Heterogeneous Firms, the Structure of Industry, & Trade under Oligopoly

Transcription

1 DEPARTMENT OF ECONOMICS JOHANNES KEPLER NIVERSITY OF LINZ Heterogeneous Firms, the Structure of Industry, & Trade under Oligooly by Eddy BEKKERS Joseh FRANCOIS * Working Paer No. 811 August 28 Johannes Keler niversity of Linz Deartment of Economics Altenberger Strasse 69 A-44 Linz - Auhof, Austria * joseh.francois@jku.at hone , fax

2 Heterogeneous Firms, the Structure of Industry, & Trade under Oligooly Eddy Bekkers niversity of Linz Joseh Francois niversity of Linz & CEPR London ABSTRACT: We develo a model with endogeneity in key features of industrial structure linked to heterogeneous cost structures under Cournot cometition. We use the model to exlore issues related to cross-country differences in industry structure and the imact of globalization on markus and ricing, concentration, and roductivity. The model nests two workhorse trade models, the Brander & Krugman recirocal duming model and the Ricardian technology-based trade model, as secial cases. We examine both free entry and limited entry free exit cases. The model generates clear testable redictions on the robability of zero trade flows and the attern of exort rices, and on cross-country and industry variations in industrial structure controlling for oenness. Market rices decline as a result of trade liberalization, the least roductive firms get squeezed out of the market, exorting firms gain market share, and more firms become trade oriented. In addition, deending on the strength of underlying cost heterogeneity, falling rices are consistent with both increasing and falling industry concentration following eisodes of integration. Welfare rises with trade liberalization, unless trade costs decline from a rohibitive level in the short run free exit case. Variation across industries and markets in markus, concentration, and ricing structures is otherwise a function of market size and the variation in cost heterogeneity across industries. Keywords: Firm heterogeneity, Cournot cometition, Comosition effects of trade liberalization JEL codes: L11, L13, F12 rintdate: August 27, 28 Thanks are due to articiants in Tinbergen Institue and CEPR workshos and the ETSG annual meetings. Address for corresondence: niv. Prof. Dr. J. Francois, Johannes Keler niversity Linz, Deartment of Economics, Altenbergerstraße 69, A - 44 Linz, ASTRIA. joseh.francois@jku.at, web:

3 Heterogeneous Firms, the Structure of Industry, & Trade under Oligooly ABSTRACT: We develo a model with endogeneity in key features of industrial structure linked to heterogeneous cost structures under Cournot cometition. We use the model to exlore issues related to cross-country differences in industry structure and the imact of globalization on markus and ricing, concentration, and roductivity. The model nests two workhorse trade models, the Brander & Krugman recirocal duming model and the Ricardian technology-based trade model, as secial cases. We examine both free entry and limited entry free exit cases. The model generates clear testable redictions on the robability of zero trade flows and the attern of exort rices, and on cross-country and industry variations in industrial structure controlling for oenness. Market rices decline as a result of trade liberalization, the least roductive firms get squeezed out of the market, exorting firms gain market share, and more firms become trade oriented. In addition, deending on the strength of underlying cost heterogeneity, falling rices are consistent with both increasing and falling industry concentration following eisodes of integration. Welfare rises with trade liberalization, unless trade costs decline from a rohibitive level in the short run free exit case. Variation across industries and markets in markus, concentration, and ricing structures is otherwise a function of market size and the variation in cost heterogeneity across industries. keywords: Firm heterogeneity, Cournot cometition, effects of trade liberalization JEL codes: L11, L13, F12. 1 Introduction Research on the imact of globalization on firms has shown that the reallocation effects of trade are an imortant mechanism linking oenness to roductivity. Bernard and Jensen 24 find that almost half of the rise of manufacturing total factor roductivity in the SA between 1983 and 1992 is linked to a reallocation effect of resources towards more roductive and trade oriented firms. Eisodes of liberalization in develoing countries also show the imortance of changes in firm comosition comosition effects Tybout 21. A number of models of heterogeneous roductivity have been ut forward in the recent theoretical trade literature to exlain comosition effects of trade. A standard result is that rocesses of firm formation involving heterogeneous cost structures across firms imly beneficial reallocation effects from trade liberalization linked to rationalization of the oulation of firms. Less efficient firms roducing for the domestic market are squeezed out by more efficient trading firms. For examle, Melitz 23 introduces heterogeneous roductivity in a monoolistic cometition framework with CES-references, while Bernard, et al 23 include heterogeneous roductivity in a model with Bertrand cometition. Working with 1

4 monoolistic cometition models, Baldwin and Robert-Nicoud 28 examine linkages between trade and growth given firm heterogeneity, while Ghironi and Melitz 27 examine macroeconomic dynamics. In contrast, in this aer we exlore heterogeneous roductivity in a model with oligooly characterized by Cournot cometition. Basic asects of market structure markus, industrial concentration, relative firm ositions, and rices for domestic and exort markets are endogenous. They deend on the interaction between the technology set, market size, and trade oenness. The model we develo is a two-country, multi-sector model of trade under Cournot cometition. 1 The value added of this aroach is threefold. First, the model is arsimonious, while generating a rich set of results linked to comosition effects. This includes welfare effects of trade liberalization and the endogeneity of market structure. Moreover, we do not need to assume a secific distribution of roductivity, as is the case with Bernard, et al 23 and Melitz and Ottaviano 28, to generate our results. Second, the model nests two workhorse trade models, the Brander and Krugman 1983 recirocal duming model and the Ricardian model, as secial cases. Third, the model generates clear testable redictions on the robability of zero trade flows and exort rices, as well as redictions about linkages between oenness and industrial market structure across industries and countries. The attern of zeros and unit values has emerged as a articularly imortant issue in the recent emirical trade literature. See Baldwin and Harrigan 27, Baldwin and Taglioni 26. In the model develoed here, a larger distance between countries leads to a higher robability of zero trade flows and lower fob exort rices. The size of the imorter country also influences the robability of zero trade flows and decreases the fob exort rice. A number of other results stand out. In the free entry case, falling trade costs raise welfare unambiguously. However, in the case without free entry, welfare increases as well only when certain conditions are laced on the distribution of costs. In addition, falling rices from trade liberalization can go hand and hand with increased firm concentration. Finally, we note the ossibility of delocation effects with heterogeneous countries. nilateral liberalization then leads to higher market rices in the liberalizing country. All results are derived without secifying a secific distribution of costs. Preferences are assumed to be CES. The aer is organized as follows. In Section 2 we lay out the basic model. Section 3 1 Van Long et al. 27 also address firm heterogeneity in an oligooly model. Their aer is focused on a different set of issues however, the interaction of trade and R&D. 2

5 goes into the case of trade without free entry and section 4 addresses the case of trade with free entry. Section 5 exlores the heterogeneous countries case. Section 6 concludes. 2 The Basic Model This section lays out the basics of the model without trade or identically for an integrated or single global economy without trade costs. Industrial concentration emerges endogenously as a function of the degree of firm heterogeneity and market size, while the relationshi of concentration to rice deends on the cost structure of industry. We start by assume that there are Q + 1 sectors in the economy, oligoolistic Q sectors roducing q j and 1 sector roducing z under conditions of erfect cometition. In the first sections it is assumed that the Cournot sectors are symmetric. Later on this assumtion is relaxed when asymmetries in national technology sets, country size, and olicy are exlored. Throughout it is assumed that there are sufficient sectors in the economy so that the effect of a rice change on demand through the rice index is negligible for firms. There is no numeraire roblem. There are L equal agents each sulying 1 unit of labor. All rofit income from the Cournot sectors goes to the economic agents. The utility function of each agent is CES. The otimization roblem of the consumer generates the following market demand functions in the Cournot sectors q j and in the erfect cometition sector z: q j = IP σ 1 σ j 1 z = IP σ 1 2 The rice of good z is normalized at 1 and I is the endogenous income of all agents, the sum of labor and rofit income. P is the consumer rice index, corresonding to one unit of utility: Q P = j=1 j σ 1 1 σ = [ Q 1 σ + 1 ] 1 1 σ 3 ntil we relax out symmetry assumtions, we will focus on one reresentative Cournot sector. We will warn the reader when we dro these assumtions. This means we can dro the sector index j for now. Labor is the only factor of roduction and there is a labor force of size L. One unit of labor is needed to roduce one unit of the erfect cometition good y. 3

6 This means the wage is equal to 1. In the q sectors roductivity is heterogeneous. One unit of labor can be transformed into 1/c i units of q for the i-th firm which has marginal cost of roduction c i. There are no fixed costs of roduction. Therefore the cost function of firm i is given by C i q i = c i q i 4 There is Cournot cometition between the different firms in the q-sectors. So, firms maximize rofits towards quantity sulied, taking the quantity sulied by other firms as given. Profit of firm i is given by: π i = q i c i q i 5 The first order condition is defined as: [ π i = 1 1 q i σ ] q i c i = 6 q With q = n q i. n is the number of firms in the market. sing the first order condition, the second order condition can be written as follows derivation in aendix A: 1 σ q [ ] σ + 1 ci σ 1 < 7 sing the definition for market share, θ i = q i q, the first order condition can be rewritten as: 1 θ i = c i 8 σ θ i = σ c i 9 The marginal revenues on the LHS of equation 9 should be at least as large as the marginal costs on the RHS. The larger is market share θ i, the lower is marginal revenue. So, for ositive sales θ i which are imlicitly imosed, a firm can satisfy the FOC by just reducing its market share as long as its marginal cost is smaller than the market rice. There is a cutoff cost level c with which a firm would just stay in the market. This cutoff cost level c is equal to the market rice. The highest cost firm staying in the market has a cost level equal or just below the cutoff cost level and selling an amount just above zero. The equilibrium rice and quantities sold can be found for a given number of firms. Below 4

7 a free entry condition is added to endogenise the number of firms. Suose for now there are n firms. Combining the demand equation in 1 with n first order conditions in equation 6 and with the equation for the sum of market shares, one can find the following solutions for the market rice, total sector sales q and sales of an individual firm q i : = σ σn 1 n c i = σn c 1 σn 1 q = IP σ 1 c σ σn 1 σ 11 σn q i = σip σ 1 c c i c σ with c the average cost of firms, c = 1 n n c i. σn 1 σ 1 12 sing the fact that the rice is equal to the cutoff cost level, the rice equation 1 can be rewritten to solve for the number of firms as a function of the cutoff cost level and average σn cost: n = 1 σ c c c 13 On the basis of equation 13 we make the following Proosition. Proosition 1 The cost structures and market structures of industries are related to the degree of heterogeneity. The less the degree of cost heterogeneity, the more cometitive the structure of the industry. Equation 13 shows that an increase in the number of firms imlies that the firm with the highest cost needs to have a cost arameter ever closer to average cost. Therefore, the cost levels of firms become ever closer to each other with more firms in the market. Proosition 1 highlights how the market structure and the cost structure in the model are interrelated. When we observe more cometitive industries with more firms in equilibrium, this means the cost levels of firms should be closer to each other. 2 2 Working with a more restricted model without entry, Van Long and Soubeyran 1997 find similar results. They show that the variance of the cost distribution and the Herfindahl index of industry concentration are ositively related in a model with Cournot cometition: a larger variance leads to more industry concentration. From equation 13 above, it is clear that this result is more general, and holds with entry and exit. 5

8 Next, free entry is allowed in the model. This will endogenise the number of firms n. Free entry is introduced like in Melitz 23. Firms have to ay a sunk entry cost f e to draw a cost arameter c i randomly from a certain distribution of costs F c i. Hence, uncertainty about roductivity is a barrier to entry for firms. They start to roduce when they can make ositive oerating rofits. When they cannot make ositive rofits, they take their loss and leave the market immediately. Producing firms leave the market with a certain fixed death robability δ in each eriod or when market conditions have changed such that they cannot make ositive rofits anymore. The sunk entry costs use labor. As free entry leads to zero exected rofits, all rofit income on average is used to ay labor in the entry sector. Therefore, total income in the economy is fixed and equal to the amount of labor with wages normalized at 1. The entry and exit rocess described leads to a zero cutoff rofit condition ZCP and a free entry condition FE. Together these two conditions can be added to the no free entry equilibrium equations, equations The number of firms n can then be determined. The ZCP can be derived from the fact that zero rofit imlies that rice should be equal to marginal cost. The FOC in equation 6 shows that this firm will reduce market share to just above zero, to satisfy the first order condition and make non-negative rofit. One finds as ZCP: = c 14 The FE is given by equalizing the ex ante exected rofits from entry with the sunk entry cost: F c 1 δ j π = f e 15 j= π = δf e F c 16 π is the exected rofit conditional uon entry. It can be written as: π = c [ c q c cq c] µ c dc = q c θ c c µ c dc 17 µ c is the truncated df of all firms roducing, µ c = 1 F c f c.3 Continuing the deriva- 3 Remember that q is the sum of sales of all firms in a Cournot sector 6

9 tion, leads to the following FE: π = LP σ 1 c σ c σ c 2c + c2 c µ c dc = δf e F c LP σ 1 c σ σ c 2Ec + E c2 c = δf e F c The exectation aearing in equation 19 is a truncated exectation, i.e. Ec = Ec c c. All exectations aearing in the remainder of the aer are the aroriate truncated exectations. Combining the FE and ZCP generates the following equation: LP σ 1 σ σ 2Ec + E c2 = δf e F 2 The combined FE/ZCP equilibrium condition generates a stable rice equilibrium. Rewriting equation 18 using average rofit unconditional uon entry π = F π, gives: π = σ 1 LP σ σ 2c + c2 f c dc = δf e 21 Aendix A shows that the LHS of equation 21 rises in the market rice from to when the SOC is imosed, imlying that there is a unique equilibrium. The FE and ZCP can be used to solve for the cutoff cost level. An exlicit solution requires the choice of an initial cost distribution. Once the cutoff cost level c is known the number of firms can be determined. In steady state average cost is equal to exected cost, c = Ec c c. So, the number of firms is equal to: n = Ec c c = 1 1 Ec c 22 Equation 22 can be log differentiated with resect to the market rice and the number of firms n: ˆ = Ec c 1 ˆn 23 1 ε Ec, ε Ec, is the elasticity of equilibrium average costs with resect to the equilibrium market rice. Equation 23 imlies the following: 7

10 Proosition 2 When the equilibrium average cost varies less than roortionally with market rice i.e. it falls slower with a corresonding dro in market rice, a lower market rice is coincident with a larger number of firms. Or equivalently, a lower market rice is coincident with more firms when the average marku declines in equilibrium with falling market rices. When the average cost varies more than roortionally in equilibrium with lower market rices, a decreasing market rice is coincident with less firms. Proosition 2 follows from equation 22. As the market rice is equal to the cutoff cost level, the relation between the market rice and the number of firms deends on the distribution of costs. 4 Intuitively, a lower market rice can either be caused by more firms in the market or by more efficient firms in the market. When average costs resond less than roortionally to the market rice, a lower market rice is caused by more firms in the market. When average costs resond more than roortionally to the market rice, a lower market rice is caused by more efficient firms in the market. In this situation a lower market rice can go along with less firms, because the least efficient firms are squeezed out of the market. A related result can be derived on the effect of market size L on the number of firms. Proosition 3 The number of firms rises in the size of the market L when equilibrium average costs decline less than roortionally with equilibrium market rice. The combination of Proositions 1, 2 and 3 leads to the following corollaries about industrial market structure and market size. Corollary 1 The mix of rice and concentration deends on the distribution of firm costs from Proosition 1. While larger markets imly lower rices, larger markets will only have both more firms and lower rices as long as the equilibrium average cost varies less than roortionally with equilibrium market rice equation 23. Larger markets will have more concentration but also lower rices as long as the equilibrium average cost varies more than roortionally with market rice again as defined in equation 23. Corollary 2 The relationshi of markus to market size also deends on cost heterogeneity. Larger markets imly both larger markus and greater concentration when the equilibrium 4 With a Pareto distribution, the truncated mean is linear in the truncation oint. Therefore, the number of firms will be fixed. Simulations show that with a lognormal distribution sensible results can be generated with a reasonable number of firms. Moreover, with a lognormal distribution the number of firms declines in the market rice. 8

11 average cost varies more than roortionally with market rice as defined in equation 23, and otherwise they imly lower markus and less concentration if equilibrium average cost varies less than roortionally with market rice. From Proosition 1, the latter case is more likely to hold in industries with lower cost heterogeneity linked to the technical distribution of ossible costs for a firm. From Corollary 2, a systematic variation between market size, markus, and concentration for examle in cross-country comarisons or markus and concentration can be taken as an indirect indicator of cost heterogeneity. The combined FE/ZCP in equation 21 can be totally differentiated towards and L: d dl = L c 2 f c dc σ + 1 c σ 1 f c dc < 24 The denominator is ositive by the SOC in equation 7. Equation 24 shows that a larger market leads to a lower market rice. From Proosition 2 it is known that the number of firms rises in the equilibrium market rice when the decline in equilibrium average cost is less than roortional to a decline in the equilibrium market rice, which imlies Proosition 2. Intuitively, a larger market can be served in two ways: through more firms or through an increase in the sales er firm. Deending on the distribution of costs one or the other dominates. 5 The number of firms can increase with a larger market, but the number of firms can also decrease with a larger market, when enough of the least efficient firms are squeezed out of the market. This result contrasts with the monoolistic cometition model of Melitz, where the number of firms is linear in market size and the increase in market size is served through a roortional increase in the number of firms. Here, concentration is an indicator of underlying heterogeneity, as is rice. 3 International Trade without Free Entry: the Short Run We next introduce international trade between two countries s, r = H, F with markets effectively segmented by trading costs. The countries are symmetric in size and technology 5 With a Pareto distribution the number of firms is fixed, so the increase in sales as a result of the larger market is fully realized through more sales er firm. With a lognormal distribution, also the number of firms changes considerably. 9

12 sets. In articular we now introduce iceberg trade costs τ in the Cournot sectors, meaning that marginal cost for roduction and delivery is increased at the rate τ relative to roduction and delivery for the domestic market. There are no fixed or beachhead trade costs, and the trading costs reclude return exorts. We do not have free entry we return to this in the next section though existing firms can exit. This can be seen as a short-run or free-exit case. We focus on the imact of increased globalization i.e. falling trade costs. Consistent with the emirical literature Tybout 21, increased globalization through falling trade costs means that average markus from domestic sales decline and average markus from exorting sales rise with falling trade costs. nder our assumtions about trade costs, the equilibrium market rice in the reresentative Cournot sector becomes: with c s = [ nds 1 n r c ids + nxs τc ixs ] s = effect of trade liberalization on the market rice: σn s σn s 1 c s 25 and n s = n ds + n xs. In equation 25, there is a direct exorting firms have lower costs and therefore average costs decline. And there is an indirect effect, because firms roducing for the domestic market can disaear and exorting firms can aear on the market. It can be shown that this indirect effect is at the margin see aendix B. Therefore, the relative change in the market rice is equal to: P s = n ds n xs τc is τ 26 c is + nxs τc is Variables with a hat denote relative changes, x = dx x. The elasticity of the market rice with resect to trade costs, ε,τ, is between and 1: ε,τ = n ds n xs τc is From equations 26 and 27 we make the following roosition: 27 c is + nxs τc is Proosition 4 With a decline in trade cost τ, the market rice also declines. Equation 26 shows that a decline of trade costs τ drives down the market rice. The 1

13 domestic cutoff marginal cost is equal to the market rice, so it also declines. Several other Proositions can be made on the effect of trade liberalization. Proosition 5 Some of the least roductive firms are squeezed out of the market with a decline in trade cost τ. How many firms are squeezed out of the market deends on the rice distribution of the firms, i.e. it deends on how far the highest cost firms are from the old market rice. Proosition 6 More of the remaining firms exort with a decline in trade cost τ. More firms can enter the exort market, as the exorting cutoff marginal cost rises when τ declines: c xr = P s τ 28 ĉ xr = P s τ = 1 ε,τ τ 29 Proosition 7 Average markus from domestic sales decline and Average markus from exorting sales rise with a decline in trade cost τ. Markus of all domestic sales decline, as the costs of the firms remain equal, whereas the market rice declines. Markus of the exorting firms rise with trade liberalization, as the effect of the declining trade costs dominates the effect of the decrease in market rice in the exorting market. sing the letter m to indicate marku, the following can be derived: m ixs = P r τc is 3 ˆm ixs = ˆP r ˆτ = ε,τ 1 ˆτ 31 The effect on average domestic and exorting markus can be calculated as well. The markus of firms are weighted by market shares in calculating average markus, so as to give more weight to larger firms 6 : m ids = m ixs = n ds n xs s n ds θ ids = c is r n xs θ ixs = τc is σ s c is c is 32 σ r τc is τc is 33 6 Imlicitly it is assumed that the robability of firms to be in the market is equal for all marginal costs, i.e. that the distribution of costs is uniform. 11

14 Relative changes of the average exorting and domestic markus are equal to: m ids = n ds n ds m ixs = n ds s c is ε,τ ˆτ 34 s c is θ ids n ds r τc is 1 ε,τ ˆτ 35 r τc is θ ixs So, average markus from domestic sales decline and average markus from exorting sales rise. 7 Declining markus in the domestic market fit well with emirical findings reorted in Tybout 21 from develoing countries. Various studies find that more imort cometition goes along with declining markus. As in almost any model of international trade for examle Armington firms increase their market share on the exorting market and their market share is reduced in domestic markets. But the relative gain and loss of exorters and domestic roducers dislays an interesting attern: Proosition 8 Large low cost firms lose less market share on the domestic market than small high cost firms and small high cost exorting firms gain more market share on the exort market than large low cost firms Proosition 8 follows from totally differentiating the exressions for market shares: dθ ids = σ c ids ε,τ τ 36 dθ ixs = σ c ixr ε,τ 1 τ 37 Therefore small firms lose relatively more market share on the domestic market and small firms gain relatively more market share on the exorting market than large firms. So, more efficient big firms do not gain more from imroved market access abroad than less efficient small firms. Essentially, big firms already have a strong osition in an exorting market, so they cannot grow as much as a result of trade liberalization as small firms. 8 7 Indirect effects because domestic roducing firms disaear from the market and exorting firms enter the market are, because the averages are weighted by market shares and market shares are zero for entering and exiting firms. 8 This set of results, related in articular to Proosition 8, has interesting olitical economy imlications 12

15 Consider next the welfare effect of trade liberalization. This is comlicated by the fact that income is endogenous as it deends on rofit income in the imerfect cometition sector. With free entry rofit income is driven to zero, but in the no free entry case rofit income is non-zero and varies. Welfare in country s is equal to utility in that country: W s = s = I s P s = L s + Π s P s 38 Π s is total rofit income in the economy. Elaborating uon this equation see aendix B assuming that both countries are equal, one arrives at the following exression: W = L Q + σ σ + Q c 1 39 P c are the market share weighted average costs, c = n d c i θ id + nx τc i θ ix. Log-linearizing welfare towards trade costs τ from equation 39 and treating the rice and the market share weighted average costs as endogenous, one finds derivation in aendix B: [ Ŵ = σ σ Q + σ ] σσ σ ˆ + Q c Q σ d c 4 + Q c The first term in 4 is the welfare gain through a decline in rice. As exected the gain for the consumer from lower rices outweighs the loss of a lower rofit income with lower rices. The second term measures the ossible gain from trade liberalization of lower costs leading to a higher rofit income. Elaborating on the cost effect, d c, one gets: [ Ŵ = ] σσ σ ˆ + Q c σ σ Q + σ [ Q nd ] n x n x σ c i θ idˆθid + τc i θ ixˆθix + τc i θ ixˆτ + Q c 41 beyond the scoe of this aer. As trade liberalization rogresses, the dominant domestic firms gain relative domestic osition known as standing in the antiduming and trade safeguards literature. Assuming that lobbying efficiency is a function of industry concentration, increased concentration of firms with standing i.e. the domestic industry may increase their ability to organize and seek rotection or relief against further dros in trade costs and foreign cometition. 13

16 [ Ŵ = σ σ Q + σ Q σ + Q c [ nd ] σσ σ ε,τ ˆτ + Q c σ c2 i ε,τ n x σ τ 2 c 2 i 1 ε,τ + n x τc i θ ix ] ˆτ 42 Equation 41 and 42 can be interreted as follows. In both equations is the first term on the RHS again the welfare gain from a lower market rice. The second term on the RHS measures the effect on rofit income through changed costs. In both 41 and 42 the first term between the second brackets measures the gain from the declining market share of domestic roducing firms. The second term between the second brackets measures the loss from the rising market share of exorting firms. The third term measures the welfare gain from lower trade costs with trade liberalization. Proosition 9 Like in Brander and Krugman 1983 the welfare effect of trade liberalization can be negative at first when the tariff is reduced from a rohibitive level, due to the increased costs of cross-hauling associated with the first units traded. However, unlike Brander and Krugman, the welfare effect can also be ositive when the tariff is reduced from a rohibitive level. nlike in the model of Brander and Krugman 1983 the welfare effect of trade liberalization when the tariff is reduced from a rohibitive level is ambiguous. It deends on the cost structure of firms whether the welfare effect is ositive or negative. It can be shown under what condition the welfare effect is negative in general, but this condition is cumbersome and does not lend itself to any interretation. See footnote 9 below for roof by examle. 9 The ambiguity vanishes for low trade costs. Proosition 1 The welfare effect of trade liberalization is unambiguously ositive when the tariff is negligible or small, like in Brander and Krugman As roof of ambiguity, we can offer two examles to show that the welfare effect can go both ways. First an examle of a negative welfare effect from trade liberalization. Suose there are two identical countries with each three firms. They have marginal costs of 1, 1 and 2. The autarky market rice will be 2. The iceberg trade costs are equal to 2. This imlies that 2 firms can exort, but with a market share of. Substitution elasticity σ is equal to 1. Equation 42 can be alied to show that a marginal reduction of the Q 1+Q tariff decreases welfare with 1. An examle where the welfare effect is ositive is the following. Again 2 there are two identical countries with each three firms. Marginal costs are 1, 2 and 3. The autarky market rice is 3. Iceberg trade costs are 3. So, only one firm can exort. Furthermore, the substitution elasticity σ is 1, so utility is Cobb-Douglas. There are two sectors in the economy and the Cournot sector has CES-weight Cobb-Douglas arameter α. When the tariff is reduced from the rohibitive level, the welfare effect from equation 42 is equal to 1 α 5 4 So, when the Cournot sector is small enough α < 1/5, the welfare 9 9 effect of trade liberalization is ositive. 14

17 Proosition 1 follows immediately from equation 42. When the tariff is equal to 1, the first two terms between brackets in equation 42 are equal. So, only negative terms are left and therefore the welfare effect from trade liberalization is ositive. Brander and Krugman 1983 only show that the welfare effect is ositive when the tariff is negligible. In the resent heterogeneous roductivity model one can say more on when the welfare effect is ositive. Elaborating uon equation 42, the following exression can be derived for the welfare effect of trade liberalization see aendix B: [ σ σ ] Ŵ = Q + σ σσ σ ˆ + Q c Q σn n x σ + Q c 2 τc i [nµ σn 1 c µ c + 2τc i + n 1 V ar c i ] ˆτ 43 In equation 43 µ c and V ar c i are resectively the mean and variance of the marginal costs of domestic and exorting firms, µ c = 1 n V ar c i = [ nd 1 n 1 ] n x c i + τc i nd 44 n x c 2 i + τ 2 c 2 i nµ 2 c. 45 Note that the summation in equation 43 is over all the terms between brackets. It can also be shown that the welfare effect is ositive when the following condition is satisfied: V ar c i µ 2 c n σn 1 n 1 46 From equation 43 and 46 the following statements can be made: Proosition 11 The welfare effect of trade liberalization is ositive when the exorting firms are efficient relative to average market costs. In articular, the welfare effect is unambiguously ositive when all exorting firms have marginal costs inclusive of trade costs lower than the average of market rice and average costs. Proosition 1 The welfare effect of trade liberalization is ositive when the coefficient of variation of the cost distribution is larger than the square root of 15 n σn 1n 1.

18 Proosition 11 follows from equation 43. When µ c + is larger than 2τc i all terms in equation 43 will be negative and hence the welfare effect of trade liberalization will be ositive. Intuitively, when the exorting firms are roductive, their gain in market share at the exense of domestic roducing firms reresents a welfare gain. More roductive firms relace less roductive firms. But when the exorting firms marginal costs inclusive of trade costs are larger than the marginal costs of the domestic roducing firms, the shift in market share towards exorting firms can reresent a loss. In some cases this loss can be larger than the welfare gain due to lower rices and lower trade costs, as shown by the examle above. Proosition 1 follows from 46. It can be interreted as follows. When the variance of firms costs is large relative to average firms costs, the fraction of relatively inefficient exorting firms will be small. So, the welfare loss from an increasing market share of relatively inefficient exorting firms will be smaller than the welfare gain from a decreasing market share of domestic roducing inefficient firms. The next section shows that the welfare effect from trade liberalization is unambiguously ositive with free entry. 4 International Trade with Free Entry: the Long Run In the free entry case, the welfare effect of trade liberalization deends entirely on the effect of liberalization on the market rice as rofit income remains zero. Showing that trade liberalization leads to a lower market rice is sufficient to show that liberalization raises welfare. In this section we focus on market conditions with falling trade costs based on the combined ZCP and FE conditions. Trade liberalization does indeed lead to a lower market rice and thus to higher welfare. Firms can make rofits from domestic and exorting sales, if they are roductive enough to exort. Average rofit is defined as: π s = π ds + F c xs F c π xs 47 ds π ds and π xs are the exected rofits from resectively domestic and exorting sales, condi- 16

19 tional uon entry. There are two ZCP for domestic and exorting sales: c ds = s 48 c xs = r τ 49 Elaborating on exected rofits as in the closed economy case, generates the following equilibrium equations deriving from the ZCP and FE: δf e = L sp σ 1 s s δf e F c ds s σ s 2c + c2 f c dc + L rp σ 1 r s σ r = LSP σ 1 s s [ ] σ s 2Ec ds + E c ds 2 s r σ r 2c + c2 f c dc 5 + F r [ ] 51 τ L r P σ 1 r F s σ σ r 2τEc xs + τ 2 E c xs 2 r r To determine the imact of trade costs on the market rice, one can totally differentiate the free entry condition in equation 5 towards the cutoff cost level which equals the market rice and trade costs. Both the imact of sectoral trade liberalization and trade liberalization in all Cournot sectors can be addressed. The effect of sectoral trade liberalization on the market rice is larger. Totally differentiating towards and τ one finds the following exressions for the effect on market rice of sectoral and economywide liberalization resectivelyderivation in aendix C: r ˆ = ˆ = A = B = C = τ 2 τ 2 τc τc 1 τc A + B 1 τc A + B + C f c dc f c dc θ d c σ + 1 c σ 1 f c dc θ x c σ + 1 τc σ 1 f c dc Q 1 σ Q 1 σ + 1 π d + π x ˆτ = ε,τ,sect,f Eˆτ 52 ˆτ = ε,τ,nat,f Eˆτ 53 17

20 ε,τ,sect,f E and ε,τ,nat,f E are the elasticities of the market rice with resect to trade costs in the free entry case with sectoral and nationwide trade liberalization resectively. By the SOC in equation 7 the denominator in both equations is ositive and hence the fraction is ositive as well. This gives rise to the following Proosition: Proosition 12 Trade liberalization or otherwise falling trade costs τ leads to a lower market rice and higher welfare in the free entry case. Welfare rises when the market rice of q declines as income is fixed with free entry. 1 Hence, welfare rises in this model as a result of trade liberalization. By Proosition 2 a lower market rice goes along with more or less firms in the market deending on how much average costs decline when the market rice declines. This result can be combined with Proosition 12. The imlication is that the lower market rice as a result of trade liberalization can go along with more but also with less firms in the market, deending on how many of the least efficient firms are squeezed out of the market. Hence, the conventional insight of the recirocal duming model that trade liberalization leads to lower market rices, because there are more firms in the market has to be relaxed. Trade liberalization can also lead to less firms in the market and still decrease market rices, because enough of the least efficient firms are squeezed out of the market. The various effects of trade liberalization described in the section on no free entry can also be examined in the free entry case. The following effects of trade liberalization are found: Proosition 13 The least roductive firms get squeezed out of the market with falling trade costs τ in the free entry case. Proosition 13 follows from the fact that the cutoff cost level is equal to the market rice. A lower market rice imlies that the highest cost roducers have to leave the market. Next, the effect on market shares from domestic and exorting sales is calculated. Proosition 14 Market shares from domestic sales decline and market shares from exorting sales rise with declining trade costs τ in the free entry case. 1 = L P, Û = Q1 σ 1+Q 1 σ ˆ 18

21 Log-differentiating the exressions for market shares, defined imlicitly in equations 9 and using equation 52 gives: c i c i θid = 1 ˆ = 1 ε,τ,f Eˆτ 54 σ c i σ c i θix = 1 τc i ˆ τ = 1 τc i 1 ε,τ,f E ˆτ 55 σ τc i σ τc i The market share from domestic sales declines for all firms. Therefore, the market share from exorting sales should rise, either because more firms can exort or because the market share of firms that already exorted should rise. The market share of firms that enter the exorting market is zero. Therefore, the market share of firms already exorting should rise. Alying this line of reasoning, equation 55 imlies that the elasticity of the market rice with resect to iceberg trade costs in equations 52 and 53 is smaller than 1. This result is useful in the remainder. Proosition 15 The elasticity of the market rice with resect to trade costs is between and 1. Proosition 15 can immediately be used in the following two Proositions. Proosition 16 More of the remaining firms are able to exort with declining trade cost τ in the free-entry case. The exorting cutoff cost level c x is equal to τ. Log-differentiating shows that the exorting cutoff cost level declines with trade liberalization, imlying that more firms can exort: ĉ x = ˆ ˆτ = ε,τ,f E 1 ˆτ 56 Proosition 17 Markus from domestic sales decline and markus from exorting sales rise for remaining individual firms with declining trade cost τ in the free entry case. Markus from domestic sales and exorting sales are equal to c and τc, resectively. Log differentiating shows that markus from domestic sales decline and markus from exorting sales rise with trade liberalization: ˆm d = ˆ = ε,τ,f Eˆτ 57 ˆm x = ˆ ˆτ = ε,τ,f E 1 ˆτ 58 19

22 While we have clear results for individual firms, the imact on the average across firms deends on the underlying structure of cost distributions, much like the closed economy case in Section 2. Basically, market exansion through globalization with falling trade costs τ is analogous to market exansion in the closed economy case. We summarize this oint with the following roosition: Proosition 18 While deeer integration through falling trade cost τ imlies falling rices, the imact on average markus across firms and average firm size whether they rise or fall on average deends on the underlying distribution of costs. Average markus from domestic and exorting sales weighted by market shares are defined, resectively, as: m d = m x = c σ c µ c dc = τc σ τc µ c dc = σ c c σ τc τc f c dc 59 F f c F dc 6 τ Log-differentiating these exressions shows that average markus from domestic sales decline and average markus from exorting sales rise: m d = σ τ f µ c dc c F c µ c dc ε,τ,f E 61 m x = σ τ τc µ c dc f τ τ F τ τc µ c dc ε,τ,f E 1 62 The terms in f F reresent the increased robability weight of all firms in the market, when the cutoff oint declines as a result of trade liberalization. Basically, as in the closed or integrated economy case, the effect of trade liberalization which is somewhat analogous to market exansion on average domestic and exorting markus is ambiguous and deends on the cost distribution of roductivities. As in the closed economy case, larger or more integrated markets imly lower rices, but these lower rices may involve lower or higher average markus. It deends on the structure of cost heterogeneity. 2

23 Similarly, as in the case of the closed or integrated economy, we find a similar result for average firm size and hence for concentration as well. Average firm size from domestic sales and exorting sales is defined, resectively, as: r d = = P σ 1 L σ 1 q d c µ c dc = P σ 1 L σ 1 θ d c µ c dc σ c µ c dc = P σ 1 Lσ 1 σ 1 c σ µ c dc 63 r x = = P σ 1 L σ 1 q x c µ c dc = P σ 1 L σ 1 σ τc θ x c µ c dc µ c dc = P σ 1 Lσ Differentiating these exressions towards trade costs generates: r d τ = τ P σ 1 L σ σ 1 1 θ d c µ c dc f F 1 τc σ 1 σ σ c µ c dc 64 µ c dc ε,τ,f E 65 r x τ L 1 σ 1 τ = P σ 1 + P σ 1 σ 1 L f τ τ 2 F τ [ 1 θ x c 1 ε,τ + σ 1 ] σ θ x c µ c dc σ τc σ µ c dc [1 ε,τ,f E ] 66 So, like with average markus, the effect on average domestic and exorting firm sales deends on the distribution of costs. 5 Asymmetric Countries So far we have focused on strict symmetry across countries in terms of technology sets and size. In this section the symmetry assumtions are relaxed. Three sets of results are derived. First, we show that unilateral liberalization can lead to higher rices in the liberalizing 21

24 country in the long run. Second, the imact of country size and distance on the robability of zero trade and on exorting unit values is derived. Third, we resent the Ricardian model with roductivity differences as a nested model of the resent framework. The setu in this section is as follows. There are two countries s, r = H, F. The countries dislay differences in country size, in trade costs and in their technology sets cost distributions. Productivity differences are modeled by a different lower frontier for the marginal cost distribution, c s c r. The combined FE/ZCP conditions in both countries become: δf e = L sp σ 1 s σ s + L rp σ 1 r σ r r τsr c s s c s σ s 2c + c2 f s c dc s σ r 2τ sr c + τ 2 src 2 r f s c dc 67 δf e = L rp σ 1 r σ r + L sp σ 1 s σ s s τrs c r r c r 5.1 asymmetries in trade costs σ r 2c + c2 f r c dc r σ r 2τ rs c + τ 2 rsc 2 s f r c dc 68 nilateral liberalization can be studied using the above two equations. Assuming that the two countries are equal in all resects excet their trade costs, one can log-linearize the above system of equations towards market rices s, r and trade costs τ sr, τ rs. Aendix D shows that this leads to the following result: ˆ r = 2 σ ˆ s = 2 σ qs q r dc ds dc xτrˆτ rs dc xr dc xτsˆτ sr dc ds dc dr dc xs dc xr 69 qr q s dc ds dc xτsˆτ sr dc xs dc xτrˆτ rs dc ds dc dr dc xs dc xr 7 dc ds, dc dr, dc xs, dc xr, dc xτs and dc xτr are resectively the marginal effects on exected rofit from domestic and exorting rice changes and from trade liberalization in country s and r, 22

25 defined as follows: dc ds = dc xs = dc xτs = s s τsr r τsr θ ds σ + 1 c σ 1 s f c dc 71 θ xs σ + 1 c σ 1 r f c dc 72 θ xs c τ sr cf c dc 73 The variables in r are defined accordingly. The marginal effects from domestic rice changes on exected rofit dc ds and dc dr are larger than the marginal effects from exorting rices on exected rofit dc xs and dc xr, because the domestic market shares θ d are larger than the exorting market shares θ x and the integration frontier is larger for the domestic cost variables than for the exorting cost variables. Equation 26 shows that in the short run unilateral liberalization leads to a lower market rice in the imorting country. Equations 69 and 7 show that unilateral liberalization in country s, i.e. a negative τ rs, decreases the market rice in the exorting country s and increases the market rice in the imorting country r in the long run. This gives rise to the following Proosition: Proosition 19 nilateral liberalization causes a decreasing market rice in the liberalizing imorting country in the short run. In the long run, however, the market rice in the imorting country increases and the market rice in the exorting country decreases. Hence, the welfare effect of unilateral liberalization is negative in the imorting country and ositive in the exorting country. The short-run effect of unilateral liberalization is as one would exect. The long-run imact is due to industrial delocation effects. 11 Due to unilateral liberalization in country s, exected rofit rises in country r. Therefore, there will be more entry in country r. At the same time, the decreasing market rice in country s reduces entry in that country. The effect of this entry and exit is that the market rice in the exorting country s declines and the market rice in the imorting country r rises With a different model, but also characterized by cost heterogeneity, Melitz and Ottaviano 28 obtain a similar result. 12 Mathematically, the reason for the declining market rice in the exorting country s and the rising market 23

26 5.2 asymmetric size, distance, and zero trade flows We next focus on the imact of distance and imorter country size on the robability of zero trade and on exort rices. We concentrate on country r as the imorter country. First consider the effect of a change in distance. We take as roxy a change in trade costs. Equations 69 and 7 show the effect of lower trade costs on market rices. Equalizing the change in trade costs, i.e. ˆτ rs = ˆτ sr = ˆτ, one finds: ˆ r = 2 σ q s q r dc ds dc xτr dc xr dc xτs dc ds dc dr dc xs dc xr ˆτ = ε r τ,cˆτ 74 ˆ s = 2 σ q r q s dc dr dc xτs dc xs dc xτr dc ds dc dr dc xs dc xr ˆτ = ε s τ,cˆτ 75 nless country sizes differ a lot leading to strong delocation effects, market rices decline with lower trade costs in the imorting country r. sing the same reasoning as in the equal country case, one can rove that the elasticity of rice wrt trade costs, ε r τ,c, has to be between and 1. Market shares of domestic roducers in country r and exorters from country s can be log differentiated to get: c ir c ir θidr = 1 ˆ r = 1 ε r τ,cˆτ 76 σ r c ir σ r c ir θixs = 1 τc is ˆ r τ = 1 τc is 1 ε r τ,c ˆτ 77 σ r τc is σ r τc is When distance becomes smaller, the market rice in country r, r, declines if there are no strong delocation effects. As a result the domestic market shares in the imorting country, θ idr decline. Hence, the θ ixs have to rise to get a total market share of 1 and therefore < ε r τ,c < 1. This imlies that r /τ will decline, as the denominator τ declines at a larger rate than the numerator r. r /τ is both the exort rice and the cutoff cost value for exorts from country s to country r. When the cutoff cost value of exorts declines, the robability of zero trade rises. It becomes more likely that no firm is able to exort rice in the imorting country r is the following: the marginal effect on exected rofit of a changing domestic rice, as reresented by c dr and c ds, is larger than the effect on exected rofit of a changing rice in the exort market, reresented by c xr and c xs. Therefore, when the exected rofit from exorts in country s rise due to unilateral liberalization in country r, the FE can be restored by decreasing rices in the exort market r and/or in the domestic market s. The rices in the two markets should go in oosite directions, however, because the FE in foreign should also be satisfied. Because the marginal effect of domestic rice changes is larger, the domestic rice in s has to decrease and the exorting rice in r has to rise. With decreasing exort rices in r and rising domestic rices in s, the FE s could never be satisfied. 24

27 rofitably. Therefore, we have the following result: Proosition 2 A lower distance between trading artners leads to both a lower robability of zero trade flows and a lower fob exort rice. Consider next the effect of imorting country size on the robability of zero trade flows and exort rice. The combined FE/ZCP equations, 68 and 67, are log differentiated wrt r, s and L r, leading to 13 : ˆ r = d cds π dr d crx π sx d cdr d cds d crx d csx q r ˆLr 78 ˆ s = d csx π dr d cdr π sx d cdr d cds d crx d csx q s ˆLr 79 d cdr, d cxr, d cds and d cxs are resectively the marginal effects on exected rofit from domestic and exorting rice changes in country r and country s, as defined in equations 71 and 72 for country s. As the effect of domestic rice changes on exected rofit are larger, because market shares in the domestic market are larger, the denominator in both equations 78 and 79 is ositive. When roductivity differences between the two countries are not too large, exected rofits from domestic sales of roducers in country r, π dr are larger than exected rofits from exorting sales of exorters from country s, π sx. This imlies that the numerator is also ositive. Hence, the market rice in country r decreases in its market size. The fob rice of exorters from country s, r /τ, also decreases. Therefore, we have the following result: Proosition 21 A larger market size of the imorting country leads to a higher robability of zero trade flows and lower fob exort rices. Baldwin and Harrigan 27 comare different models of international trade on their redictions of the effect of distance and imorting country size on the robability of zero trade flows and fob rices. From table 1 in their aer it is clear that the Cournot model in this aer generates the same redictions as the Melitz and Ottaviano 28 model in this regard. The redictions are different from the model roosed by Baldwin and Harrigan 27, which seems to align with the emirical findings resented in their aer. However, whereas 13 Derivation available uon request. The derivation is similar to the log differentiation wrt r, s and τ discussed in aendix D. 25