Lesson 6: Economics of International Trade PDF

The new orthodoxy: Intraindustry trade Lesson #6 Economics of International Trade [EM1057] Prof. A. Paradiso Copyrighted work. Do not copy, cite, or distribute without permission of the aut...

The new orthodoxy: Intraindustry trade Lesson #6 Economics of International Trade [EM1057] Prof. A. Paradiso Copyrighted work. Do not copy, cite, or distribute without permission of the author. Contents 1 Introduction 2 2 From Traditional Theory to the New Theory 3 3 Imperfect competition 4 3.1 Monopoly....................................... 4 3.2 Oligopoly (Markusen, 1981)............................. 6 3.2.1 International trade pattern.......................... 9 3.3 Brander and Krugman (1983) oligopolistic model of international trade..... 11 4 Economies of scale 15 4.1 External economies of scale and international trade................ 16 4.2 Internal economies of scale and international trade................. 16 5 Product dierentiation and variety eect 17 5.1 Model assumptions and specications........................ 18 5.2 Demand side...................................... 19 5.3 Supply Side...................................... 19 5.4 Welfare........................................ 21 5.5 International trade pattern.............................. 22 6 Conclusions 22 A Consumption Level is the Same for all Varieties in Equilibrium 25 1 1 Introduction Classical theories of international trade emphasize technological dierences between countries, while neoclassical theories focus on dierences in factor endowments. In both frameworks, these dierences determine comparative advantage, which, in turn, drives international trade. According to these theories, international trade primarily involves the exchange of goods from dierent sectors, a phenomenon known as `intersectoral trade' or `interindustry trade'. When countries open to trade, they specialize in the production of goods in sectors where they have a comparative cost advantage. This advantage can stem from technological superiority (as highlighted by classical theory) or relative factor endowments (as per neoclassical theory). Consequently, in these models, a country cannot simultaneously export and import goods from the same sector. However, empirical evidence shows that these traditional theories explain only a limited portion of international trade. In reality, a signicant share of trade occurs between countries that are quite similar in terms of technology, factor endowments, and productivity, and it often involves the exchange of goods within the same sector. This type of trade is referred to as `intrasectoral trade' or `intraindustry trade'. The focus on intraindustry trade marked a signicant shift in the eld of international economics, giving rise to what is known as the `new theory of international trade' or the `new orthodoxy'. This paradigm shift occurred in the late 1970s and early 1980s, when a group of economists recognized that applying insights from industrial organization theory could help address long-standing issues in international trade that had been dicult to model using traditional approaches. Prominent economists such as Avinash Dixit, Elhanan Helpman, Paul Krugman, and Vic- tor Norman sought to explain the so-called `Linder paradox', named after Swedish economist Staan Linder, who, in the early 1960s, highlighted one of the key limitations of traditional trade theories. Linder pointed out that traditional theories failed to explain why similar coun- triesin terms of income levels, technology, and factor endowmentstend to trade more with each other. According to traditional theories, international trade arises from dierences between countries, and in their absence, trade should not occur. Yet, empirical evidence suggested the opposite, showing that similar countries engage in substantial trade. The rest of these lecture notes is structured as follows. In section 2, we discuss the limi- tations of neoclassical trade theories, the Linder paradox, and the transition to models based on imperfect competition. Section 3 explores the eects and role of international trade in economies with sectors characterized by market power, such as monopolies and oligopolies. In section 4, we examine the impact of relaxing the assumption of constant returns to scale and introducing increasing returns to scale in international trade. Section 5 focuses on analyzing the implications of product dierentiation in trade. Finally, section 6 presents the conclusions. 2 2 From Traditional Theory to the New Theory The emergence of the new theory of international trade marked a signicant turning point in economic thought during the 20th century. This shift involved moving away from the Walrasian paradigm of perfect competition, where prices are set by an `auctioneer' through a process known as `tatonnement', and towards models in which rms, previously considered mere `price- takers', also play a role in determining market prices. Traditional theories of international trade, linked to economists like Heckscher, and Ohlin, and later expanded by Jones and Samuelson, are based on the Walrasian model, which assumes perfect competition and constant returns to scale. In this view, trade between countries occurs due to major dierences in their preferences, technology, or factor resources. These theories suggest that when countries are quite similar, the potential for mutually benecial trade is reduced. In the extreme case where countries are identical, traditional theory suggests that no trade would take place at all. However, empirical evidence shows that a substantial portion of international trade occurs between countries that are quite similar in terms of income, technology, and factor endowments. Moreover, much of this trade involves the exchange of goods within the same industrial sector, a phenomenon known as `intraindustry trade'. This observation challenges traditional theories of trade, which are primarily based on intersectoral dierences, and forms the basis of the so-called `Linder paradox'. The Linder paradox, named after Swedish economist Staan Linder, arises from two main observations: (i) the vast majority of international trade occurs between countries that are quite similar in terms of economic characteristics, and (ii) a signicant portion of this trade is intrasectoral, meaning that countries export and import products within the same industrial sector. Linder's work in the early 1960s demonstrated that traditional trade theory could not adequately explain these patterns. In fact, traditional models predicted that trade should only occur between countries that are very dierent from each other, particularly in terms of technology and resource endowments. To address this paradox and to explain trade between similar countries, it became clear that the assumptions of perfect competition and constant returns to scale needed to be abandoned. However, until the 1970s, economic theory lacked the analytical tools necessary to model im- perfect competition and increasing returns to scale in a coherent and tractable way. It was only during this period, with the development of industrial economics, that models were created to bridge the gap between the extremes of perfect competition and monopoly. This led to the for- malization of intermediate market structures, such as oligopoly and monopolistic competition, which better reected real-world trade dynamics. It is important to recognize that these intermediate market forms, though useful, are not per- fect models of imperfect competition. Monopolistic competition, in particular, has been widely applied in international trade analysis. Each of these market forms is better suited to explain specic aspects of trade, depending on the particular problem at hand. Although the formal 3 rigor and generality of the Walrasian worldexemplied by the Arrow-Debreu modelhave been partially sacriced, the new theory of international trade provides international economists with more exible and powerful tools for addressing the Linder paradox and other complex is- sues in the eld of trade. In summary, the new theory of international trade has allowed economists to move beyond the limitations of traditional models, oering explanations for patterns of trade that occur between similar countries and within the same sectors. This shift has signicantly enhanced our understanding of international trade in the modern, globalized economy. 3 Imperfect competition In the context of the traditional theory, identical countries do not engage in international trade because they do not derive any benet from it. However, we can make some modications to this model to introduce an incentive for international trade. The rst step involves removing the assumption of perfect competition while maintaining the assumption of constant returns to scale. This modication will be highlighted through a comparison between the equilibrium in autarky and the equilibrium in the case of free trade. 3.1 Monopoly We start with the simplest model: monopoly. The following assumptions apply: 1. Consider an economy where there is only one good, denoted by X , with a price PX. 2. In the market, there is only one rm producing a quantity x, equal to the entire quantity demanded in the market, so x = X.1 3. The total cost of producing the quantity X is c · X , implying that the marginal cost is constant and equal to c. 4. The individual demand function is xd = D(PX ), where xd represents the demand of a single individual, and PX is the price of the good X. 5. There are m identical consumers, and the total demand is X d = m · D(PX ). The market equilibrium requires that the quantity produced equals the quantity demanded: X = m · D(PX ). We assume that the individual demand follows a constant elasticity pattern: xd = D(PX ) = PX−σ , (1) 1 From now on, X represents both the good and the total quantity produced in the market. 4 where −σ (with |σ| > 1) is the elasticity of individual demand with respect to price. It is dened as: ∂D(PX ) PX PX · = −σ · PX−σ−1 · = −σ. (2) ∂PX D(PX ) | {z } D(PX ) =∂D(PX )/∂PX | {z } σ+1 =PX Since D(PX ) = X/m, we can also write: ∂(X/m) PX ∂X PX · = · = −σ, (3) ∂PX (X/m) ∂PX X where we have used X = m · PX−σ. The price is the inverse of the demand function PX (X), and it is dened as: −1/σ Xd  PX (X) =.2 (4) m We know that in equilibrium X d = X s = X , so that:  −1/σ X PX (X) =. (5) m The monopolist maximizes prot (Π): ΠX = PX (X) · X − |c {z · X}. (6) Total costs | {z } Price×Quantity The rst-order condition (F.O.C.) is:   ∂ΠX ∂PX (X) ∂X = · · X + PX (X) − c = 0. (7) ∂X ∂X ∂X From (5), we can calculate:  −1/σ−1 ∂PX (X) 1 X 1 =− · ·. (8) ∂X σ m m Substituting (5) and (8) into (7), we get: "  −1/σ−1 #  −1/σ 1 X 1 X − · · ·X + − c = 0, (9) σ m m m 2 Since the monopolist controls the supply, the price it can charge is determined by the demand curve. Specically, the monopolist faces a downward-sloping demand curve, meaning that as it increases the quantity supplied, the price it can charge decreases. The inverse demand function PX (X) expresses the price as a function of the quantity X the monopolist chooses to produce. It is worth noting that PX (X) and PX refer to the same concept: the price of the good as a function of the quantity X. The notation PX (X) emphasizes that the price depends on the quantity, which is essential in the monopolist's problem, as controlling the supply allows the monopolist to inuence the price through the demand curve. 5 from which: "  −1/σ #  −1/σ 1 X X − · + − c = 0. (10) σ m m X −1/σ Factoring out , we obtain:
m  −1/σ   X 1 1− = c. (11) m σ | {z } =(σ−1)/σ From the previous equation, we can derive the total equilibrium quantity of output in monopoly (XM ):  −σ σ X M = xM ≡ m · ·c , (12) σ−1 where σ/(σ − 1) represents the mark-up on marginal costs. The equilibrium price in monopoly (PM ) is found by substituting (12) into (5): σ PM ≡ · c. (13) σ−1 Observing equations (12) and (13), we note the following: 1. Since σ/(σ − 1) > 1, we have PM > c, meaning that the monopoly price exceeds the perfect competition price. It is also noteworthy that as σ → ∞, PM → c.3 2. From equation (12), it is evident that if the price is higher than in perfect competition, the quantity produced is also lower, since quantity varies inversely with price. A higher price and a lower quantity represent a welfare loss compared to the perfect competition scenario. Opening up to international trade reduces the monopolist's market power, as it increases the elasticity of demand.4 Therefore, the monopolist is compelled to lower the price and increase production. As a result, free trade improves a country's welfare (pro-competitive eect). 3.2 Oligopoly (Markusen, 1981) Further insights can be gained by extending the analysis to the case of oligopoly. The model presented here is based on the work Trade and Gains from Trade with Imperfect Competition, published by Markusen in 1981. The assumptions of the model are as follows: 1. Consider an economy in which there is only one good, denoted as X , with a price PX. 2. In the market, there are n identical rms competing, each of which produces a quantity x. The total quantity produced is therefore X = n · x. 3 Multiplying both the numerator and denominator of σ/(σ − 1) by 1/σ , we obtain 1/[1 − (1/σ)], which tends to 1 as σ → ∞ because 1/σ → 0. 4 Elasticity measures how much the quantity demanded responds to price changes. In a highly competitive market, consumers are more responsive to price changes, which is reected in a higher value of elasticity σ. 6  3. The total cost to produce a certain quantity x is c · x, implying that the marginal cost is constant and equal to c. 4. The individual demand function is xd = D(PX ) = P −σ , where σ represents the elasticity of individual demand. 5. There are m identical consumers, and the total demand is X d = m · D(PX ). 6. The oligopoly operates under Cournot competition: each rm chooses its production quantity, denoted as x, while taking as given the quantity produced by the other rms, which is (n − 1) · x̄. The typical rm maximizes its prots: Πx = PX (X) · x − c · x, (14) where PX (X) is the inverse demand function, dened as in equation (4) and, under market equilibrium conditions, as in equation (5).5 The rst-order condition (F.O.C.) is:   ∂Πx ∂PX (X) ∂X = · · x + PX (X) − c = 0. (15) ∂x ∂x ∂x Since X = x + (n − 1) · x̄, we have ∂X/∂x = 1, so we can rewrite the F.O.C. as:   ∂Πx ∂PX (X) X = ·1 · + PX (X) − c = 0, (16) ∂x ∂x n where we used x = X/n. Since indeed ∂X/∂x = 1, we obtain:  −1/σ−1 ∂PX (X) ∂PX (X) 1 X 1 = =− · ·. (17) ∂X ∂x σ m m Substituting (5) and (17) into equation (16), we get: "  −1/σ−1 #  −1/σ 1 X 1 X X − · · · + − c = 0, (18) σ m m n m from which: "  −1/σ #  −1/σ 1 X 1 X − · · + − c = 0, (19) σ m n m 5 Even for the oligopolist, the price depends on the quantity produced. Refer to footnote #2 for further details. 7  X −1/σ Factoring out , we obtain:
m  −1/σ   X 1 1− = c. (20) m n·σ | {z } =(n·σ−1)/(n·σ) From the previous equation, we can immediately derive the total equilibrium quantity in an oligopoly (XO ):  −σ n·σ XO = m · ·c. (21) n·σ−1 The equilibrium quantity produced by a single rm is simply:  −σ XO m n·σ xO = = · ·c. (22) n n n·σ−1 The equilibrium price in an oligopoly is found by substituting equation (21) into equation (5): n·σ PO = · c. (23) n·σ−1 From equations (22) and (23), the following points emerge: 1. Firms set a price determined by a mark-up (equal to nσ/(nσ − 1)) proportional to the marginal cost c. 2. Market power introduces distortion because the price is higher than in perfect competition (PX = c), and, given the inverse relationship between price and quantity demanded, the quantity supplied is lower than in perfect competition. 3. The mark-up decreases as n increases. When n = 1, the mark-up is maximum, resulting in a monopoly outcome. When n → ∞, we obtain the result of perfect competition.6 Now, let us assume that two identical countries (A and B) open up to international trade. In an open economy, we have PXA = PXB = PO since n rms compete in each national market. With free trade, the two markets merge into a single market, so now we will have nA +nB = 2·n rms competing with each other. Therefore, from equation (23), we will have: 2·n·σ PeOA = PeOB = PeO ≡ · c < PO. (24) 2·n·σ−1 Given that the two countries are identical, we also have mA + mB = 2 · m. Therefore, by imposing the global market equilibrium condition (2 · n · x = 2 · m · Pe−σ ), we get: O  −σ m 2·n·σ eA x O = eB x O eO ≡ =x · ·c > xO , (25) n 2·n·σ−1 6 As n → ∞, the term nσ/(nσ − 1) = 1/(1 − 1/nσ) → 1 since nσ → 0. Thus, the mark-up approaches one, as in the case of perfect competition. 8  eA = X X O eB = X O eO = n · x eO > n · xO. (26) | {z } =XO Once again, we observe a pro-competitive eect: increased competition reduces the price of the commodity (now corresponding to the world price), increases the output produced by each individual rm, and increases the total quantity produced. This latter result is further highlighted through a numerical simulation presented in Table 1. From Table 1, it is interesting to note (column #3) that when two countries are identical (mA = mB and nA = nB ), the demand in each country can be fully satised by domestic rms, thus there is no need for trade with foreign countries: each domestic sector is able to meet domestic consumption. This can be understood by observing that in equilibrium, with international trade, the production share of countries A and B is identical (nA /(nA + nB ) = nB /(nA + nB ) = 1/2), and this is equal to the demand share (mA /(mA + mB ) = mB /(mA + mB ) = 1/2). As a result, the demand of each country can be satised by domestic rms without the need for international trade. There is no international trade, yet the competitive discipline eect still operates. Table 1: Comparison between Monopoly, Oligopoly Autarky, and Oligopoly with International Trade Monopoly Oligopoly autarky Oligopoly int. trade n 1.00 3.00 6.00 (= nA + nB ) σ 2.00 2.00 2.00 m 5.00 5.00 5.00 (= mA + mB ) c 0.50 0.50 0.50 PA 1.00 0.60 0.55 xA 5.00 4.63 5.60 XA 5.00 13.89 16.81 mark-up 2.00 1.20 1.09 3.2.1 International trade pattern So far, we have discussed the benets of international trade that manifest through increased competitiveness, resulting in lower prices and higher quantities in the market, which is advan- tageous for consumers. However, in the example above, with identical countries, there is no room for international trade. For international trade to occur in Markusen's model, two key conditions must be intro- duced: (i) the two countries must dier in some way (either in terms of size or eciency, such as the number of rms in the oligopolistic sector), and (ii) a second competitive sector must be incorporated into the analysis. Case #1 The assumptions of the example are as follows: 1. The world is composed of two countries: A and B. 9  2. Within each country, there are two sectors: one characterized by oligopoly and the other by perfect competition. 3. Neither country has a comparative advantage in the production of the good in the com- petitive sector. 4. Country A is larger than country B: mA > mB. 5. The number of rms in the oligopolistic sector is identical in both countries: nA = nB. Based on assumptions 4 and 5, we know that in an open economy equilibrium in the oligopolistic sector, the spending share of country A is larger than that of country B (mA /(mA + mB ) > mB /(mA + mB ), while the production share in the oligopolistic sector is the same for both countries (nA /(nA +nB ) = nB /(nA +nB ) = 1/2). Consequently, in the oligopolistic sector, we have: mA 1 nA A + mB > = A + nB , under assumptions 4 and 5. (27) m | {z } 2 n | {z } Demand of A Supply of A Since we have assumed that the world is made up of only two countries (assumption 1), country A must import the oligopolistic good and in exchange export the other good from the competitive sector. Case #2 Let us assume that assumptions 1, 2, and 3 from Case #1 still hold. However, assumptions 4 and 5 are modied as follows: 4a. Countries A and B are of equal size: mA = mB. 5a. Country A is more ecient (i.e., has a more competitive market) than country B: nA > nB. In this case, in the oligopolistic sector, we have: nA 1 mA A + nB > = A + nB , under assumptions 4a. and 5a.. (28) |n {z } 2 |n {z } Supply of A Demand of A Thus, in this case, the more ecient country A becomes an exporter of the oligopolistic good and an importer of the competitive good. In summary, in Markusen's model (1981), international trade occurs when two countries dier in size (mA ̸= mB ) or in eciency (nA ̸= nB ). However, once again, international trade remains intersectoral. 10 3.3 Brander and Krugman (1983) oligopolistic model of international trade Brander and Krugman, in their work A 'Reciprocal Dumping' Model of International Trade (1983), demonstrate under which conditions the oligopolistic model can generate intrasectoral trade and therefore provides a rst explanation for Linder's paradox. To reach this result, it is necessary to assume that between two identical countries there are 'intermediate' situations between autarky and free trade. These intermediate situations allow for trade between countries but with some restrictions. The existence of these barriers reduces competition and the possibility of arbitrage in international markets, allowing rms to implement price discrimination policies between dierent countries. In other words, rms can engage in 'dumping' behavior, where in order to penetrate foreign markets, they are willing to apply a smaller mark-up on their foreign sales compared to the mark-up applied to domestic sales. Assumptions of the model The assumptions of the Brander and Krugman model are as follows: 1. There are two countries, A and B. 2. There is a single good, X , with a marginal production cost equal to c. 3. Technology is the same in both countries, which means that the marginal cost is identical. 4. Each country hosts a single operating rm. For simplicity, we will refer to rms by the name of the country in which they are based.7 In this way, rm A is the rm that is based in country A and rm B is the rm that is based in country B. 5. Firm A sells a quantity X Aa within its own country and a quantity X Ab abroad. Similarly, country B sells X Ba in country A and X Bb in its domestic market. 6. International trade barriers are of the `iceberg' type, meaning that a percentage (1 − τ ) of the product 'shipped' from one country to another never reaches its nal destination. In other words, only a fraction τ of the product sent through international trade arrives at its destination. Here, τ represents a value ranging from 0 to 1, with τ = 0 corresponding to autarky and τ = 1 indicating free trade. 7. The interaction between the markets of the two countries is limited by additional barriers that render rm decisions independent of what happens in the other country (segmented markets). 7 Forthis reason, in this case, using the notation x or X to indicate the quantity produced by a single rm or by an entire economy is irrelevant. In the analysis of the Brander and Krugman model that follows, we will use the notation X. 11 The last assumption implies that the two markets can be analyzed separately. For simplicity, we assume that Z A ≡ X Aa + X Ab and Z B ≡ X Ba + X Bb , so that Z A and Z B represent the quantity of good X produced by country A and country B, respectively. Furthermore, we dene X A ≡ X Aa + X Ab and X B ≡ X Ba + X Bb as the total amount of good X produced by country A and country B, respectively. Country A Let us focus on country A. The rm in A seeks to maximize prots with the following function: ΠX A = PZ A (Z A ) · X Aa + PZ B (Z B ) · τ · X Ab − c · X A , (29) where PZ A (Z A ) and PZ B (Z B ) indicate the inverse demand function associated with D(PZ A ) and D(PZ B ), respectively. Obviously, these prices depend on the quantity sold in the market by the rms. In the domestic market, where the rm sells quantity X Aa , the condition for prot maxi- mization is given by setting the derivative of the prot function with respect to X Aa equal to zero: ∂PZ A (Z A ) ∂Z A   ∂ΠX A = · · X Aa + PZ A (Z A ) − c = 0, (30) ∂X Aa ∂X Aa ∂X Aa where ∂Z A /∂X Aa = 1 since the domestic rm takes the output of the foreign rm as given. Since: −1/σ ZA  A PZ A (Z ) = , (31) mA and that ∂Z A /∂X Aa = 1, it is immediate to nd that: −1/σ−1 ∂Z A (Z A ) ∂Z A (Z A ) ZA  1 1 A = Aa =− · ·. (32) ∂Z ∂X σ mA mA Substituting (31) and (32) into (30), we get: " −1/σ−1 #  A −1/σ ZA  1 1 Z − · Aa · A ·X + − c = 0. (33) σ mA m mA X Aa If we dene sA ≡ ZA , the equation (33) can be written as follows: " −1/σ−1 #  A −1/σ ZA  1 1 Z − · A A · A ·s ·Z + − c = 0, (34) σ mA m mA so that it is immediate to nd, after some manipulations, that: −1/σ  ZA sA   · 1− = c, (35) mA σ 12 ovvero che: sA   A PZ A (Z ) · 1 − = c. (36) σ Equation (36) can be interpreted as the reaction function of rm A. It expresses the price that rm A will charge based on the quantities produced by both rms (A and B). The price is inuenced by rm A's market share sA , the elasticity of demand σ , and its marginal cost c. Although the equation appears to involve prices, it implicitly determines the quantity that rm A should produce in order to maximize its prots. This is because the rm's optimal quantity in the domestic market directly inuences the price via the market share sA , and in an oligopolistic setting, rms adjust their production levels in response to their competitors' output. Thus, equation (36) outlines the rm's best response in terms of production for each level of output chosen by rm B. Country B Now let us focus on country B and the prot maximization problem faced by its rm. Firm B maximizes its prots with the following function: ΠX B = PZ A (Z A ) · τ · X Ba + PZ B (Z B ) · X Bb − c · X B. (37) In the foreign market A, rm B's prot maximization problem with respect to X Ba is given by: ∂PZ A (Z A ) ∂Z A   ∂ΠX B Ba = Ba · Ba · τ · X Ba + PZ A (Z A ) · τ − c = 0, (38) ∂X ∂X ∂X where ∂Z A /∂X Ba = 1 since the foreign rm takes the output of the domestic rm as given. Substituting (31) and (32) into (38), we get: " −1/σ−1 # −1/σ A ZA   1 Z 1 − · · A · τ · X Ba + · τ − c = 0. (39) σ mA m mA X Ba Osservando che 1 − sA ≡ sB = ZA , it is easy to nd, dopo alcune manipolazioni matem- atiche, che: −1/σ  ZA sB   τ· · 1− = c, (40) mA σ ovvero che: sB   A τ · PZ A (Z ) · 1 − = c. (41) σ This equation (41) denes the reaction curve for rm B in market A. It indicates the price that rm B is willing to charge in market A based on its market share sB and the elasticity of demand. Just as for rm A, equation (41) implicitly determines how much rm B will produce in country A based on the level of output produced by rm A. Even though the equation is in terms of prices, it captures the rm's optimal response in terms of production, as the price in an oligopolistic market is directly tied to the rm's output level. Thus, this is rm B's best response function in market A. 13 Equilibrium market share and equilibrium price Equations (36) and (41) form a system of two equations with two unknowns: the market price, PZ A (Z A ), and rm A's market share, sA. Solving this system yields the equilibrium market share of rm A (sA ) and B (sB = 1 − sA ), and the equilibrium market price (PZ∗ A ). By setting equations (36) and (41) equal to each other, we reduce the system to a single unknown, sA , making it straightforward to solve for rm A's equilibrium market share: τ + (1 − τ ) · σ sA =. (42) 1+τ By substituting the equilibrium market share sA into equation (36), we solve for the equi- librium market price: c · σ · (1 + τ ) PZ∗ A =. (43) τ · (2 · σ − 1) By symmetry, the equilibrium in country B's market will be characterized by the same price and the same market share. In country B, the market share of rm A will be sB = 1 − sA. Several results are worth commenting on: 1. Both sA and sB take values between zero and one. This implies that in equilibrium, rms from one country hold a market share in the other country through exports. With oligopolistic rms, the segmentation of international markets (due to trade frictions) gen- erates trade even between identical countries. Since rms are selling the same products, this trade is considered intraindustry trade. 2. Equation (42) shows that rm A's market share in its domestic market increases as trade frictions (represented by τ ) rise. As τ decreases, rm B becomes more competitive in market A, reducing rm A's market share. Conversely, an increase in τ reduces the competitiveness of imports, allowing rm A to capture a larger share of its domestic market. 3. Equation (43) reveals that the equilibrium price increases as trade frictions rise (i.e., as τ decreases). This is because when rm A gains a larger share of the market, it faces a lower price elasticity of demand and thus has greater market power, allowing it to raise prices. Therefore, increased trade frictions reduce intraindustry trade and drive up prices in both markets. 4. 'Incomplete' international trade (where τ < 1) does not necessarily improve welfare com- pared to autarky (where τ = 0). For example, consider rm A. With partial market opening, rm A moves from being a monopolist to competing with rm B in a duopoly, which increases the total quantity sold and lowers prices (a pro-competitive eect). How- ever, part of the domestic production previously sold in market A is replaced by imports from rm B, sold at an additional cost due to trade frictions (represented by τ ). As a result, consumers in country A pay higher prices due to transportation costs, and rm A earns a lower price on goods sold domestically. This could mean that the total surplus in country A is lower under trade than under autarky. 14  We can therefore conclude that, in a regime of imperfect competition with constant returns to scale, opening the domestic market to international competition is generally benecial as it reduces the market power of rms. This holds true in cases of monopoly and oligopoly, but not in cases where oligopoly is created by transportation costs. 4 Economies of scale Now we examine the eect of replacing the assumption of constant returns to scale with the assumption of increasing returns to scale. In general, any productive entity exhibits economies of scale if the average cost of production decreases as the quantity produced increases. This entity can be a plant, a rm, a sector, a group of sectors, a location, or even the entire economy of a country. For our analysis, it is useful to distinguish between external economies of scale and internal economies of scale.8 External Economies of Scale External economies of scale occur when the cost advantages are not tied to the individual rm but are instead shared across an entire industry. These arise when the industry's overall output increases, leading to lower average costs for all rms operating in that industry. For example, improvements in infrastructure, better access to specialized suppliers, or the availability of a skilled labor pool can reduce costs for all rms in a particular region or industry. External economies of scale are compatible with a regime of perfect competition because individual rms do not inuence the market price directly. The cost reductions stem from the overall growth and development of the industry rather than from increases in the rm's own production scale. As a result, rms can remain small and continue to act as price-takers, which aligns with the assumptions of perfect competition. Even though individual rms cannot set prices, an overall increase in the size of the industry (due to external economies of scale) reduces the average production costs for all rms. This leads to an increase in the sector's aggregate supply in the long run. Since there is more production at lower costs, this puts downward pressure on the market price, as the increase in supply pushes equilibrium prices down. Internal Economies of Scale Internal economies of scale, on the other hand, occur when the cost advantages are specic to an individual rm. These arise when the rm's own out- put increases, leading to lower average costs due to factors such as more ecient production techniques, bulk purchasing of materials, or better use of specialized equipment. Internal economies of scale are incompatible with perfect competition because as a rm grows larger and its average costs decrease, it gains market power and can inuence the market price. In perfect competition, rms are small relative to the market and cannot inuence prices. However, with internal economies of scale, a rm can grow large enough to have signicant 8 The discussions presented in this Section follows the Section 4.4 of the book Economia Politica degli Scambi Internazionali (2001) by Basevi, Calzolari and Ottaviano. 15 control over pricing, leading to an imperfectly competitive market structure, such as monopoly or oligopoly. 4.1 External economies of scale and international trade Our reasoning is based on the following assumptions: 1. Two countries, A and B. 2. Each country produces two goods, C and G. 3. The countries are identical in terms of technology, relative and absolute factor endow- ments, and size. 4. Consumers in each country demand both goods. 5. Every rm operating in both countries and in both sectors produces under the assumption of constant returns to scale. Therefore, no internal economies of scale. 6. Each sector in both countries is characterized by increasing returns to scale. Therefore, we have external economies of scale. In autarky, the productive factors of each country are used to produce both goods by domestic rms. This limitation leads to restricted production in each sector, reducing the scope for economies of scale and the resulting reduction in prices. International trade allows each country to fully specialize in the production of one of the two goods (in a complementary way to the other country). For example, let us assume that country A specializes in the production of good C, and country B specializes in the production of good G. This specialization implies that country A will produce good C for both itself and country B, while country B will produce good G for both itself and country A. This specialization will allow country A (B) to use all its available resources in the C (G) sector only, thus maximizing the positive eects of economies of scale at the sector level (which, as we recall, lead to a reduction in the price of the good in question). Therefore, in the presence of external economies of scale at the rm level, but internal to the sector, international trade leads countries to specialize in the production of one good (resulting in intersectoral trade) to fully exploit cost advantages. In the end, consumers in both countries benet, as they can enjoy both goods at lower prices compared to those under autarky. 4.2 Internal economies of scale and international trade We assume an oligopoly model with the same assumptions as those presented in Markusen's (1981) model described in section 3.2, but with one key dierence: we assume internal economies of scale (i.e., economies of scale at the rm level). 16  The simplest way to incorporate this is by assuming that the technology used by each rm is characterized by the following total cost function: CTx = f + c · x, f > 0, c > 0, (44) where CTx represents the total cost incurred by the rm to produce a quantity x of the good, f is the constant xed cost, and c is the constant marginal cost. Based on equation (44), it is easy to verify that the average cost (CTx /x) is given by: CTx f = + c. (45) x x Therefore, the average cost decreases as the quantity produced increases. The typical rm maximizes its prots: Πx = PX (X) · x − (f + c · x). (46) Since f is a constant, the F.O.C. of this problem with respect to x is identical to equation (16). Thus, the autarky quantities and prices and quantities are still determined by equations (21) and (23), while the quantities and prices in free trade are determined by equations (25) and (24). It is easy to observe that, as in the previous case of the oligopoly model à la Markusen, international competition induces the oligopolist to reduce prices and increase the quantity produced. As seen earlier, international competition leads the oligopolist to lower prices and increase supply. This is the pro-competitive eect. However, in the presence of increasing returns to scale, average production costs decrease. The oligopolist who increases production ultimately produces at a lower average cost. Therefore, in the presence of internal economies of scale, international trade, through its pro-competitive eect, reduces average production costs (scale eect). In conclusion, it is important to emphasize that the scale eect represents a new advantage introduced by the opening of international trade. However, the presence of increasing returns to scale does not alter the trade ow implications derived from the oligopoly model presented in section 3.2.1. 5 Product dierentiation and variety eect Up to this point, we have been working with the assumption of homogeneous goods. However, in reality, most sectors of the economy are characterized by goods that are dierentiated in some way. For example, consider the automobile industry, where cars from dierent manufacturers serve the same basic function but dier in design, features, and branding. This dierentiation makes these goods only partially substitutable, even though they belong to the same sector. The key question is: what happens when traded goods are dierentiated 17 and exist in multiple varieties, each only partially substitutable with the others? This question was central to Paul Krugman's seminal papers Increasing Returns, Monopolistic Competition, and International Trade (1979) and Scale Economies, Product Dierentiation, and the Pattern of Trade (1980). 5.1 Model assumptions and specications The model is based on the following assumptions: 1. The economy contains n varieties of the same good. 2. Production exhibits increasing returns to scale. 3. All rms are identical and have the same cost function, which we will specify later. 4. Labor is the sole input for production. 5. The number of consumers m corresponds to the labor supply. 6. Consumers prefer variety, meaning they derive greater satisfaction from having access to more varieties of the same good. The rst two assumptions imply that each rm produces only one variety of the good, as producing multiple varieties would erode the gains from increasing returns to scale. Thus, n also represents the number of rms and the number of varieties available in the market. This model describes monopolistic competition, where rms produce dierentiated products but face competition from many other rms. Each rm holds some degree of market power due to product dierentiation, as consumers perceive the products to be distinct from one another. However, this market power is limited, as rms do not dominate the entire market. Instead, they must compete not only on price but also by oering a variety of products, as consumers exhibit a preference for diverse goods. The key properties of market power and competition in this model are directly derived from the specic characteristics of demand. The preference for variety means that even though each rm has some ability to set prices above marginal cost, their pricing power is constrained by the existence of many close substitutes, i.e., the other varieties oered by competing rms. As a result, demand is elastic with respect to price, meaning that any rm raising its price too much risks losing customers to other similar varieties. Furthermore, when rms earn positive economic prots, new rms are incentivized to enter the market, introducing new varieties that increase competition. This continued entry reduces the market power of each existing rm because the demand for each variety becomes more fragmented among a larger number of rms. As more rms enter, prices fall toward the level of average cost, which includes both xed and variable costs. Eventually, when the price equals the average cost, economic prots are driven to zero. At this point, the market reaches its long-run equilibrium, where no additional rms have an incentive to enter, as there are no more prots to be made. 18 5.2 Demand side The demand structure in this model follows the approach developed by Dixit and Stiglitz in their inuential paper, Monopolistic Competition and Optimum Product Diversity (1977). Consumers in this framework have a strong preference for variety, meaning they derive greater satisfaction from consuming a wide range of dierent varieties of the same good. This preference is captured through a constant elasticity of substitution (CES) utility function, which can be written as: !1/ρ n X U= Ciρ , 0 < ρ < 1, (47) i=1 where Ci represents the quantity consumed of the i-th variety, and ρ is the substitution or 'love- of-variety' parameter, which measures the degree of substitutability between dierent varieties. A key property of this utility function is that the consumption of all varieties enters sym- metrically, meaning that consuming the same amount of variety i and variety j results in the same level of utility. This formulation reects consumers' desire for product dierentiation, as they gain more satisfaction from accessing multiple distinct varieties rather than consuming a single type in larger quantities. Role of Elasticity and Variety Preference The parameter ρ plays a critical role in de- termining the degree of product dierentiation and variety preference. When ρ = 1, the goods would be perfect substitutesonly quantity would matter for utility, and variety would lose its importance. For instance, 100 units of variety i would provide the same utility as 100 units of variety j. On the other hand, if ρ = 0, the goods would be perfect complements and con- sumed in xed proportions, an extreme case that would make the utility function undened. Therefore, for variety to meaningfully aect utility, ρ must lie between 0 and 1. The parameter σ ≡ 1/(1 − ρ), derived from ρ, represents the price elasticity of demand, or how sensitive the demand for a variety is to changes in its price. A higher σ implies that consumers can more easily substitute between varieties, thus limiting the price-setting power of any single rm. As σ increases (i.e., as ρ decreases), consumers' preference for variety strengthens, and the elasticity of substitution increases, which means rms' market power is diminished due to higher competitive pressures. 5.3 Supply Side The consumers' preference for variety gives rms a certain degree of market power in setting prices. Each rm faces a downward-sloping demand curve for its variety (due to the consumers' preference for variety and the CES structure of utility), allowing it to charge a price higher than the marginal cost and earn a positive markup. The assumption of increasing returns to scale implies that there is only one rm producing each variety, which simplies the analysis. We assume that producing Xi units of variety i requires employing li units of labor, with the 19 following cost function: li = f + c · Xi , for i = 1,... , n, (48) where li represents the amount of labor needed to produce Xi units of variety i. The parameters f > 0 and c > 0 represent the xed and marginal labor input requirements, respectively. In this context, the rst-order conditions for prot maximization remain unchanged and are calculated in the usual way. However, the possibility of rm entry (or exit) when prots are positive (or negative) implies that, in equilibrium, there should be no entry or exit of rms. Therefore, the prots of the active rms in the market must be zero in equilibrium. This requires imposing not only the rst-order condition for prot maximization, but also the condition that prots are zero in equilibrium. Prot Maximization Each generic rm i seeks to maximize prots according to the follow- ing function: ΠXi = PXi (Xi ) · Xi − w · (f + c · Xi ), for i = 1,... , n, (49) where w represents the wage rate. In monopolistic competition, the number of rms in the market is large, meaning that each rm individually has a negligible impact on others. This implies that each rm considers the output of other rms as given. This setup means that each rm behaves as a monopolist in setting the price for its own variety. Formally, the F.O.C. for rm i is:   ∂ΠXi ∂PXi (Xi ) ∂Xi = · · Xi + PXi (Xi ) − c · w = 0. (50) ∂Xi ∂Xi ∂Xi The solution to this problem is analogous to that of a monopolist, so we have: w·c·σ PM C = , (51) σ−1 where PM C is the price set by each monopolist for each variety. The markup σ/(σ − 1) reects the rm's market power: the higher the elasticity of substitution σ , the smaller the markup, as consumers can easily switch between varieties. Zero Prots The zero-prot condition for rm i is: ΠXi = (PM C − c) · Xi − f = 0, for i = 1,... , n. (52) Substituting (51) into this equation and solving for Xi , we obtain the optimal quantity produced by each rm in equilibrium: f · (σ − 1) Xi =. (53) c 20  Based on this result, we can calculate the number of active rms in the market, which also corresponds to the number of varieties produced. Starting from the cost function (48), we can write: f · (σ − 1) li = f + c · xi = f + c · = f + f · (σ − 1) = f · σ. (54) c The number of varieties produced, n, is determined by dividing the total number of workers, which corresponds to the number of consumers m, by the number of workers required to produce one variety: m m n= =. (55) li f ·σ 5.4 Welfare We now evaluate welfare in autarky and compare it to the free trade scenario. Autarky In aggregate, the equilibrium condition requires that the demand for each variety equals its supply, i.e., m · Ci = xi. Using (53), we obtain: f · (σ − 1) Ci = , for i = 1,... , n. (56) c·m Since all rms have the same technology, we know that the price of all varieties is the same in equilibrium. Since the price of each variety is the same, and the demand for each variety depends inversely on its price, consumers will purchase the same quantity of each variety.9 If this is true, we can rewrite the utility function (47) as: n !1/ρ   X f · (σ − 1) U= Ciρ = (n · C ) ρ 1/ρ =n 1/ρ ·. (57) i=1 c·m Using (55) in the (57), we obtain:  1/ρ m f · (σ − 1) U = UA ≡ n 1/ρ ·C = · = γU · m1/(σ−1) , (58) f ·σ c·m where γU ≡ [f · (σ − 1)/c] · [1/(f · σ)]1/ρ. Equation (58) shows that the welfare of individuals in the country increases with the size of m. This happens because the larger the country, the more rms can operate without incurring losses, and thus, more varieties of the dierentiated good are available for consumption. Free trade Consider two countries, A and B. To evaluate the impact of trade liberalization, let's assume they are identical. In this case, we have mA = mB , which, by virtue of (55), implies that nA = nB. The opening of both countries to international trade eectively creates 9 See Appendix A for a technical demonstration. 21 a single market with size mA + mB = 2 · m. The individual welfare then becomes: e ≡ γU · (2 · m)1/(σ−1) > UA. U =U (59) Therefore, in the presence of increasing returns to scale and product dierentiation, interna- tional free trade enhances welfare because it increases the number of varieties available for consumption (variety eect). 5.5 International trade pattern Regarding trade patterns, the monopolistic competition model analyzed here diers from the oligopoly model in two key implications. Intraindustry trade. In the context of monopolistic competition, even if countries are iden- tical and trade is free, there will always be international trade in equilibrium. This occurs because, in each country, all consumers demand all varieties, but since the two countries have the same number of rms, these varieties are produced half in one country and half in the other. As a result, countries engage in intraindustry trade the exchange of dierentiated varieties of the same type of good. The role of country size in interindustry trade. Similar to the oligopoly case, we also consider a second, perfectly competitive sector. Assuming no comparative advantages between the two countries and that mA ̸= mB , Equation (55) implies: nA mA = A , (60) nA + nB m + mB which means that country A's production share equals its consumption share. This suggests that, unlike in the oligopoly model, with monopolistic competition, there cannot be interindus- try trade in the absence of comparative advantages. In other words, trade between industries would not occur unless there are inherent dierences between the countries, such as compara- tive advantages, whereas intraindustry trade naturally arises due to consumers' preferences for a variety of products. 6 Conclusions This chapter provided an overview of the key elements that underpin the modern understanding of international trade, with a focus on the transition from traditional trade theories to the new orthodoxy. Starting in the 1960s, empirical evidence showing the high volume of intraindustry trade (i.e., trade in similar goods within the same sector) revealed limitations in the traditional neoclassical framework. This led to the introduction of signicant changes, particularly with 22 the incorporation of imperfect competition into the analysis, beginning with monopoly and oligopoly models, and the role of economies of scale. With imperfect competition, international trade introduces pro-competitive eects, reducing prices and increasing production. However, the pattern of international trade remains largely based on intersectoral trade (trade in goods from dierent industries) unless we consider the possibility of imperfect international markets. In such cases (e.g., Brander and Krugman, 1983), both countries have an incentive to apply price discrimination policies in dierent markets, leading to an equilibrium where countries exchange goods within the same sector (intraindustry trade). In the presence of internal (or external) economies of scale, international trade has a pro- competitive (or pro-eciency) eect, reducing (or increasing) the average cost of production. To observe intraindustry trade ows, product dierentiation must be introduced in a model with increasing internal returns to scale, as seen in Krugman's model (1979, 1980). Despite the dominance of neoclassical theories and the "new trade theories" (NNT) within the eld of international trade, these frameworks have been subject to substantial criticism from heterodox economists, coming from schools of thought such as post-Keynesianism, Marx- ism, institutional economics, and dependency theory. These critiques generally address several conceptual and methodological issues, which can be summarized as follows: 1. Full employment assumption: Neoclassical trade theories assume that factor markets are always in equilibrium, meaning that there is full employment of labor and capital. Heterodox economists argue that this view overlooks structural unemployment and under- utilization of resources, which are common in many economies, particularly in developing countries. The post-Keynesian perspective, in particular, criticizes the idea that markets are self-regulating and that supply and demand for labor naturally nd a balance. 2. Unequal distribution of trade benets: Both neoclassical and NNT approaches tend to focus on the aggregate gains from trade, claiming that free trade benets all countries, even if one specializes in low value-added products. However, heterodox economists high- light that these theories ignore the unequal distribution of the benets from trade. For instance, industries with high capital and technology intensity often benet the most, while workers in traditional industries frequently suer from lower wages or job losses. 3. Dependency and underdevelopment: Heterodox perspectives, particularly depen- dency theory, argue that free trade perpetuates developmental disparities between the Global North and South. Rather than generating economic convergence, international trade reinforces the dependency of developing economies on developed countries. Special- ization based on comparative advantage, as advocated by neoclassical theory, often locks developing countries into low value-added sectors (e.g., agriculture or resource extraction), preventing them from developing more advanced, high-tech industries. 4. Abstraction from historical and institutional realities: Neoclassical theories, in- cluding NNT, are frequently criticized for abstracting away from historical and institu- 23  tional contexts. Heterodox economists, especially those with institutionalist and Marxist orientations, contend that international trade cannot be understood without considering the historical and power structures that shape global markets. Trade policies, interna- tional treaties, and global nancial institutions like the IMF and World Bank play a crucial role in determining who benets from trade and who does not. 5. The limited role of industrial policy: Heterodox economists emphasize that neo- classical theories and NNT often downplay or ignore the importance of active industrial policy in promoting economic development. From a heterodox perspective, countries like South Korea, Japan, and China did not strictly follow free trade principles but used pro- tectionist policies and industrial development strategies to build technological capabilities in high value-added sectors. This contradicts the neoclassical approach, which suggests that reducing trade barriers is always the optimal path to economic growth. 6. Neglect of monetary and nancial dynamics: A recurring criticism is the lack of consideration for monetary and nancial dynamics. Neoclassical trade theories often over- look the importance of the international monetary system and global nancial imbalances, such as trade decits and surpluses. Heterodox economists argue that these dynamics are crucial to understanding the real power relations in the world economy, and that ignoring them leads to an incomplete and distorted analysis of international trade. In summary, heterodox critiques highlight how neoclassical theories and NNT often neglect fundamental issues related to inequality, distribution, market power, and historical and institu- tional dynamics, resulting in a partial and incomplete understanding of international trade. For this reason, studying alternative approaches, such as Marxian and Keynesian perspectives, can provide valuable insights into understanding phenomena like the uneven development between nations, the role of state intervention in shaping economic outcomes, and the importance of addressing structural unemployment and nancial imbalances in the global economy. These approaches emphasize the need to consider broader social, political, and economic factors that inuence international trade and its eects on dierent countries and communities. 24 Appendix A Consumption Level is the Same for all Vari- eties in Equilibrium We can analytically demonstrate why, if prices are equal in equilibrium, the demand for each variety is the same using the CES utility function and the associated demand system. To illustrate this point, we need to solve the consumer's problem. Let us proceed step by step. Optimization Problem The consumer maximizes their utility (47) subject to the budget constraint. The problem is: n !1/ρ n X X max Ciρ , s.t. PXi · Ci = I, (61) Ci i=1 i=1 where PXi is the price of variety i, and I represents the consumer's income. First-Order Condition We write the Lagrangian: n !1/ρ n ! X X L= Ciρ +λ· I− PXi · Ci , (62) i=1 i=1 where λ is the Lagrange multiplier. Taking the derivative of the Lagrangian with respect to Ci and setting it equal to zero, we obtain the rst-order condition (F.O.C.): n !(1/ρ)−1 ∂L X = Ciρ · Ciρ−1 − λ · PXi = 0. (63) ∂Ci i=1 Ratio of Demands To nd the relationship between the consumption quantities of dierent varieties, we can take the ratio of the F.O.C.s for two varieties i and j : Ciρ−1 PXi ρ−1 =. (64) Cj PXj Equal Demand for Equal Prices If the prices of all varieties are equal, i.e., PXi = PXj for all i and j , then from the above equation, it follows that: Ciρ−1 = 1, (65) Cjρ−1 which implies Ci = Cj. This shows that if prices are equal, the demand for each variety will also be the same. 25 References and selected readings For further insights or additional details on neoclassical models of intra-industry trade, it is recommended to refer to the following texts: ˆ Basevi, G., Calzolari, G. and Ottaviano G. (2001), Economia politica degli scambi inter- nazionali. Carocci Editore, Roma, Ch. 4. ˆ Lichtenstein, P. M. (2016), Theories of international economics. Routledge, London, 86108. ˆ van Marrewijk, C. (2017), International trade. Oxford University Press, Oxford (UK), 159205. The models cited in the text refer to the following articles: ˆ Brander, J. A. and Krugman, P. (1983), A `reciprocal dumping' model of international trade. Journal of International Economics, 15(34), 313323. ˆ Dixit, A. K. and Stiglitz, J. E. (1977), Monopolistic competition and optimum product diversity. American Economic Review, 67(3), 297308. ˆ Krugman, P. (1979), Increasing returns, monopolistic competition, and international trade. Journal of International Economics, 9(4), 469479. ˆ Krugman, P. (1980), Scale economies, product dierentiation, and the pattern of trade. American Economic Review, 70(5), 950959. ˆ Markusen, J. R. (1981) Trade and gains from trade with imperfect competition. Journal of International Economics, 11(4), 531551. The empirical evidence that criticizes the results of traditional theories is found in the following text: ˆ Linder, S. B. (1961), An essay on trade and transformation. John Wiley, New York (NY). 26