metadata: authors: 0: author: Do,Quy-Toan
1: author: Levchenko,Andrei A.
count: World
docna: 0: docna: Trade policy and redistribution when
            preferences are non-homothetic
docty: Policy Research Working Paper
subtopic: Macro-Fiscal Policy,Economic Adjustment and Lending,Public Sector Economics,Trade Policy,International Trade and Trade Rules,Rules of Origin,Public Finance Decentralization and
            Poverty Reduction,Inequality,Trade and Multilateral Issues
teratopic: Poverty Reduction,International Economics and Trade
abstracts: cdata!: This paper compares redistribution
            through trade restrictions versus domestic lump-sum
            transfers. When preferences are non-homothetic, even
            domestic lump-sum transfers affect relative prices. Thus,
            contrary to the conventional wisdom, domestic lump-sum
            transfers are not necessarily superior to distortionary
            trade policy. The paper develops this argument in the
            context of the food export bans imposed by many developing
            countries in the late 2000s.
repnme: repnme: Trade policy and redistribution when
            preferences are non-homothetic
display_title: Trade policy and redistribution when
            preferences are non-homothetic
listing_relative_url: /research/2017/03/27266926/trade-policy-redistribution-preferences-non-homothetic
topicv3: Government Expenditure m1326649 1112,Poverty m1326687 695,Trade m1326924 698,Trade Policy and Integration m1327407 775,Trade Policy m1327640 776
publishtoextweb_dt: 2017-03-14T00:00:00Z
historic_topic: Poverty Reduction,International Economics and Trade
no_of_pages: 16
author_keys: 0: author_key: 433894
1: author_key: 1132316
model_extractions: WPS8005 Policy Research Working Paper 8005 Trade Policy and Redistribution When Preferences Are Non-Homothetic _Quy-Toan Do Andrei A. Levchenko_ Development Research Group Poverty and Inequality Team March 2017
Policy Research Working Paper 8005

# **Abstract**

This paper compares redistribution through trade restrictions versus domestic lump-sum transfers. When preferences are non-homothetic, even domestic lump-sum transfers affect relative prices. Thus, contrary to the conventional wisdom, domestic lump-sum transfers are not necessarily superior to distortionary trade policy. The paper develops this argument in the context of the food export bans imposed by many developing countries in the late 2000s.

This paper is a product of the Poverty and Inequality Team, Development Research Group. It is part of a larger effort by the World Bank to provide open access to its research and make a contribution to development policy discussions around the world. Policy Research Working Papers are also posted on the Web at http://econ.worldbank.org. The authors may be contacted at abonfield@worldbank.org.

> _The Policy Research Working Paper Series disseminates the findings of work in progress to encourage the exchange of ideas about development issues. An objective of the series is to get the findings out quickly, even if the presentations are less than fully polished. The papers carry the names of the authors and should be cited accordingly. The findings, interpretations, and conclusions expressed in this paper are entirely those of the authors. They do not necessarily represent the views of the International Bank for Reconstruction and Development/World Bank and its affiliated organizations, or those of the Executive Directors of the World Bank or the governments they represent._

Produced by the Research Support Team
# Trade Policy and Redistribution When Preferences Are Non-Homothetic

Quy-Toan Do<sup>_∗_</sup> Andrei A. Levchenko<sup>_†_</sup> _Keywords:_ trade restrictions, redistribution, non-homothetic preferences. _JEL Codes:_ F13, Q17, O24

> _∗_ World Bank (qdo@worldbank.org).

> _†_ University of Michigan, NBER, and CEPR (alev@umich.edu).
# **1 Introduction**

Should restrictive trade policy be used as a means of redistribution within a country? Conventional wisdom in trade policy analysis offers an unequivocal “no” answer. The reason is that trade policy distorts prices and thus generates misallocation of resources. According to this line of reasoning purely domestic redistribution policies, ideally in the form of lump-sum transfers, are superior to trade restrictions as they generate fewer or no distortions, either domestically or internationally.

This paper shows that the presence of non-homothetic preferences importantly qualifies or even erases the superiority of domestic redistribution over trade restrictions. This is because under non-homothetic preferences, even lump-sum transfers between individuals/groups with different income elasticities of consumption have an impact on prices, making them more similar to the distortionary trade restrictions.

We develop this argument in the context of the food export bans that were imposed by a number of developing countries during the last commodity price boom. Sharma (2011) estimates that 33 countries imposed some forms of export restrictions on grains and other food commodities between 2007 and 2011. These policies met strong resistance from the international community. Then World Bank president Robert Zoellick urged countries “to remove export bans and restrictions. These controls encourage hoarding, drive up prices, and hurt the poorest people around the world who are struggling to feed themselves.”<sup>1</sup> A few years later, then U.S. Secretary of State Hillary Clinton issued a similar call: “[s]ome policies that countries enacted with the hope of mitigating the crisis, such as export bans on rice, only made matters worse. (...) And that sounder approach includes (...) abstaining from export bans no matter how attractive they may appear to be, using export quotas and taxes sparingly if at all (...).”<sup>2</sup> At first glance this setting should be a textbook application of the conventional wisdom. The trade policy implemented by these countries was an export quota, widely considered the least efficient type of trade restriction. While the redistributionary objective of these export bans was widely recognized in the global policy making circles, these countries were advised to achieve that objective by means of domestic policies. Our analysis will consider the best kind of domestic policy, namely a lump-sum transfer.

In our model, there are _N_ countries, two commodities, Food and Garments, and two types of

> 12008 High-Level Conference on World Food Security: http://go.worldbank.org/BUEP7C3NC0 2http://www.state.gov/secretary/rm/2011/05/162795.htm

2
individuals, rich and poor. Preferences are Stone-Geary in Food and Garments, with a minimum Food consumption requirement. We analyze the case in which the poor consume only Food, and compare the effects of two policies in an individual country. The first is a binding Food export quota, corresponding to the Food export bans implemented in many developing countries. The second is a lump-sum redistribution policy from the rich to the poor. When preferences are homothetic, it is immediate that a lump-sum transfer achieves the government’s redistributionary objective without distorting the world market for Food. Thus, the first-best outcome obtains.

However, under non-homothetic preferences, even lump-sum redistribution affects prices. Because the poor have a higher propensity to consume Food than the rich – indeed, in the case we analyze all of their extra income goes to Food consumption – a transfer of one dollar of income from the rich to the poor increases demand for Food, and therefore the Food price. Thus this purely domestic lump-sum transfer has, at least qualitatively, a similar effect on the price of Food as the export quota. In the limit, as non-homotheticity becomes extreme – that is, the income elasticity of Food consumption of the rich goes to zero while the poor continue consuming only Food – the domestic lump-sum redistribution policy converges to the export ban in its effect on the global Food price.

Our paper makes contact with two literatures. The first is the older debate on how trade policy compares to other policy instruments (Haberler 1950, Hagen 1958, Bhagwati and Ramaswami 1963, Corden 1974). The main thrust of this literature is that trade restrictions are not normally the most efficient way to achieve a given policy objective. We show that this conclusion must be qualified if preferences are non-homothetic. Epifani and Gancia (2009) show that countries have an incentive to increase the size of government as doing so improves the country’s terms of trade. Because government expenditure is mainly on non-tradeables, increasing it pulls labor out of the tradeable sector, reducing export supply and thus raising the prices of the country’s exports. Ours is a qualitatively different mechanism, as it does not rely on non-tradeability of governmentprovided goods, or indeed on the existence of the government expenditure on goods or services. The policy we consider is a pure lump-sum transfer.

The second is the line of research on trade policy in the presence of preference non-homotheticity. While a number of recent influential papers model non-homothetic preferences and the impact of trade opening on agents at the different points on the income distribution (Fajgelbaum, Grossman and Helpman 2011, Fajgelbaum and Khandelwal 2016), there is comparatively less theoretical or empirical work on trade policy in particular. Porto (2006) and and Faber (2014) analyze the dis3
tributional impact of individual trade agreements. Gresser (2002) documents that in the United States, tariffs are strongly anti-poor. None of these papers compare tariff reductions to alternative policies to benefit the poor. Most closely related to ours is the paper by Glazer and Ranjan (2007), who develop a theoretical framework in which an import tariff lowers the poor’s marginal utility of income and makes redistribution to them less efficient, a different interaction between trade policy and redistribution than the one we consider here. The rest of the paper is organized as follows. Section 2 presents the model and derives the main results. Section 3 concludes.

# **2 Baseline model**

## **2.1 Preliminaries**

Consider an endowment economy with two goods – Food and Garments – and _N_ equal-sized countries that trade with one another. Country _c_ has an endowment profile (Φ _c,_ Γ _c_ ) of Food and Garments, respectively. Each country is populated with two types of agents: the rich and the poor, who are assumed to be in equal number. The poor have endowment ( _λc_ Φ _, λc_ Γ) while the rich own the remaining ((1 _− λc_ ) Φ _,_ (1 _− λc_ ) Γ). Agents have non-homothetic preferences and we assume they are of the Stone-Geary form: where _f_ and _g_ are respectively the amounts of Food and Garments consumed by an individual in country _c_ and _φc_ is the minimum level of Food consumption to be met before households diversify and consume other goods.<sup>3</sup> Stone-Geary preferences imply that agents with income below a given threshold will spend it all on Food, while agents with income above will also consume Garments. Trading of Garments and Food takes place on a spot market. Denote by _pc_ and _qc_ the prices of Food and Garments in country _c_ . Trade is free of physical impediments but may be restricted by policy. Without loss of generality, we henceforth consider policies in country _c_ = 1, and restrict the analysis to the case in which only this country implements a policy.

The two available policies are a lump-sum redistribution scheme and an export quota. Denote by _τ_ 1 a lump-sum transfer from the rich to the poor in country _c_ = 1. Without loss of generality,

> 3From an empirical perspective, the higher propensity of the poor to consume food is referred to as Engel’s law and has ample empirical support; see e.g. Houthakker (1957).

4
assume that transfers are made in units of Food. The stated objective of trade insulation practices is to protect domestic net Food consumers from high international Food prices. The second policy we thus consider is a Food export quota _X_<sup> ̇</sup> 1 in country 1.

_i_ = _{rich,poor}_ An **equilibrium** of the world exchange economy is a set of consumption allocations � _Fc_<sup>_i, Gi_</sup> _c_ � _c_ =1 _,...N_ and relative prices _{pc, qc}c_ =1 _,...N_ such that (i) agents maximize their utility, and (ii) markets clear.

# **2.2 Laissez-faire equilibrium**

As there are no trade costs, the laissez-faire equilibrium prices for Food and Garments are the same for every country and denoted by ( ̄ _p,_ ̄ _q_ ). The poor dedicate their entire endowment ( _λc_ Φ _c, λc_ Γ _c_ ) to Food consumption, while the rich spend a fraction _αc_ of their adjusted income on Food. Denoting _μc_ = _λc_ + _αc_ (1 _− λc_ ), we can write aggregate Food consumption in country _c_ as Global market clearing conditions pin down equilibrium prices. Without policy interventions, the equilibrium price is: Prices are the usual preference-weighted ratio of aggregate endowments adjusted for the StoneGeary parameters.

Since we restrict the analysis to policies aimed at protecting the poor (and resulting in an increase in Food consumption by the poor), _p_<sup>_<u>q</u>_</sup> ̄<sup> ̄willbetheupper-boundforinternationalprices,</sup> while one lower-bound, which we denote _p_<sup>_<u>q</u>_</sup> ̄<sup> ̄minmin,correspondstothecasewherecountry</sup><sup>_c_=1</sup> consumes food only ( _α_ 1 = 1), i.e.

To ensure that throughout the analysis, the property that the poor in every country only consume Food, while the rich diversify their consumption, it is sufficient to ensure that for every _c_ , To that end, we make the following assumption, which we will henceforth refer to as the _Stone-_ 5
_Geary conditions_ :

**A1: Stone-Geary conditions.** For every country _c_ ,

Note that prices are functions of _λc_ , so we need to verify that the set of parameters _λc_ that satisfy (4) is not empty. To see this, note that the first argument in the bracket is positive, and (3) implies that the second also is for every value of _λc_ .

Finally, the level of Food exports by country _c_ under the laissez-faire equilibrium is given by

# **2.3 Trade insulation**

Now consider a binding export quota _X_<sup> ̇</sup> 1 _< X_<sup> ̄</sup> 1, where _X_<sup> ̄</sup> 1 is the laissez-faire level of exports from country 1. In the trade insulation equilibrium, prices in country 1 will now differ from prices in every other country in the world. The equilibrium thus features a set of two prices � _<u>pq</u>_ ̇ ̇11(( _XX_<sup> ̇ ̇</sup> 11))<sup>_,_</sup><sup>_<u>p</u>_</sup> _q_ ̈<sup> ̈</sup> (<sup><u>(</u></sup> _X_<sup>_X_ ̇ ̇</sup> 1<sup>1</sup> )<sup><u>)</u></sup> �, where _<u>pq</u>_ ̇ ̇11(( _XX_<sup> ̇ ̇</sup> 11))<sup>isthedomesticrelativepriceofFoodincountry</sup><sup>_c_=1and</sup><sup>_<u>p</u>_</sup> _q_<sup> ̈</sup> ̈<sup>istheinternational</sup> relative price of Food. Assuming that export quota _X_<sup> ̇</sup> 1 applies uniformly, country _c_ = 1 derives its income from selling _X_<sup> ̇</sup> 1 units of Food at international price<sup>_<u>p</u>_</sup> _q_<sup> ̈</sup> ̈(<sup><u>(</u></sup> _X_<sup>_X_ ̇ ̇</sup> 1<sup>1</sup> )<sup><u>)</u>and the remainder, Φ1</sup><sup>_−X_ ̇1 at</sup> domestic price<sup>_<u>p</u>_</sup> _q_<sup> ̇</sup> ̇1<sup>1</sup> (<sup><u>(</u></sup> _X_<sup>_X_ ̇ ̇</sup> 1<sup>1</sup> )<sup><u>)</u>.</sup> Aggregate consumption of Food in country _c_ = 1 is thus Other countries face international price _p_<sup>_<u>q</u>_ ̈</sup> ̈<sup><u>(</u></sup> (<sup>_X_</sup> _X_<sup> ̇ ̇1</sup> 1<sup><u>)</u></sup> )<sup>and consume</sup> 6
**International prices** International prices clear the international market for Food, i.e.

which can be solved to derive the expression for the relative price: where _γ_ 1 measures the relative size of country 1 with respect to the rest of the world, i.e.

Similarly, we define in order to express (6) as The function _θ_<sup> ̈</sup> ( _._ ) is decreasing in _X_ : as export restrictions are lifted, the upward pressure on Food prices is released. Naturally, when _X_<sup> ̇</sup> 1 = _X_<sup> ̄</sup> 1, the export restriction no longer binds and _θ_<sup> ̈</sup> ( _X_<sup> ̄</sup> 1) = 0.

**Domestic prices** The domestic market clearing condition on the other hand is given by

which after rearranging becomes where Conversely, the function _θ_<sup> ̇</sup> 1( _._ ) is decreasing: the domestic price of Food increases as more Food is being exported. We summarize these results in Proposition 1 below; the proof is in the appendix.

7
**Proposition 1: Trade insulation equilibrium** Suppose that assumption A1 holds. There exists an export quota _X_<sup> ̇</sup> 1<sup>_m_</sup> _< X_  ̄1, such that for any quota _X_  ̇ 1 _> X_  ̇ 1<sup>_m_,theequilibriumpricesofthe</sup> economy are characterized by (9) and (11) _._ ■

The implication of Proposition 1 is that by imposing an export quota on Food, country 1 improves its terms of trade, negatively affecting its average trading partner. By lowering the domestic price of Food, an export quota _X_<sup> ̇</sup> 1 benefits the poor in country _c_ = 1. However, it is accompanied by increased international prices as reflected in (9). This effect is behind the significant amount of opposition to export bans outside of the countries imposing them. We next demonstrate that in the presence of non-homothetic demand, even purely domestic lump-sum transfers have a similar effect.

# **2.4 Redistribution**

Since domestic lump-sum transfers do not impede international exchange, in the equilibrium with only domestic redistribution the prices are equalized in all countries. We denote the equilibrium world price ratio by<sup>_<u>p</u>_</sup> _q_<sup>ˆ</sup> ˆ(<sup><u>(</u></sup> _τ_<sup>_τ_</sup> 1<sup>1</sup> )<sup><u>)</u>,indexingitexplicitlybytheamountofredistribution.Equilibrium</sup> consumption of Food in country _c_ = 1 is given by Redistributing resources from the rich to the poor induces income to be transferred from agents with a low propensity to consume Food towards agents with a high propensity to do so. Aggregate Food consumption in country _c_ = 1 hence increases.

In other countries, consumption remains equal to Equalizing aggregate consumption and aggregate endowment yields As above, we define 8
which is increasing with _τ_ ; we can rewrite (13) as We summarize the results in the Proposition below, the proof is in the appendix:

**Proposition 2: Domestic redistribution equilibrium** When the Stone-Geary conditions hold, there exists a positive _τ_ 1<sup>_m_,suchthatanyredistribution</sup><sup>_τ_1</sup><sup>_∈_(0</sup><sup>_, τ_</sup> 1<sup>_m_)fromtherichtothepoorin</sup> country _c_ = 1 leads to an equilibrium relative price characterized by (15). ■

A redistributive domestic policy has international price implications when preferences are non-homothetic. In equilibrium domestic redistribution _τ_ 1 leads to higher Food prices as the size of the transfer from the rich to the poor increases. Thus, this policy also improves country 1’s terms of trade as long as it is a net exporter of Food.

# **2.5 Trade insulation as redistribution**

To compare the effect of lump-sum transfers and export quotas on the world relative price of Food, let’s consider a redistribution policy _τ_ 1 and choose a level of export quota _X_<sup> ̇</sup> 1 that keeps the poor in country _c_ at an identical welfare level. Export quota _X_<sup> ̇</sup> 1 will henceforth be said to be the _pro-poorequivalent_ of the social protection policy _τ_ 1: the values _X_<sup> ̇</sup> 1 and _τ_ 1 are characterized by equal welfare levels of the poor. Thus, choosing _τ_ 1 low enough so that the characterization of the equilibrium in Proposition 2 holds implies that its pro-poor-equivalent export quota _X_<sup> ̇</sup> 1 is also sufficiently large for the equilibrium to be properly characterized by Proposition 1. Thus, _F_<sup> ̇</sup> 1( _X_<sup> ̇</sup> 1) = _F_<sup>ˆ</sup> 1( _τ_ 1) implies where _θ_<sup> ̇</sup> 1( _._ ) and _θ_<sup> ̈</sup> ( _._ ) are defined by (12) and (8), respectively. Both left-hand and right-hand sides of equation (16) are strictly increasing in their respective arguments, which implies a one-to-one correspondence between _τ_ and _X_<sup> ̇</sup> .

Next we want to compare the price implications of using export quotas in lieu of redistribution in order to assess the inefficiencies of export restrictions. Let’s consider _τ_ a redistribution parameter in country _c_ = 1 and _X_ its pro-poor-equivalent export quota. The world Food price difference 9
between the redistribution and the export quota equilibria is: We can thus linearize (16) and establish the following proposition:

**Proposition 3: Distortions from trade insulation** For large _N_ and for any redistribution _τ_ 1 _< τ_ 1<sup>_m_</sup> adopted in country _c_ = 1, its pro-poor-equivalent export restriction _X_<sup> ̇</sup> 1 will generate increased Food prices such that

# ■

Export quotas distort prices, which induces the rich in country _c_ = 1 to over-consume Food. Export quotas could thus be viewed as a poorly targeted social transfer program that leads to negative terms-of-trade effects for the rest of the world. To further inform the comparison between lump-sum redistribution and export quotas, we next show that export-quota-related distortions vanish as preference for Food among the rich goes to zero.

**Proposition 4: Trade insulation as redistribution** Consider a sequence of economies indexed by _n ≥_ 1, where _{α_ 1<sup>_n}_characterizesconsumerpreferencesincountry</sup><sup>_c_=1.Denoteby</sup><sup>_{_∆</sup><sup>_n_(</sup><sup>_τ_)</sup><sup>_}_</sup> the associated price distortions induced by an export quota pro-poor equivalent to redistribution _τ_ . If lim _n→∞ α_ 1<sup>_n_= 0, then for every</sup><sup>_τ_, lim</sup><sup>_n→∞_∆</sup><sup>_n_(</sup><sup>_τ_) = 0.■</sup>

As _n_ increases, consumption patterns in country _c_ = 1 become fully polarized: the poor consume Food only and the rich consume Garments only (except for the minimum required _φc_ ), so that an export quota becomes akin to a lump-sum transfer from the rich to the poor. The substitution effect no longer operates: when _α_ goes to zero, domestic demand for Food becomes price inelastic. There is no longer any distortion because the rich do not increase their consumption of Food when domestic prices drop. Put another way, the distortion created by an export quota is lower when the commodity being targeted for export quotas is an inferior good, the demand for which has higher income elasticity.

For the rest of the world, we have just shown that redistribution is always preferred to the export ban by country 1, as it worsens its terms of trade by less. For country 1 which of these policies is preferred is ambiguous, as it trades off the greater terms of trade improvement under the export 10
ban against the deadweight loss of a distorting policy. We can show that a small country ( _N →∞_ ) will always prefer redistribution, as the terms-of-trade effect is zero in that case. But when the country is not small, the comparison between an export quota and redistribution is ambiguous. A fuller evaluation of this tradeoff should also acknowledge that both policies likely involve substantial additional frictions, such as rent-seeking to capture export quota rents (Krueger 1974), as well as inefficiencies and leakages that plague domestic redistribution schemes (see e.g. Murgai, Ravallion and van de Walle 2013).

# **3 Conclusion**

When preferences are non-homothetic, even lump-sum redistribution will affect equilibrium prices. We explore the trade consequences of this phenomenon, in the context of food export bans introduced by developing countries during the last commodity price boom. Export bans indeed raise the world price of food and improve the export-banning countries’ terms of trade. What has been underappreciated is that in this context, even purely domestic redistribution policies might have a qualitatively similar effect. The terms-of-trade improvement under domestic lump-sum redistribution is in the limit as large as under export quotas.

# **References**

**Bhagwati, Jagdish and Vangal K Ramaswami** , “Domestic distortions, tariffs and the theory of optimum subsidy,” _Journal of Political Economy_ , 1963, _71_ (1), 44–50.

**Corden, W Max** , _Trade policy and economic welfare_ , London: Oxford University Press, 1974.

- **Epifani, Paolo and Gino Gancia** , “Openness, Government Size and the Terms of Trade,” _The Review of Economic Studies_ , 2009, _76_ (2), 629–668.

- **Faber, Benjamin** , “Trade liberalization, the price of quality, and inequality: Evidence from Mexican store prices,” 2014.

- **Fajgelbaum, Pablo D and Amit K Khandelwal** , “Measuring the unequal gains from trade,” _The Quarterly Journal of Economics_ , August 2016, _131_ (3), 1113–1180.

- **Fajgelbaum, Pablo, Gene M. Grossman, and Elhanan Helpman** , “Income Distribution, Product Quality, and International Trade,” _Journal of Political Economy_ , 2011, _119_ (4), 721 – 765.

11
- **Glazer, Amihai and Priya Ranjan** , “Trade protection to reduce redistribution,” _European Journal of Political Economy_ , 2007, _23_ (3), 790–805.

- **Gresser, Edward** , “Toughest on the Poor: America’s Flawed Tariff System,” _Foreign Affairs_ , November/December 2002, _81_ (6), 9–14.

- **Haberler, Gottfried** , “Some Problems in the Pure Theory of International Trade,” _Economic Journal_ , 1950, _60_ , 223–240.

- **Hagen, Everett** , “An Economic Justification of Protectionism,” _Quarterly Journal of Economics_ , 1958, _72_ , 496–514.

- **Houthakker, H. S.** , “An International Comparison of Household Expenditure Patterns, Commemorating the Centenary of Engel’s Law,” _Econometrica_ , 1957, _25_ (4), 532–551.

- **Krueger, Anne O.** , “The Political Economy of the Rent-Seeking Society,” _The American Economic Review_ , 1974, _64_ (3), 291–303.

- **Murgai, Rinku, Martin Ravallion, and Dominique van de Walle** , “Is Workfare Cost-Effective against Poverty in a Poor Labor-Surplus Economy?,” Policy Research Working Paper 6673, The World Bank, Washington D.C. October 2013.

- **Porto, Guido G** , “Using survey data to assess the distributional effects of trade policy,” _Journal of International Economics_ , 2006, _70_ (1), 140–160.

- **Sharma, Ramesh** , “Food Export Restrictions: Review of the 2007-2011 Experience and Considerations for Disciplining Restrictive Measures,” FAO Commodity and Trade Policy Research Working Paper 32, Food and Agriculture Organization May 2011.

# **A Appendix: Proofs of Propositions**

## **A.1 Proof of Proposition 1**

We have left to find the conditions such that in every country, the poor do not consume any Garments, while the rich consume both. First, note that aggregate income in country _c_ = 1 is given by _p_ ̇( _X_<sup> ̇</sup> 1)(Φ1 _− X_<sup> ̇</sup> 1) + _p_ ̈( _X_<sup> ̇</sup> 1) _X_<sup> ̇</sup> 1 + _q_ ̇( _X_<sup> ̇</sup> 1)Γ1 . � � 12
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