# Oligopoly: General Equilibrium and Oligopoly

Oligopoly: The Partial Equilibrium Approach

Oligopoly: The Gains from Trade

In the general equilibrium approach, it is important to explain the pattern of exports and imports as well as the costs and benefits of trade. The first problemto overcome is how to embed oligopoly in a general equilibrium model that was designed with perfect competition in mind. Some theorists have stressed the difficulties entailed by considering large firms, such as the possibilities of monopsony (or buyer power) in factor markets or considerations about what the large firm should maximize. Following the seminal paper by Lerner (1934) for the case of monopoly, Markusen (1981), Neary (2003), and Ruffin (2003a, 2003b) assume that it ismore convenient to consider firms to be large in their industrybut small in the economy. In this case, the firmcan treat all factor prices and prices in other industries asfixed.Ruffin(2003a) shows that the firm’s profit functions are then independent of the nume´raire selected, so the problem of what the firm maximizes is avoided. In this case, clear and simple results can be reached.

Both Neary (2003) and Ruffin (2003a, 2003b) also employ the assumption that firms act asCournot oligopolists; that is, they assume the outputs of their rivals are constant. Neary (2003) takes the assumption literally that firms are small in the economy by considering a continuum of firms, whereas Markusen (1981) and Ruffin (2003a, 2003b) simply consider a finite number of firms acting as if they are small in the economy.

The general equilibrium approach is most easily exhibited in a model in which Cournot oligopolies are selling in an integrated world market. Again, it is oligopoly profits that provide the key. How does oligopoly affect the costs and benefits of international trade? Consider two countries, Home and Foreign, that are the same size,with each having a comparative advantage in a good facing the same demand and costs. Since trade economists already know the impact of different factor intensities across industries, a Ricardian model (Neary 2003; Ruffin 2003a) with only one factor of production is often used. We shall call that factor ‘‘labor’’ but it could be a bundle of resources used in the same proportions in all industries. In this case, if we assume constant returns to scale, the production-possibility frontier for the economy is linear. With these assumptions we can assume thatbothcountrieshave the samewagesunder perfect competition. Moreover, if we assume that under oligopoly all industries have the same degree of competition (same number of firms), it will also be true thatboth countrieswillhave the samewages with orwithout trade.Thus ifwe takewages to befixed per unit labor (as the unit ofmeasure), we can take dollar costs as given for each country. Thus suppose, as in table 1, that it costs Home $4 to produce a bushel of apples and $6 to produce a bunch of bananas, and it costs Foreign $6 to produce apples and $4 to produce bananas.Note that it isbest to takewages as theunit of measure rather than one of the commodities, because in imperfect competition firms are choosing commodity prices to maximize profits.

It will be useful to summarize the Cournot oligopoly model when the product is homogeneous. The key assumption is that firms conjecture that rivals will maintain their output, a conjecture that holds in the Cournot-Nash equilibrium. There is a Cournot-Nash equilibrium if no firm can make an additional profit by changing its strategy, given the strategies of all of the other firms. If D(P) is the demand for the homogeneous product,D0(P) the slope of the demand curve, xi the output of the ithfirm, and ci themarginal cost of the ith firm, then the Cournot equilibrium is:

D0(P)(P ci)þxi ¼0(1)

Sxi ¼D(P)(2)

If there are N firms, this is a systemof Nþ1 equations. The demand functions clearly must reflect all prices and incomes. Ruffin (2003b) describes the general equilibrium equations, taking account of the incomes of all factors of productionand assuming all agents have identical, homothetic utility functions. Equations (1) and (2) replicate rivals holding output constant becausewhen the ith firmadjusts its output, D0(P) is the change in its demand by the resulting change in price. The interpretation of (1) is that if the firm adjusts output by D0(P) by causing price to rise by a dollar, it loses the profit margin on those units but gains xi on the resulting sales. But this becomes greatly simplified even in the case of nonidentical firms by adding the profitmaximizing equations (1) over the N firms and defining the price elasticity of demand as e¼D0(P)P/ D, resulting in:

P ¼Sci ⁄ (N 1⁄ ") (3)

For simplicity, suppose that e ¼ 1, which works for Cournot oligopoly for 2 N (Ruffin 1971). Since oligopolists price according to elasticities of demand, this equation can be applied in general equilibrium without worrying about the impact of oligopoly profits on demand as long as we assume world symmetry so that costs can be taken to be independent. In a Ricardian trade model in which both countries have the same income and face the same demand for the good in which they have a comparative advantage, equation (3) works well because we merely have to add the costs of all the firms active in both countries and divide by 1 less than the number of firms in each world industry.

Consider first perfect competition in which prices must equal marginal costs. Table 1 shows both autarky and free trade. Thus in autarky, apples will be $4 and bananas $6 in Home, and the opposite in Foreign. Now if international trade is opened, in a competitive situation only Home would produce apples and only Foreign would produce bananas. Thus people of theworldwould pay only $4 for both apples and bananas. The gains fromtrade are simple tomeasure in this case, since equalamountsofmoney are spent on apples and bananas: The price of the importable falls by 33 percent, and the gain from trade for the economy aswell asworkers (the same in this case)would be roughly one-half of 33 percent, or about 17 percent.

Under oligopoly both workers and oligopolists share in national income. There are two situations: a tight oligopoly in which the oligopoly profits protect high-cost producers from being driven out of business and a loose oligopoly in which oligopoly profits are insufficient for high-cost firms to survive the competition from low-cost rivals. For the moment assume the same degree of oligopoly in both industries, with only 2 or 3 firms in each country producing apples or bananas. With trade, each world industry has the potential of 4 or 6 firms. In the example, a tight oligopoly is when each country has only 2 firms producing apples and bananas, and a loose oligopoly prevails when each country has 3 firms producing both goods. Applying formula 3 to the autarkic state, as illustrated in table 1, we can see that under tight oligopoly Home will sell apples for $8 and bananas for $12.When trade is opened, apples will now be produced by 2 firms with costs of $4 and 2 firms with costs of $6, so according to formula 3 the price of apples (and bananas) will be $6.67 [ ¼ {2($4)þ2($6)}/3 ¼ $20/3]. Economic logic tells us that the price must be less than $8, because there are more firms. For Home (and Foreign is symmetrical), the price of apples falls by1.33/8, or 17 percent, and bananas by 5.33/12, or 44 percent, for a weighted average of 31 percent. Since we can hold worker wages the same (as the nume´raire), workers must gain 31 percent from the opening of trade, a substantial improvement over the case of perfect competition. In this case, with equal degrees of competition between the two sectors, the gains from trade to the economywill be smaller than in the case of perfect competition because the inefficient banana industry in Home and apple industry in Foreign still operate. Accordingly, since workers gain more than under perfect competition, it follows that trade causes substantial losses to the oligopolists compared with autarky. Nevertheless, the remaining oligopoly profits of the lower-cost firms serve to protect the highercost firms from competition, just as tariffs do.

If we have looser oligopolies, the situation may be quite different. As shown in table 1 again, suppose that the number of firms in each industry prior to trade is 3.Then inHome, applying equation (3) once again shows that under autarky apples will sell for $6 and bananas for $9, with the opposite in Foreign. When trade opens, the Foreign apple industry and theHome banana industrywill be unable to compete with their low-cost counterparts. Indeed, under Cournot, they will assume that any output will lower price below $6, so that the equilibrium price of each goodwill be $6.Notice that in this casewe get a result similar to perfect competition: trade causes the shutdown of inefficient industries, and both oligopolists andworkers gain precisely the same amount as under perfect competition.

The looser oligopoly drives higher-cost firms in the other country out of business simply because price is closer to their marginal costs. This is also a measure of the robustness of a country’s comparative advantage. The more robust the comparative advantage, in the sense of the greater the difference in costs between the Home and Foreign countries, more oligopoly power is compatible with driving foreign rivals out of business. Had we assumed $4 costs for apples in Home and $8 costs for apples in Foreign, only two Home firms would have been sufficient to drive the high-cost firms out of business.

In the tight oligopoly case examined in table 1, both high-cost and low-cost firms share the market. With perfect competition or a loose oligopoly, the high-cost firms are driven out of business. In general, this means that oligopoly power can reduce the degree of specialization and so reduce the volume of international trade. This helps to explain one of the most interesting observations about world trade in the last 50 years, namely that it has increased at about twice the rate of world output. People have usually attributed this to reductions in communicationcosts, transportation costs, and trade barriers. But the deregulation of industry and the rise of domestic competition may be another cause.