Profits are total revenue minus total costs. A little algebra shows that we can compute profits from average revenue and average costs at any level of q: π =TR−TC π = TR − TC qqq TR = AR q
TC = ATC q π = AR − ATC q π =(AR−ATC)q
The equation says that we take average revenue minus average total cost (that’s profit per unit) and multiply times the number of units to get profits.
In the graph, this computation is simply the area of the shaded rectangle.

An oligopoly is a market dominated by a few producers. The market can be international, national, or local. The main characteristic of an oligopoly is that they have pricing power. However, unlike a monopoly that consists of a single firm dominating the market, an oligopolistic firm must take into consideration how the other producers will react to any changes in price. It is this mutual interdependence of the few firms producing the product that make an oligopoly different from a monopoly. Sometimes, an oligopoly will try to increase its market power by forming a cartel, which is a group of firms acting in unison.

An oligopolistic firm is generally a large firm that had to invest a lot of capital to produce the product, such as aircraft, cars, and household appliances. This large initial investment of capital is often a major barrier to entry to oligopolistic markets. Other barriers to entry include patents, control of strategic resources, and the ability to engage in retaliatory pricing to prevent firms from entering the market.

An oligopoly produces products that exhibit large economies of scale, where the cost of producing each unit declines with large quantities. Such economies of scale prevent other firms from entering the market, since there would be little market share that could be gained, and what could be gained would not be enough to be profitable. An oligopoly can produce either homogeneous or differentiated products. A homogeneous product is one that is not distinguished by quality differences from products produced by other firms. Most often such products consists of elements that are mined, such as zinc, copper, aluminum, lead, or produced from these elements, such as the production of steel. Although these products are mined from the earth, large amounts of capital are required to acquire the land, since ores that can be mined economically are located only in a few places. Then there is a large expenditure for equipment required to extract the ore and to separate the elements into a usable form.

A differentiated oligopoly produces differentiated products, much as in monopolistic competition. However, because the production of the products requires large amounts capital and exhibits steep economies of scale, the entry of firms is limited. Products produced by a differentiated oligopoly include electronics, cereals, cigarettes, sporting goods, motor vehicles, and aircraft.

Mergers

Some oligopolies start as independent businesses that grow with the economy, but many oligopolies are created by mergers, which are prevalent in such industries as airlines, banking, and entertainment. Mergers allow firms to attain a greater economy of scale by increasing their market share. A larger firm would also have more control over its prices and would have buying power for buying inputs to produce its products, thus, commanding lower prices from suppliers. The other main benefit to a merger is that it eliminates one or more competitors, since they are merged into the new company.

Industry Concentration

An oligopoly is said to exist when up at least 40% of a market is controlled by 4 firms. There are 2 commonly used measures that indicate the degree of dominance by a few firms: concentration ratios and Herfindahl Index. The concentration ratio is equal to the total percentage of output produced by the industry's largest firms. So a 3-firm concentration ratio of 85% means that 3 firms control 85% of the market. However, concentration ratios suffer from 3 flaws: localized markets, inter-industry competition, and world trade.

Since concentration ratios are generally ratios for national markets, some oligopolies may exist locally even though there are many firms across the country. For instance, the newspaper industry and TV and radio stations are dominate in local markets by a few firms, even though there are many of these firms scattered throughout the country. There are also many concrete producers nationally, but only a few firms dominate the local market, because of high transportation costs.

Concentration ratios also do not measure inter-industry competition, where some oligopolistic products have close substitutes. For instance, silver, aluminum, and copper can be used in many of the same applications, and which is used will often be determined by price.

The other thing that concentration ratios do not account for is import competition from foreign suppliers. For instance, the main competitor to Boeing is Airbus in Europe. Hence, importation helps to reduce the power of domestic oligopolies.

Herfindahl Index

A better measure of concentration ratio is what is called the Herfindahl Index, which is based on the following equation:

Herfindahl Index = %S12 + %S22 + … + %Sn2

Where the 1st term is the market share percentage of Firm 1 and the 2nd term is the market share percentages Firm 2, and so on, to the nth firm.

This yields a single concentration score that can be quickly assessed. For instance, consider a market dominated by a single firm — a pure monopoly. It would have an index of 10,000 because it would have 100% market share which one squared equals 10,000. A market dominated by 2 firms, each with a market share of 50%, would have an index of 5000, which yields 2,500 + 2,500 for a total of 5000. However, suppose the first firm had a 75% market share in the 2nd firm had 25%:

Herfindahl Index = 752 + 252 = 5,625 + 625 = 6,250

As can be seen, Herfindahl Index yields a better measure of the market power exhibited by the largest firms. Note that for monopolistic competition or even pure competition each firm's market share would be small, and thus, it would have a very small index, indicating that no firm has any market power.

Game Theory of Oligopolistic Pricing Strategies

In competitive, monopolistically competitive, and monopolistic markets, the profit maximizing strategy is to produce that quantity of product where marginal revenue equals marginal cost. This is also true of oligopolistic markets — the problem is, it is difficult for a firm in an oligopoly to determine its marginal revenue because the quantity of product that can be sold for a given price will depend on the prices charged by the other firms in the oligopoly and the quantity that they produce. Economists have examined this interdependence by using game theory, which analyzes strategies used by individual players that take into account what the other players will do.

Experimental economics studies game theory by designing scientific experiments using real individuals in specific situations to determine actual outcomes that are not dependent on statistical analysis. Nonetheless, even though statistical analysis is needed to analyze real-world scenarios, game theory offers insights into how oligopolistic firms price their product. A common scenario for applying game theory to decision-making is the prisoners' dilemma. Benny and Stella were arrested for robbing banks. Each was interrogated in separate rooms, where the interrogators offered them a choice:

• if they both confessed, they would both get 5 years in prison;
• if one confessed, the confessor would go free while the other one would get 10 years;
• if neither confessed, then they would each get 2 years.

There are 4 possibilities, which are represented by the following payoff matrix:

Prisoners' Dilemma Payoff Matrix
Stella confesses: 5 years
Bennie confesses: 5 years Stella silent: goes free
Bennie confesses: 10 years
Stella confesses: 10 years
Bennie silent: goes free Stella silent: 2 years
Bennie silent: 2 years

The best possibility for both would be if neither confessed, which would mean that they would only have to spend 2 years in prison. The worst possibility for both of them is if they both confessed — then they would have to spend 5 years in prison. However, as individuals, they may be able to do better or worse, depending on how successfully they anticipate what the other will do. If Stella confesses, the worst she can do is spend 5 years in prison, and the best that she can do is go free; likewise for Benny. In this case, confessing is what is called in game theory a dominant strategy, which yields the best outcome regardless of what other players do, especially when it is impossible to anticipate their decision. However, if Stella does not confess, then she will either spend 10 years in prison or go free, depending on whether Benny confesses or not. Stella will probably think about the likelihood that he will confess, then act accordingly.

When firms in an oligopoly must decide about quantity and pricing, they must consider what the other firms will do, since quantity and price are inversely related. If all of the firms produce too much, then the price may drop below their average total costs, causing them losses. If they can restrict quantity to that which corresponds to where marginal cost equals marginal revenue for the oligopoly as a whole, then they can maximize their profits. However, they do have one advantage over the prisoner's dilemma scenario — they usually know what the other firms did in the past, so they can decide on quantity and pricing based on the assumption that they will act in the same way in the future. But if the firm is wrong in its anticipation, then they can make corrections in its production schedule.

Where firms have a history of working together, they can choose a dominant strategy based on the choices that the other firms have made, which is called a Nash equilibrium, named after the theoretical economist John Nash, whose life was portrayed in the movie A Beautiful Mind.

Sometimes firms in an oligopoly try to eliminate guesswork by forming a cartel, where they agree on a particular output, so that they can sell their output at a profit-maximizing price.

Cartels often fail because one or more firms will be tempted to cheat, since this will allow them to earn outsized profits, especially if they are a smaller firm that contributes only a small share of the total output of the oligopoly. For that would allow the firm to sell a greater quantity at the profit-maximizing price without lowering demand, and therefore, the price. It would also improve the firm's economy of scale.

Diagram showing how much profit a cartel earns when they all cooperate, when 1 firm cheats, and when none of the firms cooperate.

• MR = Marginal Revenue
• MC = Marginal Cost
• D = Market Demand, Price

When firms in a cartel cooperate by restricting quantity for higher prices, then each firm gets Po for its product by restricting its quantity to the agreed amount Qo (it is assumed that Qo is equal to each firm's MR = MC output), and each firm earns the revenue above its marginal cost represented by the areas 1 + 3 in the diagram on the left. Hence, the oligopoly earns what a monopoly would earn. (Note that the quantity Qo would probably be different for the different firms, but the graph still represents each firm's revenue, but the quantity axis would be adjusted, depending on the firm's market share, which is usually commensurate with its size.)

When none of the cartel members cooperate, then the quantity increases to Qc and the market price declines to the competitive price Pc, and each firm in the oligopoly earns 3 + 4 above their marginal cost. (Again, the size of the 2 areas will be commensurate with the size of the firms and their corresponding market share.)

If a firm cheats, then it earns: 1 + 2 + 3 + 4 by producing more until MC = Po, which is equal to the quantity, Qcheater. This assumes that the firm produces only a small portion of the output of the oligopoly; otherwise, the firm's increased output would cause the market price to decline, and the market demand curve for the oligopoly as a whole would shift to the left.

Oligopoly Pricing Models

A pure monopoly maximizes profits by producing that quantity where marginal revenue equals marginal cost. However, it is much more difficult for an oligopoly to determine at what output it can maximize its profit. There are 2 major reasons for this: the interdependence of the firms and their diversity, especially in terms of concentration ratios. Some oligopoly's have a very high concentration ratio, allowing them to act more like a monopoly, while other industries have a much lower concentration ratio, thus, making it much more difficult to determine the best pricing strategy, since the number of possible responses by competitors is greatly increased. There have been 2 prominent characteristics of oligopolies observed over the years.

1. In a stable economy, oligopolies' prices change much less frequently than under any other market model, such as pure competition, monopolistic competition, and even monopoly.
2. When prices do change, the firms generally move in the same direction and by the same magnitude in their price changes, which may be the result of collusion.

There are 3 basic theories about oligopolistic pricing: kinked-demand theory, or non-collusive oligopoly, the cartel model, and the price leadership model.

Kinked-Demand Theory

Consider a firm in an oligopoly that wants to change its price. How will the other firms react? There are 2 possibilities: they can either match the price changes or ignore them. But what the other firms will actually do it will probably depend on the direction of the price change. If one firm raises its price, the others probably will not follow, since that will allow them to take market share from the price changer. This makes the demand curve more elastic, since as the firm raises its price, then many of its customers will buy from the other firms, lowering the revenue of the higher-priced firm.

If the firm lowers its price, then the other firms would surely follow, to prevent any loss of market share. This part of the demand curve is much more inelastic, since all of the firms are acting in concert. This creates a kink in the demand curve, where the change in demand goes from very elastic at higher prices to inelastic at lower prices. Since the marginal revenue curve depends on prices, the marginal revenue curve is also kinked. At lower prices, the marginal revenue curve drops downward creating a gap. The marginal cost curves of both scenarios will intersect the same quantity being produced by the oligopoly, represented by the vertical line in the graph; therefore, there is no change in quantity produced as prices are lowered, as long as the change in marginal cost is within the marginal revenue gap.

Graph showing how the demand and marginal revenue curves become kinked when an oligopolistic firm raises its price but the others do not follow, but if it lowers its price, then the other firms match the price decreases.

• P1 = Product Price of the Oligopoly

• If a firm raises its price (D1), but the others do not match the increase, then revenue will decline in spite of the price increase.

• If the firm lowers its price (D2), then the other firms will match the decrease to avoid losing market share.

• Because there is a kink in the demand curve, there is a gap in the marginal revenue curve (MR1 - MR2). Since firms maximize profit by producing that quantity where marginal cost equals marginal revenue, the firms will not change the price of their product as long as the marginal cost is between MC1 and MC2, which explains why oligopolistic firms change prices less frequently than firms operating under other market models.

The kinked-demand curve explains why firms in an oligopoly resist changes to price. If one of them raises the price, then it will lose market share to the others. If it lowers its price, then the other firms will match the lower price, causing all of the firms to earn less profit.
Critics of the kinked-demand model point out that while the model explains why oligopolies maintain pricing, it doesn't explain how its products were initially priced. The other thing it doesn't explain is that when the economy changes significantly, especially when there is high inflation, then the firms of an oligopoly do change prices often. In some cases, oligopolistic firms may engage in a price war, where each firm charges a successfully lower price to gain market share.

Cartel Model Sometimes firms in an oligopoly try to form a cartel by agreeing to fix prices or to divide the market among themselves, or to restrict competition some other way. The primary characteristic of the Cartel Model is collusion among the oligopolistic firms to fix prices or restrict competition so that they can earn monopoly profits.

If the dominant firms in an oligopoly can successfully collude to fix prices, then they can be certain of each other's output, which will allow maximizing their profits by producing that quantity of output where marginal revenue equals marginal cost, just as it would be for a monopoly. However, if any of the firms cheat, then a price war may ensue, lowering the profits of all firms, and maybe even causing them to operate a loss. In most modern economies, collusion is generally against the law, however there are certain countries that engage in collusion to maximize their profits from their natural resources.

The best example of a cartel today is the Organization of Petroleum Exporting Countries, otherwise known as OPEC, which comprises 12 oil-producing nations that supply 60% of all oil traded internationally. Prices are maintained by restricting each country of the OPEC cartel to a specific production allocation. The OPEC cartel is largely responsible for the large fluctuations in gasoline prices that have occurred in the United States since 1973, although recently, speculation in the commodity markets has also increased volatility.

Problems Creating and Maintaining Collusion

Collusion is often difficult to detect, because it is often based on tacit or covert agreements that are made during social interactions between the executives of the oligopolistic firms. Nonetheless, there are several obstacles to collusion.

One common obstacle is differences in demand and cost. Firms that serve different geographic markets will have varying levels of demand, and, in many cases, they will also have different efficiencies, resulting in different production costs. If economies of scale are steep for an industry, then smaller firms will aggressively compete on price to increase their market share, so that they can earn reasonable profits. In such cases, it will be difficult for the firms to agree on the price, because they will have different marginal cost curves. A good example is Saudi Arabia and Venezuela in the production of oil. Saudi Arabia is efficient in producing soil, whereas Venezuela, governed by an inept communist government, is highly inefficient, so it would be very difficult for Venezuela to accept a price that would be suitable for Saudi Arabia. Consequently, there is a great temptation for inefficient producers to cheat, and if they cheat, then price competition ensues.

Another factor that increases cheating is recessions. During recessions, demand declines, which shifts the firm's marginal cost and demand curve to the left. Firms often respond by reducing prices so that they can better utilize their production capacity and to try to gain market share from the other firms.

A larger number of firms in the oligopoly make it difficult both to create and maintain collusion. If there are only 2 or 3 firms in the oligopoly, then it is fairly easy to collude to set prices or to limit competition. However, if there are 6 or more firms with a smaller share of the market, then collusion becomes increasingly difficult. Indeed, the likelihood of a successful collusion decreases as the number of firms increases.

Another possible barrier to collusion is that if prices are maintained too high, then it may allow new entrants into the industry that will provide more competition, or, smaller firms that did not have much market power can cut prices and increase production to grab market share.

The other major barrier to collusion is antitrust law. Most modern economies prohibit collusion, since it is against the public interest, although there are some exceptions. A very common exception is the pricing of insurance products, since many insurance companies depend on rating companies that gather information on insurance risks and how to price them. In the United States, insurance rating information is exempted from the antitrust provisions of the United States.

Price Leadership Model

In many industries, there is a dominant firm in an oligopoly, and the other firms often follow the dominant firm in price changes, which can be viewed as a type of implicit price collusion. Hence, the dominant firm also becomes the price leader. Since most firms have been in the business for a number of years, they can observe how their competitors react to changes in the industry, allowing them to reach an understanding of how their competitors will react to any price changes. Firms in an oligopoly do not often change prices, certainly not for minor changes in costs, but they will change prices if cost changes are substantial. Indeed, if there is a general price increase in the inputs of an industry, then all firms will surely increase their prices. Increasing price of inputs, of course, helps to protect the industries from antitrust prosecutions since they have a reasonable basis for increasing the price of their products that is not related to restricting competition.

Oftentimes, the price leader will communicate the need to raise prices through press releases, trade publications, and speeches by major executives, especially when announcing quarterly earnings.

There are many times when a price leader will limit price increases to discourage the entrance of new competitors — a practice called limit pricing. This will be particularly true if the economies of scale are not that steep, since high prices can allow the entrance of new competitors who will be able to survive on a small market share.

Sometimes price leadership breaks down and price wars result. However, price wars are self-limiting, since they will often lead to losses. Eventually the firms will capitulate and return to the practice of following the price leader.

Productive And Allocative Efficiency Of Oligopolies Pure competition achieves productive efficiency by producing products at the minimum average total cost. They also achieve allocative efficiency because they produce until their marginal cost equals price. However, because oligopolies produce only until marginal cost equals marginal revenue, they lack both the productive and allocative efficiency of pure competition.

Because oligopolies can successfully thwart competition, they restrict output to maximize profits, producing only until marginal cost equals marginal revenue — hence oligopolies exhibit the same inefficiencies as a monopoly. Because the marginal cost curve intersects the marginal revenue curve before it intersects the average total cost curve, oligopolies never reach an efficient scale of production efficiency since they never operate at their minimum average total cost. Similarly, the marginal cost curve never intersects the market demand curve; therefore, oligopolies produce less product than what the market desires, so oligopolies lack allocative efficiency.

The graph below shows the long run equilibrium for monopolies, which is similar for oligopolies. Oligopolies, like monopolies and monopolistic competitors, also have excess capacity.

Diagram showing how an oligopoly sets its profit maximizing price by finding the market price that corresponds to the quantity where marginal revenue equals marginal cost, with profits equal to the price minus the average total cost times the quantity produced.

• ATC = Average Total Cost
• MR = Marginal Revenue
• MC = Marginal Cost

Note that where MC rises above MR, the firm would incur greater costs than it would receive in additional revenue, which is why the firm maximizes its profit by producing only that quantity where MR = MC, and charging the corresponding price.

1 Productive Efficiency: MC = Minimum ATC

2 Allocative Efficiency: MC = Market Price

Oligopoly Profit = (Price - ATC) × Quantity

Although there are many major industries dominated by oligopolies, there are rarely prosecuted under antitrust laws. However, there are several factors that limit the pricing power of oligopolies, including foreign competition and technological advances. Before extensive world trade, oligopolies developed independently in many modern economies. As trade barriers fall, oligopolies find they must compete with oligopolies from other countries, which diminishes their pricing power. Technology can also diminish the pricing power of oligopolies by producing better products, by lowering the fixed costs of developing a product, and by opening markets to more competitors. For instance, brick-and-mortar retailers now have much more competition from the Internet.

Many of the technological advances originate in oligopolies, because they have a greater amount of money to invest in research and development (R&D). While monopolies also have money for R&D, the need to conduct research is lessened by the fact that the monopoly has no real competition. However, over time, technological advances eventually rode even a monopoly's power. Hence, oligopolies invest heavily in research and development to maintain their pricing power.