1

Gains from Trade, Inequality and Distribution-Neutral Fiscal Policy

Sugata Marjit*

CTRPFP, Centre for Studies in Social Sciences, Calcutta (CSSSC), India

GEP, University of Nottingham, UK

CESIfo, Munich, Germany

Sandip Sarkar

CTRPFP, CSSSC

Lei Yang

Hong Kong Polytechnic University

January, 2018

ABSTRACT

Gains from trade and inequality do not feature prominently in trade theory. The standard

criterion of Pareto efficiency indicates nothing about inequality when applied to the

redistribution of gains from trade. Yet, trade-induced inequality has become a talking point and

extremely contentious issue world-wide. In a HOS model of trade, we consider tax-transfer

policies that both do not decrease the absolute income of any group, as suggested by the

standard Pareto rule, and keep the pre-trade degree of inequality between skilled and unskilled

workers unchanged. Such a fiscal policy exists and is independent of whether the tax is

progressive or proportional. We show that the aggregate gain in real income due to trade can

be distributed to make everyone better off without increasing inequality. A generalisation of

the basic result uses a striking theoretical proposition that any Pareto Efficient allocation can

be transformed into a distribution-neutral allocation through appropriate fiscal policy.

JEL Classification: F11; J31; D63; H20; H23

Key Words: Trade Model; Inequality; Fiscal policy

*Corresponding Author – CSSSC, R 1 B.P. Township, Kolkata -700094, India,

marjit@gmail.com. Sugata Marjit is indebted to seminar participants at IGIDR Mumbai, the

Delhi School of Economics, and the IMF; and to the University of Queensland and CES-Ifo

Konstanz for their hospitality while working on the paper. Comments from Rajat Acharyya,

Gabriel Felbermayr, Ronald Jones, Roy Ruffin, Heinrich Ursprung, Pranab Das, Sanjeev

Gupta, Mick Keen, and Sajal Lahiri have been quite helpful. Financial assistance from

CTRPFP and the RBI Endowment at CSSSC is acknowledged. The usual disclaimer applies.

1. Introduction

2

The recent decision by the UK to leave the European Union marks a rare event in the history

of economic thought. This is the first formal vote of no-confidence against the policy of free

trade in goods, services and factors. A majority of Londoners voted to remain in the EU while

many industrial workers and low-skill, less educated citizens voted to leave. Many have

interpreted this as a decision against rising inequality within the UK caused by deteriorations

in the labour market and social provisions resulting from immigration from the poorer

European countries. This article assess how Brexit has enriched our understanding of standard

trade and welfare theories and to what extent inequality has become a pivotal theoretical issue

in such matters.

Certain facts need to be stated at the outset. That free trade always leads to gains for

everyone is an incorrect proposition. Economic theory argues that free trade leads to an increase

in the aggregate real income for countries engaging in trade only under ideal conditions. If the

government does not intervene, then some will lose. Those who fair worse under trade include

the current producers of goods and services that will be imported and sold at lower prices and

workers whose jobs are being outsourced. Workers who face competition in the labour market

because of immigration, legal and illegal, from Eastern Europe or from ISIS-controlled Syria

will suffer. Additionally, the British health system has a heavier burden because of blanket

social coverage and because the UK must donate a fraction of its GDP to the EU treasury. The

natural question is whether the aggregate gains from trade from integration between the EU

and the UK are enough to compensate every group for their loss and still generate a surplus for

the nation. The literature on international trade describes this as a process where the “gainers

bribe the losers”. The state must design a compensation mechanism that guarantees that

everyone remains at least at their pre-trade welfare level. Such a mechanism implies that the

state will tax the gainers and transfer enough to compensate the losers. If no one is worse off

3

and some are better, society will be better off. This is a welfare criterion suggested by Pareto

known as the Pareto criterion.

Although Pareto’s initial interest was matters of inequality, his criterion, which is

followed with devotion in the academic profession, does not mention inequality of any sort.

However, inequality has become the culprit behind the anti-globalisation movement. The fact

that some have gained substantially since Britain entered the EU while others are stuck with

what they used to have means that not everyone feels that they are as well off as before because

relative concerns are important at the individual level. Supporters of the Pareto criterion might

argue that no one is worse off, but those in the lower branch of the distribution ladder would

be concerned as they ask themselves why others are doing so much better than they are. This

raises a fundamental question regarding the perception of social inequality at the individual

level.

Civilized human beings may not like rising inequality in society independently of

whether they are personally affected by such a process. To ensure that the degree of inequality

is kept unchanged, we need a stronger rule for individual happiness. Everyone must be

provided with enough so that no individual will be concerned about inequality; i.e., the relative

position of everyone must remain unchanged and society should gain in aggregate. Many

allocations that change the distribution will disturb one or the other. We ask the following

question: does trade promise enough gains to maintain the degree of inequality of the initial

distribution and to provide more to everyone? This paper uses the well-known Heckscher-

Ohlin-Samuelson (HOS) model of international trade at an elementary level to argue that this

is always feasible.

Because trade increases the aggregate real income of the trading nation, we can

redistribute income in such a way that everyone gets at least the same level of income as before

4

and some get higher incomes. The issue of Pareto-improving transfers of aggregate gains from

trade has been discussed by Dixit and Norman (1986) and Kemp and Wan (1986). However,

this does not necessarily guarantee that relative income also remains the same; the degree of

inequality might be disturbed. Technically speaking, the Lorenz Curve or the Gini Index may

change. Someone who feels that the job is done once the Pareto principle is satisfied might be

mistaken because some people will not like if their relative income falls. In this paper, we

provide a concrete example of such an allocation by appealing to a textbook model of

international trade.

Free trade under ideal conditions generates overall gains from trade, increasing real

national income. This is a standard proposition in international trade. However, there are

distributional consequences: some gain and some lose. The general proposition is that the

gainers can bribe the losers. Political authorities should be able to generate compensation

mechanisms to help the losers. As aggregate real income increases relative to autarky,

potentially everyone can be made better off. Thus, free trade benefits all in the sense that even

those who do not gain by trade can be compensated by the state if necessary. This is as much

as trade theory can tell us.

International trade theory does not suggest anything to address rising inequality after

trade. If trade increases wage inequality between the skilled and the unskilled, absolute

compensation is unlikely to do the job. Theories of trade do not give any clues as to how gains

from trade may be redistributed to contain rising inequality. To do this, one needs to integrate

public finance with trade, i.e., to explore the feasibility of a proper tax-transfer mechanism, as

this paper does. Combining trade and public finance theories allows us to understand both

problems better. Atkinson (2000, 2009) has taken such an approach, as have Antras et al.

(2015), who went into the details of the welfare consequences of tax policies in an extended

trade model when such taxes create distortions. However, they did not discuss the elementary

5

case, which poses a fundamental question of whether a compensation mechanism that keeps

inequality in check and increases the after-tax income of skilled labour is feasible in the

standard HOS model.

Modern trade theorists did not anticipate that the status quo in terms of the initial level

of income was not good enough. Those who directly gain from trade need to be taxed more

heavily to satisfy an inequality-neutral condition where the degree of inequality remains the

same because those who are hurt by trade need to be compensated more. At the same time, it

must be ensured that those who have directly gained from trade are not losing on net. This will

put an upper bound on redistribution. Redistributive policy must not make taxpayers worse off

relative to autarky. We introduce a new welfare criterion involving inequality that is an

extension of the famous Pareto criterion. This is stated as follows. Consider two social

situations A and B. A will promise greater social welfare than B if and only if taxes collected

from better off people in A relative to B are transferred to the worse off people in A relative to

B to keep the degree of inequality in A the same as in B and the taxpayers have a greater after-

tax real income. We apply this principle in our exercise on tax policy in an open economy.

The purpose of this paper is to look for the distribution neutral income tax rate under

free trade. It is now recognized that the wage inequality between the skilled and unskilled

workers in developed countries has widened considerably with the rising volume of trade.

There is a huge body of literature dealing theoretically and empirically with this problem in the

context of relatively rich skill- and capital-abundant countries. Prominent papers include

Krugman (2000, 2008), Davis (1998, 2011), Jones and Engerman (1996), Feenstra (2001,

2010), Marjit, Beladi and Chakrabarty (2004), Badopadhyaya, Marjit and Yang (2014), Marjit

and Acharyya (2009) and Acharyya and Kar (2014). In a recent paper, Burstein and Vogel

(2017) elegantly reconfirm the notion that trade increases the skill premium and wage

inequality worldwide by quantifying a standard apparatus of international trade. In this paper,

6

we use a standard HOS model to suggest our point and then present an interesting generalised

outcome.

Even if trade benefits a nation in aggregate measures and promises long-run benefits,

affected groups would continue to suffer if sufficient compensation is not made available to

them to cope with short-run adjustments. In a democracy, rising inequality is a critical issue

for political competitors. Without proper attention, such inequality can jeopardise good

economic strategies. Thus, it seems natural to seek compensating policies to counter rising

inequality due to trade.

We characterise distribution-neutral tax policies that tax skilled workers and transfer

the proceeds to unskilled workers with a textbook model of international trade and standard

tax-transfer mechanisms. We find the necessary increase in the tax rate that keeps the wage

distribution at the pre-trade level and characterise such a tax in terms of underlying parameters.

The interesting part of the problem is to check the existence of an inequality-neutral tax rate

that is low enough to increase the net of the tax on the skilled wage relative to autarky. We

argue that such a win-win situation will exist. We consider proportional and progressive tax

rates and show that the condition for existence is met in both cases.

The rest of paper is organized as follows. In section 2 we develop the model and results

with proportional and progressive tax. In section 3 we provides a general perspective and

concludes.

2. The Model

Consider an economy producing two final goods, X and Y, with two factors of production,

skilled and unskilled labour. Assume that production of X is via a CRS and diminishing

7

marginal productivity production function. Y is the numeraire. The competitive price equations

with yields

𝑤𝑠𝑎𝑠𝑥 + 𝑤𝑎𝑙𝑥 = 𝑝 (1)

𝑤𝑠𝑎𝑠𝑦 + 𝑤𝑎𝑙𝑦 = 1 (2)

The symbols have their usual meaning a la Jones (1965). The country considered has

an abundance of skilled labour, and as trade opens, �̂� > 0, where ‘^’ denotes the percentage

change.

�̂�𝑠=𝜃𝐿𝑦𝑝

|𝜃| and �̂� =-𝜃𝑠𝑦

𝑝

|𝜃| (3)

The factor intensity assumption implies that |𝜃| = 𝜃𝑠𝑥 − 𝜃𝑠𝑦 > 0 .

This is the standard Stolper-Samuelson result. Trade increases inequality between 𝑤𝑠 and 𝑤,

with �̂�𝑠 > 0 and �̂� < 0. We now turn to the welfare policy of the government to compensate

the unskilled workers.

2.1 Proportional Tax

Suppose the government taxes the skilled workers by taxing 𝑤𝑠 with a proportional tax

𝑡 and redistributes the tax proceeds to the unskilled workers. If 𝑆 and 𝐿 are the numbers of

skilled and unskilled workers, respectively, then the after-transfer wage to unskilled workers

is given by (4)

�̃� = 𝑤 + 𝑡𝑤𝑠 .𝑆

𝐿 (4)

The after-tax wage rate of skilled labour is

𝑤�̃�= 𝑤𝑠(1 − 𝑡) (5)

8

We can easily prove the following proposition.

Proposition 1: If 𝒕 is kept unchanged, the increase in 𝒘𝒔 will be enough to compensate for

a decline in 𝒘 iff 𝜽𝑳𝒚 ≥ 𝝀, where 𝝀 = 𝒘

𝒘+𝒕𝒘𝒔𝑺

𝑳

.

Proof: �̂̃� = 𝜆�̂� + (1 − 𝜆)𝑤�̂� (6)

= �̂�𝑠 − 𝜆(�̂�𝑠 − �̂�)

= 𝑝

|𝜃|[𝜃𝐿𝑦 − 𝜆(𝜃𝑠𝑦 + 𝜃𝐿𝑦)]

= 𝑝

|𝜃|(𝜃𝐿𝑦 − 𝜆) (7)

If 𝜃𝐿𝑦 ≥ 𝜆, the increase in 𝑤𝑠 due to trade provides full compensation to the unskilled

workers for their initial loss due to trade. Thus, if the objective is to insulate the unskilled wage,

a high 𝜃𝐿𝑦 or low λ is desirable. Several observations are in order.

If the initial tax rate is low, then 𝜆 will be close to 1, and as 𝜃𝐿𝑦 < 1, the government

will not be able to compensate for the loss with the same t. Such a critical 𝑡, denoted by 𝑡, is

solved as follows.

For 𝜃𝐿𝑦=𝜆 ⇒ 𝜃𝐿𝑦 = 𝑤

𝑤+𝑡𝑤𝑠𝑆

𝐿

Or, 𝑡 = 𝑡 = (1−𝜃𝐿𝑦)

𝜃𝐿𝑦𝑤𝑠𝑤

.𝑆

𝐿

(8)

The initial tax rate must be equal to 𝑡 for �̂̃� = 0. Note that such a 𝑡 depends on the

initial relative wage (𝑤𝑠

𝑤). A higher initial

𝑤𝑠

𝑤 will reduce 𝑡̅ because there is more to redistribute.

9

A very high value of 𝐿

𝑆 will require a much higher initial tax rate t to neutralise the impact on

𝑤. The next step is to consider the case when raising w is not enough and the government seeks

to contain inequality.

For distribution-neutral tax rate, we consider the case in which the government worries

about the inequality between the after-tax skilled wage and the transfer-supported unskilled

wage. Thus, the measure is given by �̃�𝑠

�̃� instead of

𝑤𝑠

𝑤. Before trade, there is an initial value of

𝑤�̃�

�̃�, and the government considers the post-trade value of

�̃�𝑠

�̃�. Note that even if 𝑡 is kept

unchanged, the increase in 𝑤𝑠 by itself will raise the income of the unskilled. We seek to

determine the extent.

Proposition 2: If 𝒕 is kept unchanged, (�̂̃�𝒔-�̂̃�) > 𝟎; i.e., inequality must increase.

Proof: We know that �̂̃� = 𝑝

|𝜃|(𝜃𝐿𝑦 − 𝜆)for �̂�=0 (9)

Hence, (�̂̃�𝑠 − �̂̃�) = 𝜃𝐿𝑦𝑝

|𝜃|−

𝑝

|𝜃|(𝜃𝐿𝑦 − 𝜆)

= 𝜆𝑝

|𝜃|> 0 𝑸𝑬𝑫.

Proposition 2 suggests that to counter rising inequality, 𝑡 must increase.

Let us now consider the problem of the existence of a distribution-neutral tax rate 𝑡𝑛

that satisfies two conditions:

(�̂̃�𝑠- �̂̃�) =0 (10)

10

and

�̂̃�𝑠 > 0 (11)

Equation (10) implies that the degree of inequality is kept at the initial level,

neutralising the trade impact. Equation (11) implies that the after-tax skilled wage is greater

under trade. These suggest that both groups of workers are better off after redistribution.

�̂̃�𝑠 = �̂�𝑠 - �̂�𝑡

(1−𝑡) (12)

�̂̃� = 𝜆�̂� + (1 − 𝜆)(�̂� + �̂�𝑠) (13)

Now (�̂̃�𝑠- �̂̃�) = 0 ⇒ �̂�𝑠 − �̂�𝑡

(1−𝑡)− 𝜆�̂� − (1 − 𝜆)(�̂� + �̂�𝑠) =0

Or, �̂� = 𝜆(�̂�𝑠−�̂�)

(1−𝜆)+𝑡

(1−𝑡)

= 𝜆(

�̂�

|𝜃|)

(1−𝜆)+𝑡

(1−𝑡)

(14)

The neutral tax rate 𝑡𝑛 is given by 𝑡𝑛 = 𝑡(1 + �̂�)

�̂�𝑠–�̂�𝑡

(1−𝑡)> 0 [from (11) & (12)]

⇒ 𝜃𝐿𝑦𝑝

|𝜃|> �̂�

𝑡

(1−𝑡) (15)

Substituting for �̂� from (14), we obtain

𝜃𝐿𝑦 >𝜆𝑡

𝜆𝑡+(1−𝜆) (16)

Equation (16) summarises two conditions. First, inequality is contained at the pre-trade

level and taxation allows both groups to be better off. However, the problem is whether such a

condition is satisfied, which would guarantee the existence of a 𝑡𝑛.

11

We simplify condition (16) further:

𝜃𝐿𝑦 >𝜆𝑡

𝜆𝑡+(1−𝜆)=

1

1+1

𝑡(

1

𝜆−1)

(17)

From the definition of 𝜆 ≡ 𝑤

𝑤+𝑡𝑤𝑠𝑆

𝐿

, equation (17) becomes

𝜃𝐿𝑦 >1

1+1

𝑡(𝑡

𝑤𝑠𝑤

.𝑆

𝐿)

= 1

1+𝑤𝑠𝑤

.𝑆

𝐿

(18)

Proposition 3: Such a tax transfer mechanism will always exist.

Proof: Because (18) does not contain t, manipulation reveals that a sufficient condition for (18)

to hold is

𝑤𝑠

𝑤> (

1

𝜃𝐿𝑦− 1)

𝐿

𝑠 (19)

This boils down to (S/L) > ( asy / asy )

Note that as the country in a typical HOS economy exporting skill-intensive goods is

incompletely specialised, this must hold, as the endowment ratio must lie within the cone of

diversification, (asx / alx) > S/L > (asy / aly ). QED

We know that free trade does not guarantee that everyone will gain due to trade;

however, the gainers should be able to bribe the losers. A problem is that such compensation

is not enough to tackle the rising inequality due to trade. This is a concern that trade theory has

never considered. The standard compensation criteria did not have any formulation to design

distribution-neutral compensation mechanisms. We have proved that a distribution-neutral tax

12

transfer mechanism that guarantees a rise in the after-tax wage of the skilled worker and

maintains the degree of inequality at the pre-trade level does exist.

2.2 Progressive Tax

Now we redo the exercise with a progressive tax that increases with 𝑤𝑠 . In particular, we

propose a tax elasticity 𝜖 such that �̂� = 𝜖�̂�𝑠. Working through the same process as before, we

obtain

�̂̃�𝑠= �̂�𝑠(1 − 𝜖𝑎) (20)

where 𝑎 = 𝑡

(1−𝑡)

�̂̃� = 𝜆�̂� + (1 − 𝜆)(1 + 𝜖)�̂�𝑠 (21)

�̂̃�𝑠 − �̂̃� = 𝜆𝑝

|𝑄|− 𝜖(1 − 𝜆 + 𝑎)

𝑝

|𝑄|𝜃𝐿𝑦 (22)

where (22) is obtained from (20) and (21) by substituting for �̂�𝑠 and �̂� from (3).

Note that with 𝜖 = 0, equation (22) boils down to the case of a proportional tax.

�̂̃�𝑠 − �̂̃� = 0 iff 𝜖 =𝜆

𝜃𝐿𝑦(1+𝑎−𝜆) (23)

�̂̃�𝑠 > 0 iff 1 > 𝜖𝑎 (24)

1 − 𝜖𝑎 > 0 iff 1+𝑎−𝜆

𝜆𝑎>

1

𝜃𝐿𝑦

Substituting for 𝑎 and 𝜆, we obtain

1 − 𝜖𝑎 > 0 iff

𝑤𝑠

𝑤> (

1

𝜃𝐿𝑦− 1)

𝐿

𝑠 (25) [using (23)]

13

Note that condition (25) is exactly the same condition required in the case of

proportional tax.

We have shown that if we could design an appropriate income tax for the skilled worker

and a wage subsidy for the unskilled worker, there will be no change from the pre-trade

distribution of income between the skilled and unskilled workers. One could also check

whether the overall national income valued at world prices is increasing after trade, as this is a

standard outcome in international trade theory. The idea is equally applicable to the distribution

of aggregate gains from trade.

2.3 Generalisation and Implication

What we have shown so far is that if we redistribute appropriately, the relative income of the

skilled workers will not change and rising inequality will not be a cause for agitation by the

unskilled workers. Now consider that there are 𝑛 factors of production and they can produce

m goods. It is a well-known result in trade theory that if this economy opens up to trade and

face a set of world prices externally given for the case 𝑚 > 𝑛 under autarky, at most 𝑛 goods

will be produced under free trade with competition and neo-classical technology. Number of

goods actually produced under free trade cannot exceed number of factors of production. [

Beladi et al. (2016)]

Let (𝑤1, … … … … … , 𝑤𝑛) be the factor prices, (𝐿1, … … … … … … . , 𝐿𝑛) be the labour

endowment and ( 𝑋1, … … … … … . . 𝑋𝑛 ) and ( 𝐷1, … … … … … … . . , 𝐷𝑛 ) are production and

consumption vectors. At the set of world prices (𝑃1, … … … … … … … , 𝑃𝑛) following must be

true

∑ 𝑃𝑖𝑋𝑖𝑛𝑖=1 = ∑ 𝑃𝑖𝐷𝑖

𝑛𝑖=1 (26)

14

The revealed preference approach to gains from trade provides an aggregate measure

of gains from trade as

∑ 𝑃𝑖𝑑𝐷𝑖𝑛𝑖=1 = ∑ 𝑑𝑃𝑖(𝑋𝑖 − 𝐷𝑖)𝑛

𝑖=1 (27)

(with the use of envelop condition ∑ 𝑃𝑖𝑑𝑋𝑖 = 0𝑛𝑖=1 )

Aggregate gains from trade imply on average if 𝑑𝑃𝑖 > 0, 𝑋𝑖 > 𝐷𝑖 i.e. for goods facing

higher prices in the world market should be exported. i.e. (𝑋𝑖 − 𝐷𝑖) > 0. Free trade satisfies

this condition. If 𝑃𝑖0 represents the set of autarkic prices we know

∑ 𝑃𝑖0𝑋𝑖𝑛𝑖=1 < ∑ 𝑃𝑖𝑋𝑖

𝑛𝑖=1 (28)

Then ∑ 𝑑𝑃𝑖𝑋𝑖 =𝑛𝑖=1 ∑ (𝑃𝑖 − 𝑃𝑖0)𝑋𝑖

𝑛𝑖=1 > 0 (29)

Also ∑ (𝑃𝑖 − 𝑃𝑖0)𝑋𝑖𝑛𝑖=1 = ∑ (𝑊𝑖 − 𝑊𝑖0)𝐿𝑖 =𝑛

𝑖=1 ∑ 𝑑𝑊𝑖𝐿𝑖 > 0𝑛𝑖=1 (30)

Note the conceptual difference between the change in aggregate factor income and

gains from trade.

∑ 𝑃𝑖𝑑𝐷𝑖 =𝑛𝑖=1 ∑ 𝑑𝑊𝑖𝐿𝑖 −𝑛

𝑖=1 ∑ 𝑑𝑃𝑖𝐷𝑖𝑛𝑖=1 (31)

Or, ∑ 𝑑𝑊𝑖𝐿𝑖 = ∑ 𝑃𝑖𝑑𝐷𝑖 + ∑ 𝑑𝑃𝑖𝐷𝑖𝑛𝑖=1

𝑛𝑖=1

𝑛𝑖=1 (32)

Therefore aggregate factor income may exceed or fall short of aggregate measure of

gains from trade depending on the sign of ∑ 𝑑𝑃𝑖𝐷𝑖𝑛𝑖=1 .

However, in public policy debate factor income measures become the focal point.

Hardly the consumption gains from trade through lower prices of imports becomes part of the

debate. In our 2 × 2 example we have precisely done that. Let us now focus on the following

factor income vectors.

(𝑤10, … … … … … , 𝑤𝑛0) under autarky

15

(𝑤1, … … … … … , 𝑤𝑛) under free trade before redistribution.

(�̃�1, … … … … … , �̃�𝑛) after redistribution.

What we need is �̃�𝑖

�̃�𝑗=

𝑤𝑖0

𝑤𝑗0 ∀ 𝑖, 𝑗 (33)

and

∑ �̃�𝑖𝐿𝑖 =𝑛𝑖=1 ∑ 𝑊𝑖𝐿𝑖

𝑛𝑖=1 (34)

It is straightforward to argue that

for �̃�𝑖 = (∑ 𝑊𝑖𝐿𝑖

𝑛𝑖=1

∑ 𝑊𝑖0𝐿𝑖𝑛𝑖=1

) 𝑊𝑖0 (35)

both (8) and (9) will hold. This guarantees �̃�𝑖 > 𝑊𝑖0 ∀ 𝑖 (36)

Thus proper redistribution of income after trade will keep the distribution intact. In fact

condition (33) and (34) guarantee that Gini, Lorenz and Atkinson indices of inequality along

with others that are consistent with the relative income measure will remain the same after

trade. This has been printed out in a policy related application paper by Gupta, Marjit and

Sarkar (2017).

Similar principle will follow if we do the same exercise in the utility space. Let us use

the well known box-diagram to highlight the welfare implication of the result.

𝑥1

16

𝑥2

Along the contract curve CC all points are Pareto superior to A – the autarkic levels of

welfare. Free trade will take this two person economy, in a pure exchange no production

framework on a point along CC. All such points are non-comparable in the sense of Pareto,

with relative gains of two agents being different at each point but reflects that the aggregate

utility is higher. Thus the conventional reason that Pareto efficiency does not seem to take care

of inequality since any point on CC is better, but some of them can be highly unequal relative

to A.

The conventional wisdom falls short of the fact that any allocation on CC can be

transformed through redistribution into another point on CC, a unique allocation which has

exactly the same degree of inequality as in A. This is what we have shown in the income space

and in our 2×2 example. The same method applies here. Among the non-comparable Pareto

points on CC we propose a selection criterion that is distribution neutral and we can show that

it always exists and it is unique. The contribution of our paper is that we negate the

misconception that Pareto efficiency tells us nothing about inequality.

C

C

𝑈1

𝑈2

𝑥1

𝑥2

A

17

Any set of Pareto efficient allocation relative to a reference allocation will contain a

unique Pareto efficient allocation which is distribution neutral relative to the initial

allocation.

3. Conclusion

We started with the question of whether one can design a compensation mechanism that not

only protects the absolute income of everyone but also guarantees that the degree of inequality

remains unchanged from the autarchic level. We use a standard HOS model with skilled and

unskilled labour and a trade-induced rise in skilled wage and decline in unskilled wage to show

that without increasing the tax rate, the rise in skilled wage will not provide enough resources

to keep inequality under control. However, a proportional or progressive tax rate will always

exist that, if implemented, will serve the purpose: inequality will remain the same and skilled

workers will still gain. This result modifies the well-known Pareto ranking hypothesis, which

does not consider rising inequality when making welfare comparisons. The losers must be

compensated more than what is needed to keep them on the same level of real income as before

if inequality is rising. The simple workhorse model of trade theory shows that such

compensation can be designed through a transfer from gainers. This paper proves that there is

nothing inherent in the process of international trade that should lead to greater inequality if

the appropriate fiscal policy is adopted by the state. It also suggests that compensation

mechanisms that focus only on Pareto efficient allocations stop short of addressing inequality.

Interestingly and quite strikingly, any Pareto efficient allocation can be transformed into a

distribution-neutral allocation.

Future work involves the question that distribution neutral fiscal policy may impose

huge cost on those that are paying the tax and hence can lead to negative incentive effects. This

18

is similar to the issues raised by Antras et.al (2016) which deals with costly redistribution

effects. The query in the context of this paper or the way we invoke the distribution neutral

policy is to what extent we can tolerate the costs of redistribution or negative incentive effects

while keeping the distribution intact in the post trade situation. The conjecture is that if the

country under consideration suffers from relatively high degree of inequality in autarky, such

tolerable costs to the government will be relatively high. In other words the policy will be easier

to be implemented. Thus if the richer countries are less unequal to start with they will have

tougher situation.

19

References

Acharyya, Rajat and Saibal Kar, 2014. International Trade and Economic Development.

Oxford University Press, UK.

Antras, Pol, Alonso de Gortari, and Oleg Itskhoki, 2015. Inequality, Costly Redistribution and

Welfare in an Open Economy. Working paper, Harvard University.

Atkinson, Anthony B, 2009. Factor shares: The principal problem of political

economy? Oxford Review of Economic Policy 25: 3-16.

Atkinson, Anthony B, 2000. The changing distribution of income: Evidence and

explanations." German Economic Review 1 (1): 3-18.

Bandyopadhyay, Subhayu, Sugata Marjit, and Lei Yang, 2014. International oligopoly, barriers

to outsourcing and domestic employment. Canadian Journal of Economics 47(4): 1372-1386.

Beladi, H, A. Chakrabarti and S. Marjit 2016- Competitive General Equilibrium with Finite

Change and Theory of Policy Making – Economics and Politics, 28 (1) , 1-7

Burstein, Ariel and Jonathan Vogel, 2017. International Trade, Technology and Skill Premium.

Journal of Political Economy, 125(5): 1356 -1412.

Davis, Donald R., 1998 Does European unemployment prop up American wages? National

labor markets and global trade. American Economic Review 88(3): 478 - 494.

Davis, Donald R. and James Harrigan, 2011. Good jobs, bad jobs, and trade

liberalization. Journal of International Economics 84 (1): 26-36.

Dixit Avinash, and Victor Norman, 1986. Gains from trade without lump sum compensation.

Journal of International Economics 21: 111-122.

20

Feenstra, Robert C., 2010. Offshoring in the global economy: microeconomic structure and

macroeconomic implications. Cambridge, MA: MIT Press.

Feenstra, Robert, and Gordon Hanson, 2001. Global production sharing and rising inequality:

A survey of trade and wages. National Bureau of Economic Research working paper.

Gupta, S., S. Marjit and Sadip Sarkar, 2017. An Application of Distribution Neutral Fiscal

Policy. IMF Working paper (WP/18/12)

Jones, Ronald W. and Stanley L. Engerman, 1996. Trade, technology, and wages: a tale of two

countries. The American Economic Review 86 (2): 35-40.

Kemp, Murray C., 1986. The Gains from trade with or without lump sum compensation.

Journal of International Economics 21: 99-110.

Krugman, Paul R., 2000. Technology, trade and factor prices. Journal of International

Economics 50 (1): 51-71.

Krugman, Paul R., 2008. Trade and wages, reconsidered. Brookings Papers on Economic

Marjit, Sugata, Hamid Beladi, and Avik Chakrabarti, 2004. Trade and wage inequality in

developing countries. Economic Inquiry 42 (2): 295-303.

Marjit, Sugata and Rajat Acharyya, 2009. Trade and Wages in Rajan and Reinhart (eds),

Princeton Encyclopaedia of Global Economy, Princeton University Press.