# The New Trade Theory. Monopoly and oligopoly in trade. Luca De Benedictis 1. Topic 3. 1 University of Macerata

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1 The New Trade Theory Monopoly and oligopoly in trade Luca De Benedictis 1 1 University of Macerata Topic 3

2 A new generation of models Main characteristics and insights: Countries do not trade, rms do. Insights from Grubel and Lloyd (1975) analysis [new international data] Trade volumes are largely dominated by trade between similar countries Trade volumes are largely dominated by trade in similar goods this is at odds with comparative advantage theory New models of imperfect competition in the IO literature Strategic interactions [oligopoly models] Product dierentiation [monopolistic competition] Demand: ideal and love of varieties [Dixit-Stiglitz utility function] A new view and new gains from trade.

3 Part I Monopoly

4 Monopoly The frame: one rm producing as a monopolist in the domestic market Assume we are in autarky. One good X, with price p, total cost c(x), marginal cost c (x) where x is the quantity produced by the single rm. There are m consumers having an individual demand function D(p). Assume: (1) c(x) = c x, this implies that c(x) x = c (x) = c > 0: constant returns to scale; (2) the price elasticity of demand is σ > 1 Under monopoly x X and aggregate demand is X = m D(p).

5 Monopoly (2) The monopolist rm maximizes prots (it can chose either p or X ) Π(X ) = p(x ) X c X where p(x ) = D 1 ( X ) is the inverse demand function. m From the rst order condition: dπ(x ) dx = [dp(x )/dx ] X +p(x ) c = p (X ) X +p(x ) c = 0. In perfect competition: p (X ) = 0 (perfectly elastic [horizontal] demand) p C = p(x ) c. Under monopoly there a price (and quantity) distortion

6 Monopoly (3) The monopoly distortion (Proof) Wright the rst order condition as: dπ(x ) dx = p (X ) X + p(x ) c = p(x )[1 + p (X ) X p(x ) ] c = p(x )[1 1 σ ] c = 0. Therfore p M = p(x ) σ σ 1 c (1) From equation 1 we know that the monopolist set a mark-up on c, and that the mark-up is xed and proportional to σ. σ Since σ > 1 σ 1 > 1 p M > c = p C therefore p M c = c indicates that the distortion is σ 1 reduced as σ.

7 Monopoly and trade Introducing trade (market integration vs market segmentation) Trade means more elastic demand (the horizontal sum of two demand functions) and more competitive market. Gains from trade are related to the induced competition (expressed by σ ) in a former monopolist market: this is the pro-competitive eect of trade. Do countries trade? If they are identical (m = m with one monopoly rm for each country) no! The perception of a more open marked is sucient to induce a more pro-competitive attitude (contestable market theory), but trade will not take place.

8 Monopoly and trade Introducing trade (market integration vs market segmentation) Trade means more elastic demand (the horizontal sum of two demand functions) and more competitive market. Gains from trade are related to the induced competition (expressed by σ ) in a former monopolist market: this is the pro-competitive eect of trade. Do countries trade? If they are identical (m = m with one monopoly rm for each country) no! The perception of a more open marked is sucient to induce a more pro-competitive attitude (contestable market theory), but trade will not take place.

9 Monopoly and trade Introducing trade (market integration vs market segmentation) Trade means more elastic demand (the horizontal sum of two demand functions) and more competitive market. Gains from trade are related to the induced competition (expressed by σ ) in a former monopolist market: this is the pro-competitive eect of trade. Do countries trade? If they are identical (m = m with one monopoly rm for each country) no! The perception of a more open marked is sucient to induce a more pro-competitive attitude (contestable market theory), but trade will not take place.

10 Part II Oligopoly

11 Oligopoly without strategies: the Markusen (1981) model Each country is composed of n identical rms producing a homogeneous good X (X = n x). Conditions (costs, demand (p(x ) = D 1 (X /m) from the equilibrium condition), constant returns to scale) are the same as in the monopoly model. Every rm is a Cournot player (chooses x taking as given the quantity chosen by the other n 1 players: (n 1) X n. The f.o.c. for prot maximization is: dπ(x ) = [dp(x )/dx] x + p(x ) c = 0. dx Since X = x + (n 1) X n, dx /dx = 1 and dp(x )/dx = p (X ) m. we can wright [ c = p(x ) 1 + p (X ) x p(x ) m ] [ = p(x ) 1 + p (X ) X x p(x ) m X ].

12 The Markusen (1981) model (2) All the previous algebra boils down to c = p(x ) [ 1 1 σ 1 n]. And the core equation is What is the eect of trade? p O = p(x ) n σ c. (2) n σ 1 Markets are now integrated. Comparative static exercise on σ and n. Interaction eect of n and σ (perceived elasticity σ n vs true elasticity σ). Welfare conclusions are the same as in monopoly: there is a pro-competitive eect of trade due to σ, n and σ n.

13 The Markusen (1981) model (2) All the previous algebra boils down to c = p(x ) [ 1 1 σ 1 n]. And the core equation is What is the eect of trade? p O = p(x ) n σ c. (2) n σ 1 Markets are now integrated. Comparative static exercise on σ and n. Interaction eect of n and σ (perceived elasticity σ n vs true elasticity σ). Welfare conclusions are the same as in monopoly: there is a pro-competitive eect of trade due to σ, n and σ n.

14 The Markusen (1981) model (2) All the previous algebra boils down to c = p(x ) [ 1 1 σ 1 n]. And the core equation is What is the eect of trade? p O = p(x ) n σ c. (2) n σ 1 Markets are now integrated. Comparative static exercise on σ and n. Interaction eect of n and σ (perceived elasticity σ n vs true elasticity σ). Welfare conclusions are the same as in monopoly: there is a pro-competitive eect of trade due to σ, n and σ n.

15 The Markusen (1981) model (3) Do countries trade? If they are identical (m = m and n = n ) no! Trade: impose asymmetry m > m (the home country's market is larger). Trade: introduce an other good (produced under perfect competition). Trade: the larger country imports the oligopolistic good and export the competitive good. Trade: impose asymmetry n > n (the home country's market is more competitive) Trade: the more competitive country exports the oligopolistic good and import the competitive good.

16 The Markusen (1981) model (3) Do countries trade? If they are identical (m = m and n = n ) no! Trade: impose asymmetry m > m (the home country's market is larger). Trade: introduce an other good (produced under perfect competition). Trade: the larger country imports the oligopolistic good and export the competitive good. Trade: impose asymmetry n > n (the home country's market is more competitive) Trade: the more competitive country exports the oligopolistic good and import the competitive good.

17 The Markusen (1981) model (3) Do countries trade? If they are identical (m = m and n = n ) no! Trade: impose asymmetry m > m (the home country's market is larger). Trade: introduce an other good (produced under perfect competition). Trade: the larger country imports the oligopolistic good and export the competitive good. Trade: impose asymmetry n > n (the home country's market is more competitive) Trade: the more competitive country exports the oligopolistic good and import the competitive good.

18 The Markusen (1981) model (3) Do countries trade? If they are identical (m = m and n = n ) no! Trade: impose asymmetry m > m (the home country's market is larger). Trade: introduce an other good (produced under perfect competition). Trade: the larger country imports the oligopolistic good and export the competitive good. Trade: impose asymmetry n > n (the home country's market is more competitive) Trade: the more competitive country exports the oligopolistic good and import the competitive good.

19 The Markusen (1981) model (3) Do countries trade? If they are identical (m = m and n = n ) no! Trade: impose asymmetry m > m (the home country's market is larger). Trade: introduce an other good (produced under perfect competition). Trade: the larger country imports the oligopolistic good and export the competitive good. Trade: impose asymmetry n > n (the home country's market is more competitive) Trade: the more competitive country exports the oligopolistic good and import the competitive good.

20 The Markusen (1981) model (3) Do countries trade? If they are identical (m = m and n = n ) no! Trade: impose asymmetry m > m (the home country's market is larger). Trade: introduce an other good (produced under perfect competition). Trade: the larger country imports the oligopolistic good and export the competitive good. Trade: impose asymmetry n > n (the home country's market is more competitive) Trade: the more competitive country exports the oligopolistic good and import the competitive good.

21 Strategic Oligopolists: the Brander-Krugman (1983) model In the Markusen (1981) model markets where perfectly integrated and strategic interaction is hidden. What if markets are still partially segmented (trade impediments, distance, protectionism) and the role of strategic interaction is highlighted? This is what the Brander-Krugman (1983) model is about. The setup: Two countries, H and F ; one rm for each country; one homogeneous good (the H rm sells x on the H market and x on the F market, the F rm sells y on the H market and y on the F market); costs and demand are as usual. Trade is limited by transport costs: Iceberg costs (of every quantity sent abroad only a portion τ [0, 1] arrives, the rest (1 τ) is melt away). What if τ = 0?

22 Strategic Oligopolists: the Brander-Krugman (1983) model In the Markusen (1981) model markets where perfectly integrated and strategic interaction is hidden. What if markets are still partially segmented (trade impediments, distance, protectionism) and the role of strategic interaction is highlighted? This is what the Brander-Krugman (1983) model is about. The setup: Two countries, H and F ; one rm for each country; one homogeneous good (the H rm sells x on the H market and x on the F market, the F rm sells y on the H market and y on the F market); costs and demand are as usual. Trade is limited by transport costs: Iceberg costs (of every quantity sent abroad only a portion τ [0, 1] arrives, the rest (1 τ) is melt away). What if τ = 0?

23 The Brander-Krugman (1983) model (2) Market segmentation implies that the two markets can be separately analyzed. Every rm is a Cournot player (chooses x taking as given the quantity y chosen by the other player) and is a prot maximizer. The prot function is Π X (x, x ) = p(x + y) x + p (x + y ) τ x c(x + x ) The f.o.c. for prot maximization of the H rm in the H market is: dπ X (x,x ) = p (x + y) x + p(x + y) c = 0. dx If we dene s x, we can wright: x+y [ ] c = p(x + y) 1 + p (x+y) x p(x+y) = p(x + y) [ ] 1 s σ.

24 The Brander-Krugman (1983) model (3) The reaction function of the H rm is: c = p(x + y) [ 1 s σ ], the meaning of best response: dominant strategy. (digression) best responses in Cournot and Bertrand games: strategic substitutes and strategic complements. (digression 2) the Herndahl Index: H n i=1 s2 i The reaction function of the H rm can be written as: p(x + y) c = [ ] s σ p(x + y). Analyzing only the H market (as if for rm H τ H = 0 and for rm F τ F = 1), Π X = x (p(x + y) c) = x [ ] s σ p(x + y), we can sum the prots for all rms Π i=x,y i = i=x,y q i( [ s i ] σ ) p(x + y)), i =x,y Π i X p(x+y) = q i ([ s i ] [ i=x,y X σ ) = 1 ] [ i=x,y s2 i σ = H 1 ] σ,

25 The Brander-Krugman (1983) model (4) For the F rm Π Y (y, y ) = p(x + y) τ y + p (x + y ) y c(y + y ) and the f.o.c. for a max in the H market is dπ Y (y,y ) = p (x + y) τ y + p(x + y) τ c = 0. dx and the reaction function of the F rm is: [ c = τ p(x + y) 1 (1 s) σ ]. (3) Together with the reaction function of the H rm is the core of the B-K model [ c = p(x + y) 1 s ], (4) σ Solve the system of equations and obtain s and p(x + y)

26 The Brander-Krugman (1983) model (5) Solve for s s = τ+(1 τ) σ 1+τ, and substitute in one of the two reaction functions p(x + y) = c σ(1+τ) τ (2σ 1), Analysis: Both s and (1 s) are positive; Trade take place in segmented markets (τ > 0) even between identical countries trading a homogeneous goods (Intra-industry trade); dumping. Is trade benecial? Yes (Pro-competitive eect) and no (consumers pay for the transportation cost). Comparative statics: If τ : s? With τ = 1? Prices?

27 Oligopoly models: summing-up Strategic thinking by rms is good for consumers, but not always if trade is costly. Market shares depend on c: Strategic trade policy More gains from trade: Increasing returns: scale eect (Adam Smith) magnify the pro-competitive eect (p and X ) Some rms exit: defragmentation eect (Helpman, 1984). But how the selection works? More varieties: this eect is better analyzed using dierentiated products in monopolistic competition.

28 Oligopoly models: summing-up Strategic thinking by rms is good for consumers, but not always if trade is costly. Market shares depend on c: Strategic trade policy More gains from trade: Increasing returns: scale eect (Adam Smith) magnify the pro-competitive eect (p and X ) Some rms exit: defragmentation eect (Helpman, 1984). But how the selection works? More varieties: this eect is better analyzed using dierentiated products in monopolistic competition.

29 Oligopoly models: summing-up Strategic thinking by rms is good for consumers, but not always if trade is costly. Market shares depend on c: Strategic trade policy More gains from trade: Increasing returns: scale eect (Adam Smith) magnify the pro-competitive eect (p and X ) Some rms exit: defragmentation eect (Helpman, 1984). But how the selection works? More varieties: this eect is better analyzed using dierentiated products in monopolistic competition.

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