TX of the parameters generating a “trembling trade” in the set of all the parameters for
8
TX is open, so ( , , , , , )g h x y a bˆ ˆ TX also holds true for each ( , )g hˆ ˆ that belongs to a sufficiently close neighborhood of ( , )g h in 2.
19
which trade is quadruply gainful, namely 2 X? The results presented thus far are existential in nature: while we showed that such a set is open and, therefore, the phenomenon of a quadruply gainful trembling trade is not singular, it is possible that this open set is so small that its real-life applications are limited. In particular, it seems possible that a trembling trade may occur only from small gains from trade, and only for utility functions in which a major part of value arises from the disutility of low relative income. In general, such a problem has no clear solution: we do not have a natural, well-defined measure on the space of parameters so that even the formal definition of the problem is unclear. Fixing utility functions and considering the size of the set of vectors ( , , , ) [0,x y a b M]4n generating a “trembling trade” will provide us with different results, depending on the choice of utility functions.
Having said that, it is helpful to refer again to the example presented in Section 2 in order to somewhat dispel the doubts. Trade in that example is quadruply gainful and is trembling, and the gains from trade are far from tiny: the income of every individual increases by at least 8.3% (in the case of the richest individual), the income of the poorest individual increases by 200%. At the same time, according to our calculations, more than 20% of the space of utility functions satisfying (13) (measured by the parameter ) guarantees that trade is trembling. Thus, we conclude that the set TX does not have to be very small.
5. Conclusion
Trade that increases the incomes of the members of the trading populations and reduces the income gaps between and within populations can intuitively be considered to be gainful. However, we showed that even under very favorable assumptions as given by a quadruply gainful trade, it is possible that when trade occurs global social welfare may not improve. Acknowledging that individuals take into consideration not only the comfort of absolute income but also the discomfort of low relative income, we noted that the dismay brought about from expansion of the social space of the members of the trading populations can override the gains from trade. This finding could help explain anti-trade sentiments among populations that engage in a seemingly advantageous trade. For example, Nguyen (2015) argues that concern for inequality is an important factor of the
20
decreasing support for liberal trade policies in the American public, and that, in general, individuals who are more concerned about income inequality are more likely to support protectionist measures. Burgoon (2013) finds that income inequalities encourage support for political parties with protectionist and anti-globalist agendas in OECD countries.
Consequently, as Marktanner and Sayour (2009) show, countries characterized by higher levels of income inequality are less likely to liberalize trade as they perceive trade to exacerbate inequality. Distaste for low relative income may also be a reason why Scheve and Slaughter (2006) find that anti-trade sentiments are stronger in countries with higher unemployment rates. On the other hand, in developing countries (for example, in the Philippines, as pointed out by Pasadilla and Liao, 2005), even the wealthiest may be concerned about income comparisons with potential trade partners abroad and, therefore, they oppose unrestricted trade.
Our analysis bears significantly on policy design because it implies that often-prescribed policy recommendations aimed at redressing a downside of trade can well fall short. To see this vividly, we refer to a May 2018 interview of the Economist magazine with John Van Reenen of MIT.9 When asked “What are the downsides of free trade?” he replied as follows: “There are well-known downsides. The way I like to think about it is that free trade increases the size of the pie. The overall amount of material wellbeing expands. But just because the size of the pie expands, it doesn’t mean that everyone is better off. There are going to be some losers whose slice of the pie is so much smaller that they would have been better off with less trade. However, because the overall size of the pie has got bigger, the government can compensate the losers which can still make everyone better off.” This response is telling because it implies that when trade occurs, everyone’s income will increase - if not directly because of trade then indirectly because of a governmental redistribution of the higher aggregate income conferred by trade - social welfare will rise. The approach taken in this paper does not share this perception:
higher incomes of all members of the trading economies do not necessarily translate into a global welfare gain. Interestingly, in another part of the interview John Van Reenen intimates that “With free trade, you come into more contact with . . . new people.” We
9 https://www.economist.com/open-future/2018/05/04/a-healthy-re-examination-of-free-trades-benefits-and-shocks
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showed that when this consequence is weighed in the calculus of the gains from trade, trade can be trembling.
In closing, it is tempting to ponder what the social welfare fallout would be from a situation in which a relatively poor economy that geographically neighbors a richer economy but trade-wise is detached from the richer economy, embarks on full blown trade with the richer economy. The perspective elaborated in this paper can serve as a warning sign of a possible adverse outcome.
22 Appendix: Proofs of Lemmas 1-4
Proof of Lemma 1.
From Stark (2013, Claim 1), we know that if two populations merge while the incomes of their members remain unchanged, then the sum of the post-merger levels of relative deprivation of the individuals who belong to these populations is not lower than the sum of the pre-merger levels of relative deprivation of the same individuals. Thus, for inequality (8) to hold strictly, we only need to prove that equality does not occur if x y. To this end we assume that z=(z1,z2,,z2n) is an ordered vector of incomes of population P1P2 (namely the sequence z consists of elements of the sequences x and y in an ascending order). For k {1, , 2 },n we define h kx( ) as the number of individuals in population P1 whose incomes are less than or equal to zk, and we define
y( )
h k as the number of individuals in population P2 whose incomes are less than or equal to zk.
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which is equivalent to stating that1 1 can rewrite the formula of function presented in (7) as follows:
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Because the functions g, h, and RD are continuous, is also continuous. Q.E.D.
Proof of Lemma 3.
We fix g, hh, ( , )x y [0,M]2n, assuming that x y. We let
( , , 0, 0) ( , ) 0
POST PRE
H x y −H x y = . As already noted following (5), because h is continuous, then HPOST is continuous too. And because of the continuity of HPOST, there exists U1 - an open neighborhood of (0, 0) such that for each ( , )a b U1:
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