Alexander Tarasov: Trade Liberalization and Welfare Inequality: a Demand-Based Approach

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1 Alexander Tarasov: Trade Lieralization and Welfare Inequality: a Demand-ased Approach Munich Discussion Paper No Department of Economics University of Munich Volkswirtschaftliche Fakultät Ludwig-Maximilians-Universität München Online at

2 Trade Lieralization and Welfare Inequality: a Demand-ased Approach Alexander Tarasov y University of Munich January 2010 Astract There is strong evidence that di erent income groups consume di erent undles of goods. This evidence suggests that trade lieralization can a ect welfare inequality within a country via changes in the relative prices of goods consumed y di erent income groups (the price e ect). In this paper, I develop a framework that enales us to explore the role of the price e ect in determining welfare inequality. There are two core elements in the model. First, I assume that heterogenous in income consumers share identical ut nonhomothetic preferences. Secondly, I consider a monopolistic competition environment that leads to variale markups a ected y trade and trade costs. I nd that trade lieralization does a ect the prices of di erent goods di erently and, as a result, can ene t some income classes more than others. In particular, I show that the relative welfare of the rich with respect to that of the poor has a hump shape as a function of trade costs. Keywords: nonhomothetic preferences, income distriution, monopolistic competition. JEL classi cation: F12 An earlier version of the paper was circulated under the title "Gloalization: Intensive versus Extensive Margins". I am grateful to Kala Krishna and Andrés Rodríguez-Clare for their invaluale guidance and constant encouragement. I also would like to thank Pol Antràs, James Tyout, Kei-Mu Yi, conference participants at the Spring 2008 Midwest International Economics meetings and 2008 North American Summer Meeting of the Econometric Society for helpful comments and discussion. All remaining errors are mine. y Seminar for International Economics, Department of Economics, University of Munich, Ludwigstr. 28, 80539, Munich, Germany. alexander.tarasovlrz.uni-muenchen.de.

3 1 Introduction It is well known that di erent income classes consume di erent undles of goods. This evidence suggests that trade lieralization can a ect welfare inequality within a country through at least two e ects. First, trade lieralization can lead to changes in income distriution in a country and, therey, a ect the income inequality (the income e ect). Secondly, trade lieralization can have a di erent impact on prices of di erent goods, a ecting welfare inequality through changes in the relative prices of goods consumed y di erent income groups (the price e ect). While the income e ect is intensively explored in the trade literature (see Golderg and Pavcnik (2007)), the price e ect is not paid much attention. In this paper, I construct a general equilirium model of trade etween symmetric countries that enales us to examine the role of the price e ect in determining welfare inequality. The core element of the model is nonhomothetic consumer preferences. 1 Indeed, trade models with homothetic preferences are not appropriate for studying the impact of trade lieralization on welfare inequality through the price e ect, as irrespective of their income, consumers purchase identical undles of goods. In contrast, in the present model, nonhomotheticity of preferences leads to that some goods (luxuries) are availale only to the rich. Another key element is a monopolistic competition environment. Imperfect competition induces variale markups and, therefore, allows us to explore the e ects of trade lieralization on prices set y rms. In particular, I nd that trade lieralization does a ect the prices of di erent goods (necessities and luxuries) di erently and, as a result, can ene t some income classes more than others. The key assumption aout consumer preferences is that goods are indivisile and consumers purchase at most one unit of each good (see Murphy et al. (1989) and Matsuyama (2000)). This implies that, given the prices, goods are arranged so that consumers can e considered as moving down a certain list in choosing what to uy. For instance, in developing countries, consumers rst uy food, then clothing, then move up the chain of durales from kerosene stoves to refrigerators, to cars. Furthermore, consumers with higher income uy the same undle of goods as poorer consumers plus some others. 2 1 There is strong empirical evidence that consumer preferences are nonhomothetic (see for example Deaton and Muellauer (1980) and Hunter and Markusen (1988)). 2 This structure of consumer preferences has enough exiility to e applied as to the whole economy as to a certain industry where goods di er in quality. On the one hand, each good can e interpreted as a distinct good 1

4 I assume that each good is produced y a distinct rm and goods di er according to the valuations consumers attach to them. 3 Depending on the valuations placed on their goods, rms decide whether to serve oth domestic and foreign markets, to serve only the domestic market, or not to produce at all. I limit the analysis in the paper to a two-class society (the rich and the poor). 4 Then, given the preferences, rms serving a certain market face a trade-o etween selling to the oth income classes at a lower price and selling only to the rich at a higher price. Speci cally, rms with su ciently high valuations nd it pro tale to sell to all consumers, while rms with low valuations decide to sell only to the rich. Hence, availale goods in each market are divided into two groups: the necessities include goods that are consumed y oth income classes, while the luxuries include goods that are consumed y the rich only. Since the income distriution in the model is exogenous, I focus only on the price e ect and do not explore the impact of trade lieralization on income distriution. I nd that the reduction in trade costs a ects the prices of necessities and luxuries di erently and, therefore, changes welfare inequality within a country via the price e ect. In particular, I show that the relative welfare of the rich with respect to that of the poor has a hump shape as a function of trade costs. If trade costs are su ciently low, then further trade lieralization ene ts the poor more, while if trades costs are high enough, then the rich gain more from the reduction in trade costs. To understand etter the intuition ehind these ndings, consider separately two sumarkets: one for the necessities and one for the luxury goods. Since the rich consume the same undle of goods as the poor plus the luxuries, the relative welfare in the model is determined y the relative prices of the luxuries with respect to those of the necessities. If trade costs are su ciently low, then exporting rms nd it pro tale to serve oth income classes in a foreign market: exporting rms with high valuations of their goods serve all consumers, while exporting rms with lower sold in the market. On the other hand, we might think that rms sell not distinct goods ut some characteristics of a good produced in a certain industry. For instance, consider a car industry. Each good can e treated as some characteristic of a car. The poor purchase main characteristics associated with a car, while the rich uy the same characteristics as the poor plus some additional luxury characteristics. That is, oth groups of consumers uy the same good ut of di erent quality. 3 y the valuation of a good, I mean the utility delivered to consumers from the consumption of one unit of this good. 4 Income heterogeneity in the model is introduced y assuming that consumers di er according to the e ciency units of laor they are endowed with. That is, the income distriution is exogenous and shaped y the relative income of the rich and the fraction of the rich. Hence, I focus only on the price e ect and do not explore the impact of trade lieralization on income distriution. 2

5 valuations serve only the rich. In this case, a rise in trade costs leads to that some exporting rms exit from oth foreign sumarkets. 5 This reduces the intensity of competition in the sumarkets and, therefore, drives up the prices. However, since exporting rms that exit from the sumarket for the necessities do not stop exporting, ut enter the sumarket for the luxury goods (increasing the intensity of competition in this sumarket), the prices of the luxuries rise y less than those of the necessities. This in turn implies that the rich lose relatively less from a rise in trade costs than the poor do. I nd that, depending on the parameters of the model, the rich can even gain from higher trade costs. In contrast, if trade costs are high enough, then exporting rms nd it pro tale to serve only the rich. Then, a rise in trade costs does not have a direct impact on the poor and, as a result, the rich lose relatively more. This paper is closely related to Fajgelaum et al. (2009), who develop a general equilirium model with nonhomothetic preferences for studying trade in vertically di erentiated products. Their framework also implies that trade lieralization can a ect welfare of di erent income groups di erently. However, the mechanism developed in their paper is ased on the home market e ect (à la Krugman (1980)), while the present paper provides another, possily complimentary, view, which is ased on the price e ect. Ramezzana (2000) and Foellmi et al. (2007) use the similar preference structure in a monopolistic competition framework to examine how similarities in per capita incomes a ect trade volumes etween countries. In these papers, consumers are assumed identical within a country and the impact of trade on relative welfare is not explored. Mitra and Trindade (2005) also consider a model of monopolistic competition with nonhomothetic preferences. However, they focus on the income e ect of trade lieralization rather than on the price e ect. The present paper also complements a road strand of literature that explores the role of supply-side factors in determining trade patterns. Markusen (1986) extends the Krugman type model of trade with monopolistic competition and di erences in endowments y adding nonhomothetic demand. He examines the role of per capita income in interindustry and intraindustry trade. Flam and Helpman (1987), Stokey (1991), and Matsuyama (2000) develop a Ricardian model of North-South trade with nonhomothetic preferences. They examine the 5 Some exporting rms that served all consumers start selling only to the rich, whereas some rms that served only the rich stop exporting at all. 3

6 impact of technological progress, population growth, and redistriution policy on the patterns of specialization and welfare. Stiora and Vaal (2005) extend the model in Matsuyama (2000) y studying the e ects of trade lieralization. They show that the South loses in terms of trade from unilateral trade lieralization, while the North may gain y lieralizing its trade. Fieler (2009) modi es a Ricardian framework à la Eaton and Kortum (2002) y introducing nonhomothetic preferences and technology distriution across sectors. This modi cation allows her to separate the e ects of per capita income and population size on trade volumes. The rest of the paper is organized as follows. Section 2 introduces the asic concepts for the closed economy case of the model. Section 3 extends the analysis to the open economy case and explores the e ects of trade lieralization on prices, market structure, and consumer welfare. Section 4 concludes. 2 Closed Economy The structure of the closed economy version of the model is adopted from Tarasov (2009). 2.1 Consumption In the model, all consumers have identical preferences that are represented y the following utility function: Z U = 2 ()x()d, where is the set of availale goods in the economy, () is the valuation of good, and x() 2 f0; 1g is the consumption of good. Note that goods are indivisile and consumers can purchase at most one unit of each good. To nd the optimal consumption undle, consumer i maximizes suject to her udget constraint Z U i = Z 2 2 ()x i ()d (1) p()x i ()d I i, (2) 4

7 where I i is the income of consumer i and p() is the price of good. This maximization prolem implies that x i () = 1 () () p() Q i, (3) where Q i is the Lagrange multiplier associated with the maximization prolem and represents the marginal utility of income of consumer i. In words, consumer i purchases good if and only if the valuation to price ratio () p() 2.2 Production of this good is su ciently high. The only factor of production in the economy is laor. There is free entry into the market. Each good is produced y a distinct rm. To enter the market, rms have to pay costs f e that are sunk. If a rm incurs the costs of entry, it otains a draw of the valuation of its good from the common distriution G() with the support on [0; ]. I assume that G 0 () = g() exists. This captures the idea that efore entry, rms do not know how well they will end up doing due to uncertainty in valuations of their products. Such di erences among goods generate ex-post heterogeneity across rms. Depending on the valuation drawn, rms choose whether to exit from the market or to stay. Firms that decide to stay engage in price competition with other rms. I assume that marginal cost of production is identical for all rms and is equal to c, i.e., it takes c units of laor (which are paid a wage of unity) to produce a unit of any good. In the paper, I limit the analysis to a framework with two types of consumers indexed y L and H. A consumer of type i 2 fl; Hg is endowed with I i units of laor where I H > I L. The fraction of consumers with income I H in the aggregate mass N of consumers is given y H. Then, the total laor supply in the economy is equal to N ( H I H + (1 H ) I L ). I assume that each consumer owns a alanced portfolio of shares of all rms producing the goods. Note that due to free entry, the total rm pro ts are equal to zero in the equilirium. This implies that the value of any alanced portfolio is equal to zero. Hence, the total income of consumer i is equal to her laor income I i. Using (3), the udget constraint in (2) can e rewritten as follows: Z : () p() Q i p()d = I i. 5

8 It is straightforward to see that given the prices and the valuations, the left hand side of the equation is decreasing in Q i. This suggests that the marginal utility of income is lower for richer consumers, i.e., Q H < Q L. Hence, the preferences considered in the paper imply that rich consumers purchase the same goods as the poor plus some others. That is, availale in the economy goods can e divided into two groups: the necessities include goods that are purchased y all consumers; the luxuries includes goods that are purchased only y the rich. As a result, the demand for good is given y 8 >< N, if () p() Q L, D(p()) = H N, if Q L > () p() >: Q H, 0, if () p() < Q L. (4) Taking Q L and Q H as given, rms maximize their pro ts () = (p() c)d(p()). (5). The following proposition holds. Proposition 1 Goods from the same group have the same valuation to price ratio in the equilirium. Proof. Suppose the opposite is true. Then, there exists some group, in which there are at least two goods with di erent () p() group, the rm producing the good with higher () p() ratios in the equilirium. Since oth goods elong to the same can raise its p() without a ecting the demand. This in turn would increase its pro ts contradicting the equilirium concept. A direct implication of Proposition 1 is that if good is purchased y all consumers in the equilirium, then its price is equal to () Q L. Indeed, a lower price would not a ect demand for the good and, therey, would reduce the pro ts, while a higher price would exclude the poor from purchasing. Similarly, if good elongs to the luxury goods, then it price is given y () Q H. Hence, if a rm with valuation () serves all consumers, its pro ts are given y () (p() c) N = Q L c N, 6

9 6 Figure 1: Pro t Functions ( Q L ( Q H c)n c) H N - 0 L M c H N cn while if the rm serves only the rich, its pro ts are given y () (p() c) H N = Q H c H N. In other words, to maximize their pro ts, rms choose etween selling to more people at a lower price and selling to fewer of them, ut at a higher price. In the equilirium, the price of good depends only on (). Therefore, hereafter I omit the notation of and consider prices as a function of. Let us denote M as the solution of the equation Q L c N = Q H c H N. (6) Then, Q L Q L c N c N < Q H Q H c H N; if M ; c H N; otherwise. Thus, if a rm draws M, then it is more pro tale for the rm to serve oth types of consumers. Otherwise, the rm serves only the rich or exits. Firms with valuation M are indi erent etween selling to all consumers or only to the rich (see Figure 1 ). In Figure 1, L is the exit cuto such that rms with valuations < L exit from the market ecause of negative 7

10 potential pro ts. 2.3 The Equilirium Let us denote M e as the mass of rms entering the market. One can think of M e as that there are M e g() di erent rms with a certain valuation. In the equilirium, two conditions should e satis ed. First, due to free entry, the expected pro ts of rms have to e equal to zero. Second, the goods market clears. De nition 1 o The equilirium in the model is de ned y n L, M, M e, fp()g L, fq i g i2fl;hg such that 1) Consumers solve the utility maximization prolem resulting in (3). 2) y setting the prices, rms maximize their pro ts. 3) The expected pro ts of rms are equal to zero. 4) The goods market clears. Further, I derive the equations that are su cient to descrie the equilirium in the model. Rememer that rms with valuation L have zero pro ts. This implies that Q H = L c. Using this expression for Q H and the equation (6), we can nd Q L as a function of L and M. Namely, the following lemma holds. Lemma 1 In the equilirium, 8 >< p() = >: 8 >< () = >: Q L Q H = c H L + (1 H) M ; if M, = c L ; if 2 [ L ; M ), H L + (1 H) M 1 cn; if M, L 1 c H N; if 2 [ L ; M ). Due to free entry, the ex-ante pro ts of the rms are equal to zero in the equilirium. This means that Z 0 (t)dg(t) = f e. 8

11 Using Lemma 1 and taking into account that rms with < L exit, the last equation is equivalent to where H(x) = G(x) + x f e cn + 1 = HH( L ) + (1 H )H( M ); (7) tdg(t) x. The goods market clearing condition implies that for any i 2 fl; Hg, Z 2 p()x i ()d = I i. Using the ndings in Lemma 1, it is straightforward to see that H I L = cm e + (1 Z H) tdg(t), (8) L M M I H I L = cm e L Z M Therefore, dividing the second line y the rst one, we otain L tdg(t). (9) R M L tdg(t) M tdg(t) = IH 1 H + L(1 H ) : (10) I L M Hence, given the parameters I H, I L, H, f e, c, N, and the distriution of draws G(), we can nd the endogenous variales M and L from the following system of equations: 6 8 >< >: R M L tdg(t) tdg(t) M = IH IL 1 H + L(1 H ) M f e cn + 1 = HH( L ) + (1 H )H( M )., (11) Note that if we know L and M, we can nd the equilirium value of Q L and Q H using Lemma 1. Furthermore, the mass of entrants into the industry producing the di erentiated good can e found from equation (8) or (9). 6 The existence and uniqueness of the equilirium are proved in Tarasov (2007). 9

12 3 Open Economy This section focuses on the open economy extension of the model descried aove. In particular, I develop a model of trade etween two symmetric countries. The notation in this section is the same as in the previous one. 3.1 Production and Exporting In the model, trade costs take the Samuelson s iceerg form and equal to. To simplify the analysis, I assume that there are no xed costs of trade. Since the countries are symmetric, it is su cient to descrie the equilirium conditions only for one country. As efore, I assume that there are two types of consumers. That is, given the preferences, goods are divided into two groups: the necessities and luxuries. The presence of trade costs implies that some rms nd it pro tale to serve only the domestic market, as exporting would lead to negative pro ts. Hence, a rm has three options: to exit, to serve only the domestic market, or to serve oth domestic and foreign markets. In the paper, I consider pricing-to-market. I assume that the markets are segmented and rms are ale to price discriminate etween domestic and foreign markets. Furthermore, it is not possile for any third party to uy a good in one country and then to resell it in the other to aritrage price di erences. Let us denote D () and F () as the pro ts of a rm with valuation from selling at home and aroad, respectively. Then, the total pro ts of a rm with are given y 8 >< 0; if the rm exits, () = D (); if the rm serves only the domestic market, >: D () + F (); if the rm serves oth the markets. (12) y analogy with the results in the previous section, rms with valuations 2 [ M ; ] serve all consumers at home, while rms with 2 [ L ; M ) serve only the rich. Therefore, the pro ts from selling at home are given y 8 >< D () = >: Q L Q H c N = H L + (1 H) M 1 cn; if M, c H N = L 1 c H N; if 2 [ L ; M ). (13) Similarly, as the countries are symmetric, it is straightforward to show (see Figure 2 ) that 10

13 Figure 2: Pro t Functions: Open Economy cn Home,,, cn F oreign 6 6 ( Q L c)n (,, Q L ( Q H c) H N,,, ( Q H - - 0,,, L M 0 L M c H N c H N,,, c)n c) H N 8 >< F () = >: Q L Q H c N = H L + (1 H) M c H N = L cn; if M, c H L; if 2 [ L ; M ). (14) Thus, rms with < L exit, rms with 2 [ L ; L ) serve only the domestic market, while rms with L serve oth domestic and foreign markets. In addition, as illustrated in Figure 3, domestic goods with valuations 2 [ M ; ] and imported goods with 2 [ M ; ] are purchased y all consumers and, therey, elong to the necessities, while domestic goods with 2 [ L ; M ) and imported goods with 2 [ L ; M ) elong to the luxury goods. Note that due to transport costs, there are goods that are availale to consumers of type i at home ut not availale to consumers of the same type aroad. In particular, goods with valuations 2 [ M ; M ) are sold to all consumers at home, ut exported only to the rich in a foreign country. Hence, the model provides an explanation why some imported goods are availale to the rich and not availale to the poor. Moreover, as it can e seen, if transport costs are su ciently high ( M in the equilirium), then imported goods are so expensive that only the rich can a ord purchasing them. 11

14 Figure 3: Consumption T he P oor M domestic M imported T he Rich L M domestic L M imported Prices and Aritrage Opportunities Let us denote p D () and p F () as the prices of goods with valuation sold at home and exported, respectively. Then, 8 >< p D () = >: 8 >< p F () = >: Q L Q L Q H Q H = c H L + (1 H) M ; if M, = c L ; if 2 [ L ; M ), = c H L + (1 H) M ; if M, = c L ; if 2 [ L ; M ). Hence, the prices of goods with su ciently high and low valuations are the same at home and aroad, i.e., p D () = p F (), implying that the f.o.. (15) (16) export prices of those goods (given y p F () ) are strictly less than the prices in the domestic market. 7 This is reminiscent of reciprocal dumping in Melitz and Ottawiano (2008). Note that the assumption aout the infeasiility of aritrage is a necessary ingredient of the model. In particular, for goods with 2 [ M ; M ), p D () and p F () are di erent with p F () > p D () and, therefore, it can e pro tale for a third party to ship those goods from one country to the other to aritrage the price di erence. Namely, the asence of aritrage 7 In the model, the prices are not directly a ected y the transport costs. The impact of on the equilirium prices goes through the e ects on L and M only. 12

15 opportunities is equivalent to p F () p D () p F (). (17) In our case, inequality (17) holds for goods with 2 [ L ; M )[[ M ; ] and does not necessarily hold for goods with 2 [ M ; M ). Speci cally, for any 2 [ M ; M ), Hence, the no-aritrage condition means that p D () p F () = H + L(1 H ). M H + L(1 H ) M 1 () L M 1 H (1 H ). (18) Later in the paper, I show that the ratio L M is increasing in in the equilirium. As 1 H (1 H ) is decreasing in, this implies that there exists such that for any, inequality (18) holds. Hence, aritrage opportunities are ruled out in the equilirium if and only if the transport costs are su ciently high The Equilirium As efore, the equilirium is characterized y the free entry and the goods market clearing conditions. The free entry condition means that in the equilirium, the ex-ante pro ts of rms are equal to zero. That is, f e = Z 0 (t)dg(t), where the function (t) is given y (12). Using the expressions for D () and F () (see (13) and (14)), the last equation can e rewritten as follows: where H(x) = G(x) + f e cn = H (H( L ) + H( L )) + (1 H ) (H( M ) + H( M )), x tdg(t) x. 8 Notice that lies in the interval 1 1; H. 13

16 The goods market clearing condition implies that 8 >< >: I H I L = M e M p D (t)dg(t) + R M p F (t)dg(t), I L = M e R M L p D (t)dg(t) + R M L p F (t)dg(t). (19) Using the expressions for the domestic and export prices derived in the previous section and dividing the second line y the rst one, we otain R M L tdg(t) + R M L tdg(t) M tdg(t) + M tdg(t) = IH 1 H + L(1 H ) : I L M Hence, y analogy with the closed economy case, the equilirium values of M and L can e found from the following system of equations: 8 >< >: R M L tdg(t)+ R M tdg(t) R L tdg(t)+ M tdg(t) M = IH IL 1 H + L(1 H ) M f e cn = H (H( L ) + H( L )) + (1 H ) (H( M ) + H( M )) : ; (20) The existence and the uniqueness of the equilirium can e proved in the same manner as in the closed economy case (see Tarasov (2009)). 3.3 Consumer Welfare efore analyzing comparative statics of the equilirium, I focus on consumer welfare. Recall that welfare of consumer i is given y Z U i = 2 ()x i ()d. Thus, welfare of consumers with income I L is equal to Z U L = M e M tdg(t) + tdg(t). M Meanwhile, the marker clearing conditions in (19) imply that M e = I L M p D (t)dg(t) + M p F (t)dg(t) : 14

17 Therefore, using the expressions for the prices, we otain that U L = I L Q L : Welfare of the poor naturally rises with an increase in either their income or the valuation to price ratio of goods they consume. Similarly, welfare of the rich is given y U H = I L Q L + (I H I L )Q H : As the rich consume the same undle of goods as the poor plus some others, welfare of the rich is equal to welfare of the poor plus additional welfare from the consumption of the luxury goods, which is in turn equal to income spent on those goods multiplied y their valuation to price ratio. The ndings aove suggest that relative welfare of the rich with respect to the poor is given y U H IH QH = U L I L Q L Note that all changes in the relative welfare are due to two e ects: the price and income e ects. The price e ect is determined y changes in Q H Q L, while the income e ect is determined y changes in I H IL. 3.4 Trade Lieralization and Relative Welfare This section focuses on the e ects of changes in transport costs on the relative welfare. To simplify the analysis and to avoid some amiguity in the results, I assume that the aggregate utility from the consumption of goods with a certain valuation given y M e g() does not decrease too fast in. Speci cally, I limit the analysis to the case when the distriution of draws G() is such that 2 g() is increasing and convex in. 9 This assumption also guarantees that the proaility of getting higher values of does not decrease too fast with. k, 9 For instance, the family of power distriutions with G() = k > 0, satis es this assumption. convexity of 2 g() is rather a technical condition, which sustantially simpli es some proofs. The 15

18 Recall that the relative welfare is given y U H IH QH = (21) U L I L Q L To understand etter the intuition ehind the e ects of on the relative welfare, I separately consider two sumarkets: the sumarket for the necessities and the sumarket for the luxuries. First, I consider the e ects of higher trade costs on the prices of the necessities. A rise in leads to that some exporting rms exit from the sumarket for the necessities and start selling only to the rich (i.e., M rises). This reduces the intensity of competition among rms that serve all consumers and, therefore, drives up the prices of the necessities. ecause of higher prices of the necessities, some domestic rms that served only the rich consumers nd it pro tale start selling to all consumers. This implies that the domestic cuto M decreases. Notice that we should also take into account changes in the mass of entrants M e and their e ects on the cuto s and the prices. In general, the impact of on M e is unclear. On the one hand, a rise in reduces the pro ts from exporting. On the other hand, higher can raise the pro ts from selling domestically due to lower competition. The overall e ect on the expected pro ts and, therefore, on M e is amiguous. However, I nd that the results claimed in the previous paragraph hold irrespective of changes in M e. Hence, the following lemma holds. Lemma 2 Higher transport costs raise the exporting cuto M, decrease the domestic cuto M, and lead to higher prices of the necessities. Proof. In the Appendix. Similarly, higher transport costs imply that some exporting rms exit from the sumarket for the luxuries (in fact, those rms stop exporting at all), implying that the exporting cuto L rises. In addition, as it was discussed aove, some domestic rms nd it more pro tale to serve all consumers ( M decreases). oth e ects reduce the intensity of competition in the sumarket, resulting in higher prices of the luxury goods and, therey, decreasing the exit cuto L. However, there is an additional e ect working in the opposite direction. Rememer that a rise in results in higher M (see Lemma 2 ). That is, some exporting rms that served all consumers efore start serving only the rich. This creates more competition in the sumarket for the luxuries and, therefore, negatively a ects the prices. Hence, we oserve two opposite 16

19 Figure 4: The Impact of on Consumption T he P oor M domestic M - imported M T he Rich L - domestic L - M - imported e ects of changes in on the prices of the luxury goods. I nd that, in general, the overall impact is unclear. For instance, in the extreme case when the fraction of the rich is close to zero and the income di erence etween the rich and the poor is su ciently high (there is a tiny minority of very rich consumers), the rich can even gain from higher transport costs ecause of lower prices of the luxuries. In other words, in very unequal societies trade lieralization can even harm the rich. The following lemma summarizes the ndings aove. Lemma 3 Higher transport costs raise the exporting cuto L and have an amiguous impact on the exit cuto L and, therey, on the prices of the luxury goods. However, in very unequal economies, where H is close to zero and I H IL of the luxuries and ene ts the rich. is su ciently high, a rise in can reduce the prices Proof. In the Appendix. Figure 4 illustrates the results formulated in Lemmas 1 and 2. As it can e seen from the lemmas, the poor always gain from trade lieralization, while the impact on the rich is unclear in general. Hence, we might expect that the reduction in transport costs ene t the poor more than the rich. Indeed, I show that for any parameters in the model, the ratio Q H Q L is increasing in. In words, higher transport costs increase the relative prices of the necessities with respect to those of the luxuries. This is ecause exporting rms that exit from the sumarket for the 17

20 necessities in fact enter the sumarket for the luxury goods inducing tougher competition. The following proposition holds. Proposition 2 The poor gain more from a decrease in than the rich do. Proof. In the Appendix. It should e emphasized that the results aove are ased on two key features of the model: non-homothetic preferences and monopolistic competition. Nonhomotheticity of preferences implies that di erent groups of consumers purchase di erent undles of goods. While monopolistic competition allows rms to choose what group of consumers to serve and what prices to set. Note that in traditional literature with homothetic preferences, ilateral trade lieralization has the same or no impact on prices set y rms, implying that trade lieralization is ene cial for all consumers. While in the present model, it is not necessarily the case. In very unequal economies, the rich consumers can even loose from trade lieralization due to higher prices of the luxury goods When the Transportation Costs are Su ciently High In the previous analysis, I assume that imported goods are purchased y oth the rich and poor consumers. That is, the transport costs are such that M in the equilirium. However, it is not necessarily the case. If the transport costs are so high that M >, then imported goods are purchased only y the rich. In this case, the equilirium equations can e written as follows: 8> < >: R M L tdg(t)+ L tdg(t) M tdg(t) = IH IL 1 H + L(1 H ) M f e cn H = H (H( L ) + H( L )) + (1 H )H( M ): If we consider this special case, then it is straightforward to see that trade lieralization ene ts the rich more than the poor. This is explained y the fact that changes in do not directly a ect poor consumers, as they purchase only domestic goods. Therefore, the following proposition holds. ; (22) Proposition 3 If is such that M > in the equilirium, then the rich gain more from trade lieralization than the poor do. 18

21 Figure 5: Relative Welfare U H UL 6 F ree T rade No T rade 1 M = L = - Proof. In the Appendix. Hence, summarizing the ndings in Propositions 1 and 2, we can see that the relative welfare has a hump shape as a function of transport costs. Moreover, if we assume that there are no trade costs, then the trade equilirium is equivalent to the equilirium in the closed economy when the mass of consumers is douled. Meanwhile, Tarasov (2009) shows that in the closed economy, a rise in the mass of consumers ene ts the rich more than the poor. Thus, we can conclude that opening a country to costless trade always ene ts the rich more. However, further trade lieralization can reduce welfare inequality. Figure 5 illustrates these ndings A Numerical Example This susection considers a numerical example that illustrates some of the results otained aove. For certain values of the parameters, I simulate the relationship etween consumer welfare and trade costs in equilirium. Speci cally, I assume that the distriution G(x) is uniform with the support on [0; 1] and fe cn higher as the poor do (meaning that I H IL = 1. In addition, I assume that the rich have income three times as = 3) and constitute a quarter of the total population (i.e., H = 0:25). Given the assumed values of the parameters, I solve for the equilirium values of L and M as is raised from 1 (free trade) to 12 (no trade). Figure 6 shows the simulated relationship etween consumer welfare and trade costs. As it can e seen, oth types of consumers gain from trade lieralization. Note that the poor are 19

22 slightly worse o when the economy just starts moving from the autarky to costly trade ( falls from 9:4 to 7:8). This can e explained y the free entry e ect. On the one hand, lower transport costs induce tougher competition, as domestic rms have to compete with their foreign counterparts. This positively a ects the well-eing of consumers in the economy. On the other hand, lower transport costs can reduce the rm s expected pro ts and, therey, decrease the mass of rms entering the market (see Figure 7 ). This in turn negatively a ects consumers. It appears that if the poor cannot a ord to uy foreign goods (i.e., the trade costs are su ciently high), then the latter e ect can prevail over the former one and, as a result, the poor can e worse o from trade lieralization. However, further trade lieralization raises the well-eing of the poor. Figure 7 illustrates the relationship etween the relative welfare and the trade costs. As it can e inferred from the gure, the relative welfare is rst increasing and then decreasing as a function of, which is consistent with the theoretical ndings otained in the previous sections (see Figure 5 ). In particular, moving from the autarky to free trade raises the relative welfare of the rich y 9%. Furthermore, if trade lieralization does not directly a ect the poor: i.e., imported goods are purchased only y the rich, then the relative welfare rises y 23%. This suggests that the impact of trade lieralization on relative welfare through the price e ect can e of considerale magnitude. 20

23 Figure 6: Consumer Welfare and Trade Costs 0.42 Welfare of The Poor vs.trade Costs 0.8 Welfare of The Rich vs.trade Costs trade costs trade costs Figure 7: The Mass of Entrants, Relative Welfare, and Trade Costs 1.05 The Mass of Entrants vs.trade Costs 2.2 Relative Welfare vs. Trade Costs trade costs trade costs 21

24 4 Concluding Remarks In this paper, I develop a tractale framework that enales us to analyze the impact of trade and trade costs on welfare inequality through the price e ect. One of the key elements of the model is nonhomothetic preferences that feature discrete choices (among horizontally di erentiated goods) y heterogenous in income consumers. Such preference structure implies that consumers rst uy goods that are relatively more essential in consumption and then move to less essential goods. Furthermore, the rich consumers uy the same undle of goods (the necessities) as the poor consumers plus some others (the luxuries). I then incorporate these preferences in the monopolistic competition model of trade à la Melitz and Ottawiano (2008). The presence of market power and nonhomothetic preferences lead to that prices set y rms are a ected y trade and trade costs. Moreover, the prices of di erent goods (necessities and luxuries) are a ected di erently, implying that trade lieralization can ene t some income classes more than others. In particular, I nd that if trade costs are such that imported goods are availale for all consumers, then trade lieralization ene ts the poor more. While if trades costs are so high that only the rich can a ord to uy imported goods, then the rich gain relatively more from trade lieralization. In other words, the relative welfare of the rich has a hump shape as a function of trade costs. The developed framework can e easily extended in at least two directions. First, it would not e di cult to consider a similar model of trade etween two countries with di erent income distriutions and to examine how this di erence a ects trade patterns and relative welfare. Secondly, it would e interesting to explore the case when income distriution is endogenous. This framework would allow for the oth income and price e ects and, therefore, could give us an idea aout the relative magnitude of the e ects. I leave these issues for future work. 22

25 References Deaton, A. and Muellauer, J. (1980), "Economics and Consumer ehavior," Camridge University Press. Eaton, J. and Kortum, S. (2002), "Technology, Geography, and Trade," Econometrica, 70, Fajgelaum, P., Grossman, G. and Helpman, E. (2009), "Income Distriution, Product Quality, and International Trade," mimeo. Fieler, A. (2009), "Non-Homotheticity and ilateral Trade: Evidence and a Quantitative Explanation," mimeo. Flam, H. and Helpman, E. (1987), "Vertical Product Di erentiation and North-South Trade," The American Economic Review, 77, Foellmi, R., Hepenstrick, C. and Zweimueller, J. (2007), "Income E ects in the Theory of Monopolistic Competition and Trade," mimeo. Golderg, P. and Pavcnik, N. (2007), "Distriutional E ects of Gloalization in Developing Countries," Journal of Economic Literature, 45, Hunter, L. and Markusen, J. (1988), "Per-capita Income as a Determinant of Trade," in R. Feenstra (ed.), Empirical Methods for International Trade, Camridge: MIT Press, Krugman, P. (1980), "Scale Economies, Product Di erentiation, and the Pattern of Trade," American Economic Review, 70(5), Markusen, J. (1986), "Explaining the Volume of Trade: An Eclectic Approach," The American Economic Review, 76, Matsuyama, K. (2000), "A Ricardian Model with a Continuum of Goods under Nonhomothetic Preferences: Demand Complementarities, Income Distriution, and North-South Trade," Journal of Political Economy, 108,

26 Melitz, M. and Ottaviano, G. (2008), "Market Size, Trade, and Productivity," Review of Economic Studies, 75(1), Mitra, D. and Trindade, V. (2005), "Inequality and Trade," Canadian Journal of Economics, 38, Murphy, K., Shleifer, A. and Vishny, R. (1989), "Income Distriution, Market Size, and Industrialization," Quarterly Journal of Economics, 104, Ramezzana, P. (2000), "Per Capita Income, Demand for Variety, and International Trade: Linder Reconsidered", CEP Discussion Paper DP0460. Stiora, J. and Vaal, A. (2005), "Trade Policy in a Ricardian Model with a Continuum of Goods under Nonhomothetic Preferences," Journal of Development Economics, 84, Stokey, N. (1991), "The Volume and Composition of Trade etween Rich and Poor Countries," Review of Economic Studies, 58, Tarasov, A. (2009), "Income Distriution, Market Structure, and Individual Welfare," The.E. Journal of Theoretical Economics (Contriutions), 9(1), Article

27 Appendix The algera in the Appendix is mainly ased on di erentiation of implicit functions. As the intuition of this exercise is straightforward, I only present the most important details and omit unnecessary ones. To simplify the notation in the Appendix, hereafter I assume that R y x means R y tdg(t). efore proceeding x to the proofs of the lemmas and the propositions, we consider the equilirium equations rewritten in the following way: J 1 H (H( L ) + H( L )) + (1 H ) (H( M ) + H( M )) cn Z M Z M J 2 I L (I H I L ) H + Z L(1 H ) M L + L f e Z + M M 1 = 0, (23) = 0; (24) and estalish some necessary relationships. Speci cally, using the equations in (23) and (24), it is straightforward to show that 10 M = (1 H ) 2 M Z Z + M M < 0, L = H 2 L Z Z + L L < 0, = H G( L ) + (1 H )G( M ) 1 < 0, L + L M + R L (1 H ) + I L 2 M M J 2 = I L M g( M ) + 2 g( M ) M J 2 = I L L g( L ) + 2 g( L ) (1 H ) I L L J 2 = I L 2 M g( M ) Finally, from (23) and (24), we have M L + L M + R 2 Lg( L ) M J1 M M J 2 M M R M L + R M L H + L(1 H ) > 0. + J1 L L + J1 + J2 L L = 0 + J2 = 0. M < 0, R M L + R M L H + L(1 H ) M > 0, Solving for M and L, we otain that M L = = J 2 J 2 L + J2 L M D D + J1 J 2 M, (25), (26) where Next, we proceed to the proof of Lemma Recall that y assumption, 2 g() is increasing in. D = M J 2 L J 2 M L > 0. 25

28 The Proof of Lemma 2 As it can e clearly seen from (25), M < 0. That is, higher decreases the domestic cuto M. Next, I show that higher transport costs raise the exporting cuto M. We have ( M ) 0 = M + M. Plugging the expression for M in (25), the derivative can e rewritten as follows: M D + J1 J 2 ( M ) 0 = L + J2 L. (27) D Since we know that D > 0, one only needs to determine the sign of the numerator in the last expression. Plugging the expression for D, we otain that the numerator is equal to Using the expressions for Ji L, M M J 2 J 2 M J 1 + J 1 J 2 L M L J i M, and Ji = (1 H ) H( M ) + J 2 M. M derived aove, we can show that M M M J 2 M = I L 2 2 Lg( L ) + 2 M g( M ) + (1 H G( L )) ; L + L M + M + L(1 H ) M Plugging the last expressions into the numerator and using the expressions for J1 L that the numerator is equal to I L (1 H ) M +I L 2 L g( L ) R M L +I L H 2 M g( M ) 2 L + R M L H + L(1 H ) M R M L + R M L H + L(1 H ) M and J2 L, we otain H L + (1 H) M + ( H H( L ) + (1 H )H( M ) 1) L M H L + (1 H) L M M + ( H H( L ) + (1 H )H( M ) 1) L + L 2 Rememer that H(x) = G(x) + M + M I L L g( L ) (1 H ) H( M ) + x x 1 for any x 2 [0; ]. This means that H H( L ) + (1 H )H( M ) 1 > 0: M M + (1 H G( L )).. 26

29 Furthermore, since L < M and 2 g() is increasing in, 2 M g( M ) > 2 L g( L). Finally, Therefore, the part of the numerator given y L + L M + M > 1. H 2 M I g( M ) L + R 2 L L 2 L M + R I L L g( L ) (1 H ) H( M ) + M + (1 H G( L )) M M 0 R > I L g( L ) L H L + R 1 L + (1 H ) H( M ) + (1 H G( L )) A L H = I L g( L ) L L + (1 H ) M + ( H H( L ) + (1 H )H( M ) 1) > 0. L M This implies that the numerator in (27) is positive and, therey, ( M ) 0 is positive. Finally, I show that the prices of the necessities given y c H L + (1 H) M increase with a rise in. Speci cally, I show that H L + (1 H) M is increasing in. We have M M Note that H + (1 0 H) L M = = H L 2 L (1 H ) 2 M (1 H ) M 2 M J 2 L H J 2 2 L M + J2 D H (1 H ) 2 L M 2 M L. H 2 L (1 H ) 2 M (1 H ) > 0 and M L J 2 L 2 M H 2 L J 2 M < 0. As J1 0 J2 < 0 and > 0, we can see that H L + (1 H) M > 0. This nishes the proof of Lemma 2. The Proof of Lemma 3 In this section, I show that L is increasing in, while the impact of on L is unclear. We have L D + ( L ) 0 = J2 M + J1 J 2 D M. (28) Hence, it is necessary to determine the sign of the numerator given y L D + J2 + J 1 J 2 = J 1 J 2 L J 2 + J 2 M M M L M L. L 27

30 Plugging the expressions for all partial derivatives, we can show that the numerator equals to I L L (1 H ) 2 M R M L + R M L H + L(1 H ) M +I L 2 M g( M ) L + L M + M I L (1 H ) M + R M + +I L M g( M ) 2 M L + L M + M (1 H ) M M (1 H ) M M 2 Lg( L ) H H( L ) + H + H + H Taking into account that ( M ) 2 g( M ) 2 M g( M ), we derive I L 2 M g( M ) +I L M g( M ) I L M g( M ) L + L M + M L + L M + M L + L M + +I L M g( M ) M L + L M + M (1 H ) M M L L + ((1 H )H( M ) + H H( L ) 1) L L + ((1 H )H( M ) + H H( L ) 1) L L (1 (1 H )G( M )) + H L L L + ((1 H )H( M ) + H H( L ) 1) H H( L ) + H (1 (1 H )G( M )) L (1 H ) M M H H( L ) + H L + H + ((1 H )H( M ) + H H( L ) 1) L L L (1 (1 H )G( M )) This implies that the numerator in (26) is positive and, therey, ( L ) 0 > 0. Next, I consider the derivative of L with respect to. Recall that J2 J 1 L = M D + J1 As D > 0, we only need to consider the sign of the numerator. After some simpli cations, we otain that the numerator is equal to I L (1 H ) 2 M 2 M g( M ) Z Z + L L J 2 M : 2 Lg( L ) Z Z + M M. > 0. I L + L L M + R (1 H G( L ) (1 H )G( M )) M g( M ) + 2 M g( M ) M I L L (1 H ) 2 M R M L + R M L H + L(1 H ) M (1 H G( L ) (1 H )G( M )). In general, the sign of the numerator can e either positive or negative. For instance, if H is close to 28

31 unity, then the numerator is approximately equal to I L + L L M + R (1 G( L )) M g( M ) + 2 M g( M ) < 0, M implying that L is decreasing in. However, in very extreme cases when I H IL is su ciently high and H is su ciently low, it is possile that the sign of the numerator is positive. Speci cally, Tarasov (2009) shows that all else equal, higher I H IL results in lower L and higher M. Hence, if we consider such I H IL that M is close to, the numerator would e approximately equal to I L (1 H ) 2 M 2 M g( M ) Z Z + L L 2 Lg( L ) Z H I L + L L (1 G( L )) M g( M ) + 2 M g( M ) M H I L L (1 H ) 2 M R M L + R M L H + L(1 H ) M (1 G( L )), which is positive for su ciently low H. This suggests that in economies with tiny minority of very rich consumers, higher transport costs can reduce the prices of the luxuries. Finally, I show that the impact of on welfare of the rich is unclear in general and in some extreme cases, the rich can even e etter o from higher transport costs. Recall that welfare of the rich is given y U H = I L Q L + (I H Therefore, after some simpli cations, where (U H ) 0 = I L P H J L P 2 = H I L )Q H = 1 c (1 H ) J 2 M 2 M L R M Plugging the expressions for Ji, J i M, and Ji L I L M + (I H L + (1 H I L ) L H) M + J2 (1 H ) 2 M L P H 2 2 L M cd H L + (1 H) M 2, (29) L + R M L M + M H + (1 H) L M. into (29), we can show that the sign of the numerator in. 29

32 (29) is the same as the sign of the following expression: ( H G( L ) + (1 H )G( M ) 1) M g( M ) + 2 M g( M ) P 2 H 2 L + ( H G( L ) + (1 H )G( M ) 1) L g( L ) + 2 L g( L ) (1 H ) + ( H G( L ) + (1 H )G( M ) 1) (1 H) 2 M + 2 M g( M ) R M L + R M L H + L(1 H ) M L + (1 H ) 2 R M L M + R 2 L Lg( L ) 3 M L M + R M L 2 M L + L M + M H P 2 + (1 H) L As it can e seen, the sign of the last expression is unclear in general. For instance, if H is close to unity or the incomes of the poor and the rich are close to each other (implying that L is close to M ), then the sign is negative. However, if H is su ciently low and the di erence etween the incomes of the poor and the rich is such that M is close to, then the sign can e positive. A numer of simulations I conduct for a wide range of parameters con rm these ndings.. M The Proof of Proposition 2 In this section, I focus on the relative welfare, which is given y U H IH QH IH = = H + (1 U L I L Q L I L H ) L. M Hence, to examine the sign of 0 UH U L, we need to determine the sign of 0 L M = L M 2 M M L. Algera shows that the sign of 0 L M is the same as the sign of J2 M + J 2 J2 J1 L M + J 1 L. M L M L Using the expressions for Ji, J i M, and Ji L, we derive J 2 M M + J 2 L L = I L 2 M g( M ) M g( M ) M M + L L = (1 H ) M + R M M H L + L M + R 2 Lg( L ) 2 2 Lg( L ) M L + R L L. 30

33 Thus, we need to examine the sign of I L 2 M g( M ) L + L M + R 2 Lg( L ) ( H G( L ) + (1 H )G( M ) 1) M 0 R +I L 2 M g( M ) (1 H) M + R M + M L + L M + R 2 Lg( L ) M I L (1 H G( L ) (1 H )G( M )) 2 M g( M ) L + L M + R 2 Lg( L ). M To show that the last expression is positive, it is su cient to show that 2 M g( M ) L + L M + M 2 Lg( L ) > 2 M g( M ) L + L M + R 2 Lg( L ) M H L + L L 1 A and (1 H ) M + R M H L + R L + > (1 + ) (1 H G( L ) (1 H )G( M )). M L The rst inequality follows from the assumption that 2 g() is increasing and convex. The second inequality is equivalent to ( H H( L ) + (1 H )H( M ) 1) + (1 H) M > 1 H G( L ) (1 H )G( M ), M + H L L which is always true, as H H( L ) + (1 H )H( M ) 1 > 0 and Hence, we show that L M (1 H ) M M The Proof of Proposition 3 + H L L > 1 H G( L ) (1 H )G( M ) > 1 H G( L ) (1 H )G( M ). is always increasing in. This nishes the proof. In this section, I consider the equilirium where imported goods are purchased only y the rich and show that in this case, the rich gain more from trade lieralization than the poor do. If transport costs are such that M in the equilirium, then the equilirium equations are given y 8 < : R M L tdg(t)+ L tdg(t) M tdg(t)) = IH I L 1 H + L(1 H ) M f e cn H = H (H( L ) + H( L )) + (1 H )H( M ): ; 31