often flies without any passengers and with only a small amount of freight. Even without passenger revenues, these flights are profitable because their net costs are less than the rent for overnight hanger space of Kathmandu.

On the revenue side, Buddha Airways considered not only the projected revenues for the flight but also the effect on revenues of competing and connecting flights on the Buddha Airways schedule. Several Buddha airways flights which fail to cover even their out-of-pocket costs directly bring in passengers for connecting long-haul service. When the excess of additional revenue over cost on the long-haul flight is considered, Buddha airways earns a positive net profit on the feeder services.

Budhha airways use of incremental analysis extends to its schedule of airport arrival and departure times. A proposed schedule for Biratnagar Airport. For example it has two planes landing at the same time. This was expensive for Buddha airlines, because it facilitates in Biratnagar at that time were not sufficient to service two planes simultaneously. Buddha airways would have been forced to lease an extra fuel truck and to hire three new employees at an additional monthly cost of Rs. 1,800. However, when Buddha airlines began shifting around proposed departure times in other cities to avoid the congestion at Biratnagar, it appeared that the company might lose as much as Rs. 10,000 in monthly revenues, if passengers switched to competing flights leaving at more convenient hours. Needless to say the two flights were schedule to be on the ground in Biratnagar at the same time.

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Pricing decision on the basis of Cost Plus Pricing Theory

The pricing policy and pricing method depends on the objective of a firm sets for it. Cost Plus Pricing is also known as Mark-up or Average Cost or Full Cost Pricing. The Cost Plus Pricing is the most common method of pricing of a product by the manufacturing firms. The general practice under this method is to adds a ‘fair’ percentage of profit marginal to the average variable cost (AVC).

The price is set on:
P = AVC + AVC(m)

P = Price,
M = Mark-up percentage,
AVC(m) = Gross profit margin (GPM)

The mark-up percentage (m) is fixed so that to cover average fixed cost (AFC) and a net profit margin (NPM).

AVC (m) = AFC + NPM

The procedure of arriving at AVC and price fixation may be summarized as follows:
  1. The first step in pricing fixation is to estimate the AVC. For this, the firm has to ascertain the volume of its output for a given period of time, generally a fiscal year. To ascertain the output, the firm uses figures of its ‘planned’ or ‘budgeted’ output or takes into account its normal level of production. If the firm is in a position to compute its optimum level of output or the capacity output, the same is used as standard output in computing the AC.
  2. The another step is to compute the total variable cost (TVC) of the ‘standard output’. The TVC includes direct costs, i.e., cost of labour and raw materials and other variable costs. These costs added together give the total variable cost. The AVC is then obtained by dividing the TVC by the standard output (Qs).
AVC = TVC / Qs

After AVC is obtained, a ‘mark-up’ of some percentage of AVC is added to it for profit and the price is fixed while determining the mark-up, firms always take into account ‘what the market will bear’ and the competition in the market.

Given the possibility that cost-plus pricing might result in a non-optimal pricing/output decision. There are, indeed, reasons for this use, and on examination of the deviations between the basic micro economic model of the firm and the actual environment faced by the business explain why cost plus pricing is so popular.

Although micro economic theory is based on an assumed goal of value maximization, much of it is developed around a static construct in which the firm is assumed to operate so as to maximize short-run profits. Implicit in this is the assumption that continual maximization of short-run profits, coupled with proper adjustments to the physical plant as technology, factor prices, and demand change, will lead to long-run profit and value maximization.

The real world is more complicated than this model suggests. Actions taken at one time affect results in subsequent times, and wise business managers recognize this fact. Accordingly, because short-run profit maximization is seldom entirely consistent with long-run wealth maximization, firms do not focus solely on short run profit maximization.

Consider the case of a firm that sets the current price of its product below the short-run profit maximizing level in order to expand its market rapidly. Such a policy can lead to long-run profit maximization if the firm is able to secure a larger permanent market share by its action. A similar policy might also be used to forestall competitive entry into the market. From a legal standpoint, a policy of accepting less than maximum short-run profit could reduce the threat of antitrust suits or government regulation, thereby again leading to long-run profit and wealth maximization.

The existence of uncertainty in the real world is another complication that causes firms to depart from the theoretical micro economic pricing solution. Pricing under micro economic theory is based on the assumption that firms have precise knowledge of the marginal relationships in their demand and cost functions. Given these knowledge, it would be easy to operate so as to equate marginal revenue and marginal cost. However, firms know their cost and revenue functions only to an approximation, when the uncertainties of the future-economic condition, the weather, labor contract settlements and so on are added, it is abundantly clear why managers might do something other than equate marginal revenue and marginal cost when making price/output decisions.

Although the pricing corollaries of micro economic theory are far too limited to be applied without modification in actual pricing problems, the theory does not provide a useful basis for analyzing a firm’s pricing decision.

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The Cartel or Collusion Model

The cartel is an explicit agreement between the oligopoly firms. Cartel agreements represent the most complete form of collusion among the oligopolists. Under cartel agreements, firms jointly establish a cartel organization to make price and output decision, to establish production quotas for each firm and to supervise the market activities of the firm in the industry, cartel type collusions are formed with a view;

i) Eliminating uncertainty surrounding the market and 
ii) Restraining competitions and thereby ensuring monopoly gains to the cartel group.

For this, the board of control first calculates the MC and MR for the industry; MC for industry in the summation of MCs of individual firms. On the basis of industry’s MR and MC, the total output for the industry determined. The determination of industry output is shown in figure C and the share of each firm in figures A and B. For the sake of convenience, let us suppose there are only two firms in the industry, firm I and II. Their cost curves are given in figure C. The industry output is determined at OQ and price PQ on the pattern of monopoly firm.

The share of each firm in industry, quantity is determined at the level of their own output which equates their individual MC with the industry’s MC. The industry’s MC, CQ is determined by the intersection of industry’s MC and MR at point C. The market share of each firm can be obtained by drawing a line from point C and parallel to X-axis through MC to MC1 to the Y-axis. The points of intersection C1 and C2 determine the level of output for firm I and II respectively. Thus, the share of each of the two firms I and II, is determined at OQ1 and OQ2 where OQ1 + OQ2 = OQ. The total profit can be completed as (PQ – Firm’s AC) and firms output which is maximum. The total profit may be different, but there will be no motivation to change in price quantity combinations, since their individual profit is maximum.

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Price Leadership Model

Price leadership is said to exist when firms fix their prices in a manner dependent upon the price charged by one of the firms in the industry. The firm which takes the initiative in announcing its price charges is called the price leader. All other firms in the industry which either match the leader’s price or some variation thereof are termed price followers.

Price leadership may be either dominant or barometric. Dominant price leadership may occur when the leading firm is powerful enough to set a price which all other firms will be forced to follow. Barometric price leadership occurs when the leading firm is followed merely because the price it sets reflects the market forces and the needs of the other firms in the industry.

Price leadership in action is very much evident in mature and stable industries producing highly standardized product such as steel, oil, cement or building materials. It is, however, also to be found in industries characterized by considerable product differentiation.

The price leadership is generally a leader in all the markets. It may, however, frequently happen that a firm will sometimes follow in some markets and sometimes lead in others. In some industries, the price leadership shifts among major firms but more commonly a single firm remains the price leader for long periods. The price and output decisions have been explained in the following diagram.

Suppose all firms face identical revenue curves as shown by AR = D + MR. But the largest firm or the low cost firm, has its cost curves as shown by AC1 and MC1 whereas all other rival firms smaller in size have their cost curves as shown by AC2 and MC2. The largest firm has the economies of scale and its cost of production is lower than that of other firms.

Given the cost and revenue conditions, the low cost firm would find it most profitable to fix its price at OP2 = LQ2 and sell quantity OQ2. Since at this level of quantity, its MC = MR and hence its profit will be maximum. On the other hand, the high cost firms be in position to maximize their profit at price OP1 and quantity OQ1. But if they charge a higher price OP1, they would lose their customers to the low firm. The high cost firm is therefore forced to accept the price OP2, and recognize the price leadership of the low cost firm. At price OP3, the low cost firm can sell the same quantity OQ1, but it will, of course, make only normal profit.

In practice, price leadership frequently arises due to the following circumstances:
  1. Lower costs and enough financial resources: One of the firms has a clear advantage in cost or productive capacity and enough financial reserves to stand the losses of a price war without being seriously crippled.
  2. Substantial share of the market: Often, although not necessarily, the largest firm becomes the leader because it is presumed to have the greatest stage in the welfare of the industry, greater power to enforce followership and the best informed about industry demand and supply conditions and as such best equipped to determine price policy of the entire industry.
  3. Reputation for sound pricing decisions based on better information and more experienced judgment than what the other firms have: In fact, price leadership frequently arises as a natural growth within an industry due to the successful profit history, sound management and long experience of the price leader in marketing matters. The remaining firms accept the leader because of his ability to coordinate the industry’s growth with that of its members.
  4. Initiative: Often the company which first develops a product or area retains the price leadership whether or not it retains the largest market.
  5. Aggressive pricing: Often a company may grab leadership through lower prices and thereby snatch large and profitable markets from conservative rivals.

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