Discussion Paper Series No.192
Factor Price Equalization (FPE) Implies
Product Quality Equalization (PQE)

Satya P. DAS

Indian Statistical Institute – Delhi Centre

KATAYAMA Seiichi

Kobe University

June

2006

Discussion papers are a series of manuscripts in their draft form.
They are not intended for circulation or distribution except as
indicated by the author. For that reason Discussion Papers may not bequoted, reproduced or distributed without the written consent of theauthor.

Factor Price Equalization (FPE) Implies
Product Quality Equalization (PQE)
Satya P. Das, Indian Statistical Institute - Delhi Centre
email: das@isid.ac.in
AND
Seiichi Katayama, Kobe University
email: katayama@rieb.kobe-u.ac.jp
June 2006
Abstract
This paper examines the issue of the e¤ect of international trade on
quality choice by …rms in a factor-endowment framework. Factor priceequalization implies product quality equalization. In the North-South
context it means that the South catches up with the North in productquality due to the competitive pressure from international trade, notbecause of technology adoption. Free trade may induce the North, thequality-leader in autarky, to improve its product quality - and yet theSouth would leapfrog and match it in the free trade equilibrium.

1

Introduction

How does international trade a¤ect product quality? There is a large volume of analytical literature, dating back to the 70s. One would then thinkthat some bench-mark answer already exists in a ”text book” form, wellunderstood to the point of being obvious. Somewhat strangely, it is not thecase.
The literature on product quality and trade can be grouped into two
categories: one looks at the problem in a static setting and the other ina dynamic setting. Within the …rst category, there are three strands. An
early paper such as Rodiguez (1979) interprets quality as the amount ofsome uniform service that is packaged into one unit of a product and theconsumer derives utility from the total amount of services (quality times
quantity) consumed.
Later papers such as Falvey and Kierzkowski (1987) and Flam and Helpman (1987) consider general-equilibrium models of trade in which an economy has a homogenous-good sector and a vertically di¤erentiated sector.
There are high-quality and low-quality brands in a continuum of goods,
while the quality of any particular brand is …xed. In a two-factor (laborcapital) framework, Falvey and Kierzkowski (1987) assume that a higher
quality brand is associated with a more capital-intensive technology. This
leads to the prediction that the relatively capital- (labor-) abundant country will export higher- (lower-) quality brands. The Flam-Helpman model1

assumes one-factor economies: with the North (South) de…ned as having ahigher (lower) endowment of this factor (total amount of e¤ective labor). In
addition to the factor endowment di¤erence, their model assumes technology
di¤erences - with the North having a comparative advantage in producing
high-quality brands. The prediction about the e¤ect of trade is similar tothat of the Falvey-Kierzkowski model: the North (South) will specialize andexport higher- (lower-) quality brands.1
These results may be hastily interpreted as a baseline prediction of how
trade a¤ects product quality. But they are not, because the quality levels of
individual brands are exogenous. Thus, by assumption, trade cannot lead toa change in the quality of any particular brand; it only a¤ects a country’s
pattern of specialization.
The third strand in static models refers to game-theoretic models of quality, quantity and price choice (starting from Das and Donnenfeld (1989)
to Zhou, Spencer and Vertinsky (2002), among others), which are partialequilibrium and thus not designed to answer the e¤ect of opening up trade.
Finally, quality choice in terms of “rising product quality” in a dynamic
and international setting is contained in the seminal work by Grossman andHelpman (1993). Quality improvement is synonymous with product innovation. Using two factors, unskilled labor and skill-labor (human capital), and1

Copeland and Kotwal (1996) consider a modi…ed Flam-Helpman model, focussing
on trade break-downs. Murphy and Shleifer (1997) arrive at similar conclusions (in thecontext of trade between Eastern and Western Europe), while their model emphasizes
demand di¤erences across countries arising out of endowment di¤erences – namely high(low) income countries would tend to produce and demand high (low) quality goods.

2the assumption that the R&D activity is human-capital intensive, their model
predicts that international trade enables a relatively skilled-labor abundant
country to ”capture leadership positions in a large number of high-technology
industries as compared to its relative output of traditional goods.”
While this prediction is useful, we note that all quality improvements do
not stem from new blue prints or patents. Quality variation by …rms producing similar products may very well result from di¤erent levels and compositions of resource use within a given technology. There are products/services
whose technologies are quite standard and yet there are international di¤erences in quality, such as wrist watches, cloths, electric appliances and shoes- even a basic, functional car. For example, casual observation tells thatin case of electrical appliances, (at least until recently) because of superior
raw material and workmanship, those from developed countries were sturdierand more reliable, i.e. quality-wise better than the brands from developing
countries. In business-management literature, there is a concept called “total
quality control”(e.g, Deming, 1986), which emphasizes quality enhancements
in terms of removing defects, improvising product components etc. rather
than through any fundamental technological advancement.
Thus, it is our view that the e¤ect of international trade on productquality, at some basic, static level, is not something that is adequately understood as yet. The current paper addresses this issue in a 2 x 2 (skilled andunskilled labor) factor-endowment framework, assuming a given technology
of producing quality, while not assuming any di¤erence in technology or any
3brand quality being given. More speci…cally, in our model there are horizontally di¤erentiated brands and the quality level of each brand can vary. In
other words, it is a hybrid model with horizontal and vertical product differentiation. Given the 2 x 2 structure, as the title of the paper suggests,
factor-price-equalization (FPE) is quite plausible - and one of our central…ndings is that FPE implies PQE (product-quality equalization)! A particular version of this framework is contained in Das (2003), where the focus ison the e¤ect of international trade on the relative wages. In this paper we
present a much more general and complete analysis that this important issue
of international trade and product quality deserves.
In section 2 we begin with a model of monopolistic competition and tradein the tradition of Krugman (1979) and Dixit and Norman (1980). The
Dixit-Stiglitz utility function is generalized to allow for utility gain from
quality. Quality choice is a decision variable facing a …rm. There is a further
generalization: besides scale economies in producing quantity, we allow for
scale diseconomies of producing quality. Assuming that quality production
is more skill intensive than quantity production, in autarky the …rms in therelatively skilled-labor abundant North produce higher quality compared totheir counterparts in the South. As free trade is allowed, the relative wage
rises in the North and falls in the South, making quality production morecostly in the North and less in the South; hence it falls in the North and risesin the South and in the FPE equilibrium they are equalized.
However, since in monopolistic competition each …rm is small relative4

to the entire market, it cannot capture the directly pro-competitive e¤ectof opening up freer trade. In section 3, we consider oligopoly competition.
Opening up trade increases the number of rivals and hence intensi…es strategic competition a¤ecting the …rst-order rules of pro…t maximization. This
opens the possibility that …rms in both North and South increase quality
in response to international trade (because of greater competition). If we
combine this with PQE, it is then possible that while in autarky North produces a higher quality than South, as (free) trade opens, PQE occurs at aquality level, higher than that in autarky in the North. We interpret thisphenomenon as quality leapfrogging by the South.
In a nutshell, our …ndings say that (a) free trade has an element of narrowing quality di¤erences of products that are traded and (b) quality leapfrogging by the South (the developing countries) is not necessarily an outcomeof international technology transfer.

2

Monopolistic Competition

There are two countries: North (N ) and South (S). We …rst characterizeautarky and then consider free trade between these countries.
In each country, there are two sectors, M (manufactures) and Y (numeraire). The market structure in sector M is monopolistically competitive,
while perfect competition prevails in sector Y. There are two primary factors of production, skill labor and unskill labor, and North is relatively moreskilled-labor endowed than the South. Both factors are used in each sector.
5Sector M produces quantity and quality (imagine that there are two divisions,design and production lines), while the output of sector Y is homogeneousand its quality is pre-determined. In sector M, there are increasing returns
in producing quantity, while quality is produced under constant or decreasing returns to scale. To begin with, we assume constant-returns in producing
quality. The numeraire good is produced under constant-retrurns technology.
Furthermore, quality production in sector M is most skill-labor intensive,
followed by quantity production in that sector. The technology of producing
good Y is the least skill-labor intensive.
Sector M produces a di¤erentiated product. Preferences are given by
a generalized Dixit-Stiglitz utility function, similar to the one used in Das(2003):
Z n

1

# 1
#

qi c i## 1dic1y ; 0 <

<1<#<

0

where ciand cyquantity consumed of the ith variety of good M, qi

its quality

the consumption of good Y. The restrictions on parameters

and# are well-known. The rationale behind > # will be noted later. Mark that
this utility function is homothetic with respect to the quantities consumed,
while both quantity and quality are subject to diminishing marginal utility. A
representative consumer maximizes utility subject to the budget constraint:Rnp c di + cy 6 I, where pi is the price of variety i and I is the income.
0 i i
Utility maximization leads the following demand functions:

6

qi I
; where Z
p#i Z

ci =
cy

= (1
)

Z n

qi p1i # di and

#

(1)

<1

0

(2)

)I

@ci
=
@pi

ci #Z
pi

1)qi p1i #

(#
Z

< 0;

@ci
ci Z
=
@qi
qi

qi p1i #> 0:(3)Z

Turning to the production side, let ws and wu denote wage payment perunit of skilled labor and unskilled labor respectively. We express technologies
by cost functions. In the numeraire sector, let cy (ws ; wu ) denote the unit andmarginal cost function. In sector M, in producing quality, cq (ws ; wu ) de…nes
the unit and marginal cost functions. The total cost of producing quantity
xi of variety i is given by C x (ws ; wu ; xi ) = cx (ws ; wu ) f (xi ): The following
assumptions are imposed on the f (:) function:(a) f 0 > 0;(b) De…ne the scale function

(x)

f (x)
AC
=M
xf 0 (x)Csuch that(x) > 1 forall x > 0;(c) f 00i.e.,

00, which implies that the scale economies decrease with output,(x) < 0;(d) lim (x) ! 1; lim
x!0

x!1

(x) ! 1:2

Perfect competition and free entry and exit in sector Y imply the zeropro…t condition:
2
This means that scale economies are arbitrarily large at a very small level of output,
and they are nearly exhausted at an arbitrarily high level of output.

7

cy (ws ; wu ) = 1:

(4)

In sector M, the pro…t of …rm i producing variety i has the expression:i= pi xi

cx (ws ; wu ) f (xi )cq (ws ; wu )qi : As standard, in viewing thedemand function (1), …rm i treats I and Z as parameters. Hence the pro…tmaximizing rule with respect to quantity or price is given by the MR = MC
rule:

pi 1
Totally di¤erentiating1#= cx (ws ; wu ) f 0 (xi ) :(5)

i with respect to qi (and again treating I and Z areparameters), the quality-setting rule, in view of (1) again, is given by[pi

cx (ws ; wu ) f 0 (xi )]xiqi

cq (ws ; wu ) = 0:

(6)

If we substitute (5) into (6), we havexi f 0 (xi ) cx (ws ; wu )= qi ;# 1 cq (ws ; wu )(7)which relates quantity, quality and factor prices. Given our assumption of
f 00

0, quality is positively related to quantity in equilibrium. As quality

production is more skilled labor intensive than quantity production in sector
M, the ratio cx =cq decreases with the relative wage, !

ws =wu ; intuitively,

an increase in the relative wage implies a decrease in the quality produced.
Next, the zero-pro…t condition in sector M is expressed as:
8

pi xicx (ws ; wu ) f (xi )cq (ws ; wu )qi = 0:

(8)

If we substitute the price- and quality-setting rules into this condition, we
obtain, after some manipulation,(xi ) =

#
#

1

:

(9)

This is where the assumption of > # plays a critical role in the model: as it
implies< 1, the ratio ## 1 exceeds unity, such that given the assumptions(c) and (d) on the(x) function, there exists a solution to eq. (9), whichis the long-run level of …rm-output. Moreover, assumption (d) implies thesolution is unique. Let it be denoted by x.
Given xi = x, it follows that pi = p and qi = q.3 We now specify the restof the relationships in a closed economy:n [cqu (!) q(!) + cxu (!) f (x)] + cyu (!) Y = Lu(10)n [cqs (!) q(!) + cxs (!) f (x)] + cys (!) Y = Ls

(11)

wu Lu + ws Ls
= x:
np

(12)

3

Because x = x, in view of (7), quality is uniquely related to the relative wage, indicating how factor price equalization implies product quality equalization. But, as we shallsee, under oligopoly competition, the long-run output is not invariant, and yet, factor priceequalization implies product quality equalization.

9

The variable n denotes the number of …rms too. The partials of cj (:); j =q; x; y denote the respective input coe¢ cient, e.g., cqu (!)@cq (ws ; wu )=@wu

is the unskilled labor coe¢ cient in quality production; Y is the output of thenumeraire good and Lu (Ls ) is the inelastic endowment of unskilled (skilled)labor in the economy. Eqs. (10) and (11) spell the respective full employment conditions. The last equation is the market clearing condition of any
particular variety of good M.
It is easy to see from the full-employment equations that the relative
version of the Rybczinski theorem holds: a higher relative endowment ofskilled labor implies a higher relative output of good M (n=Y ), at any givenp, since both quality and quantity producing activities in sector M are moreskilled labor intensive relative to the numeraire sector. Further, given thefactor endowments, as shown in Appendix A, the n=Y ratio increases withp, i.e. the relative ‘supply curve’ is upward sloping. Hence the autarky
equilibrium is unique.
Denoting countries by respective subscripts and ‘autarky’by a, it readily
follows that pN a < pSa ; ! N a < ! Sa and in particular qN a > qSa , where !
denotes the relative wage: All these rankings are intuitive.

2.1

Free Trade

Now suppose that the two countries move to a regime of free trade. Since
there is no strategic interaction among …rms, their price/quantity and quality
decision rules remain unchanged. Assuming that both countries incompletely

10specialize, the equilibrium …rm-outputs in both countries are given by (9).
The full employment equations remain the same. The only change occurs in
the market-clearing equation (12). It is now
qr IR= xr ;1 ##pr (nN qN pN + nS qS pS1 # )(13)

where r = North, South and IR is the world income. We now prove FPE
and PQE.
Since xr = x, (14) implies
qN
q= S# :
#
pN
pS

(14)

Suppose pN < pS : Then (14) implies qN < qS : In view of (7), this implies(cx =cq )N < (cx =cq )S . As this ratio is a decreasing function of !, ! N > ! S :But, by the Stolper-Samuelson relation, pN < pS ) ! N < ! S : Hence there
is a contradiction. Similar contradiction arises if pN > pS : It then follows
from pN = pS ; implying ! N = ! S and qN = qS : That is, product quality
equalization accompanies factor price equalization. This is a central resultof our paper. Intuitively, the quality level chosen by a …rm depends on thewage ratio. This implies that, if technologies are same between the trading
countries and wages are equalized, product quality is equalized too. Let us
denote pr = pR ; wsr = wsR ; wur = wuR ; ! r = ! R and qr = qR .
How does the free-trade equilibrium compare to the respective autarky
equilibria? Factor endowment di¤erences imply that the relative wage rises
11

in the North and falls in the South. Therefore, quality production falls in the
North and improves in the South. Factor endowment di¤erences also imply
that the North exports good M to the South (proved in Appendix A).4
Proposition 1 If the two countries incompletely specialize in the trading
equilibrium, FPE holds, implying PQE. The North (South) is a net exporter(importer) of good M, and, compared to autarky, the relative wage rises (falls)
and product quality falls (rises) in the North (South).
The well-known Dixit-Norman technique of analyzing ‘integrated equilibrium’ yields the pattern of specialization. This is outlined in Appendix
A

2.2

Decreasing Returns to Scale in Quality Production

Increasing returns to scale in producing quantity in sector M capture theassembly-line nature of mass production. But producing quality is quite different. Many partial equilibrium models of quality choice assume increasing
costs – for natural reasons.5 We now show that our central results hold if
there are decreasing returns to scale (increasing marginal costs) in quality
production.
De…ne C q (ws ; wu ; q) = cq (ws ; wu ) g(q); with the properties that the scaleelasticity, qgg(q)0 (q)(q), is less than one, and

4

0

(q)

0, i.e. diseconomies

The association between trade pattern and quality response is interesting. As trade
opens, the North (South), having comparative advantage (disadvantage) in manufacturing,produces more (less) quantity of good M but less (more) quality of the same good!
5
See, for instance, Das and Donnenfeld (1989) and Zhou, Spencer and Vertinsky (2002).

12

continue to increase with quality production. The last assumption implies
that g 00

0.

A …rm’s objective function has the expression:i = pi xi

cx (ws ; wu ) f (xi )cq (ws ; wu ) g (qi ) : Its pricing rule is the same as (5), but its quality-setting
rule, after substituting (5) into it, becomesxi f 0 (xi ) cx (ws ; wu )= qi g 0 (qi ) :# 1
cq (ws ; wu )(15)

We have the zero-pro…t condition, pi xi cx (ws ; wu ) f (xi ) cq (ws ; wu ) g (qi ) =0: Substituting the price and quality-setting rules in it and eliminating pi
and cq (:), we obtain the following relationship between quantity and quality
produced:#(qi ) = (#1) (xi ) .

(16)

This equation reveals that, unlike when quality production is subject toconstant costs, the long-run output of a …rm is not independent of its quality
choice. At given factor prices, quality production and quantity production
are jointly determined by eqs. (15) and (16). These equations respectively
spell a positive and a negative locus in xi and qi , implying unique solutions.
As a simple comparative statics, we note that x0 (!) > 0 and q 0 (!) < 0;because quality production is more skill-intensive than quantity production.
Dividing (5) by (4) yields

13

f 0 (x(!))cx (ws ; wu )#p=yc (ws ; wu )# 1
Given f 00

(17)0; x0 (!) > 0 and that quantity production in sector M is moreskill-intensive than the numeraire sector, the l.h.s. of the above equation
is monotonically increasing in !: Thus ! = !(p) with ! 0 (p) > 0; i.e. theStolper-Samuelson implication holds.
The monotonic relationships between ! and x; ! and q; and ! and p
imply that, as long as the countries incompletely specialize in the trading
equilibrium, FPE and PQE hold.6

3

Oligopoly

A monopolistically competitive market structure cannot accommodate thedirectly pro-competitive e¤ect of freer trade, as each …rm being arbitrarily small compared to the whole market faces the same price and quality
elasticity of quantity demanded in both autarky and free trade. We now
assume that the market structure in sector M is an oligopoly –which allows
us to incorporate the directly pro-competitive e¤ect of trade and examine
its implication. Firms in either country will have to face more competitionx(!)
0
Since x0 (!) > 0 and q 0 (!) < 0; we can de…ne(!) > 0. The[q(!)] , such thatmarket clearing condition (13) implies that, in the free-trade equilibrium,
6(! N )=(! S )

pS
pN

#

:

Suppose pN < pS :Then the above relation implies ! N > ! S , which is contrary to the
Stolper-Samuelson e¤ect implying ! N < ! S : Hence pS pN . Similarly it can be argued
that pN pS. Thus pS = pN and this implies ! N = ! S ; xN = xS and qN = qS :14

in the presence of international trade than in its absence, and this leads toa presumption that free trade leads to quality enhancement in both countries. If PQE holds, then it implies a greater quality jump and at the sametime a catching-up by the Southern …rms, which we have termed as quality
leapfrogging by the South.
However, the formal analysis gets quite complex under oligopoly. To keep
tractability we impose two assumptions. First, let the increasing-returns
technology in producing quantity in sector M be speci…ed by …xed and variable costs, i.e., let the total cost function of producing quantity be of the form:cx (ws ; wu )(xi + ); where
quality,> 0: Second, let the scale elasticity in producing; be constant, i.e., let g(q) be of the form, g(q) = q 1+ =(1 + );0; where= 0 or > 0 signi…es constant or decreasing returns. We begin

with autarky.

3.1

Autarky

In sector Y, the zero–pro…t condition is same as (4), reproduced below forcompleteness.

cy (ws ; wu ) = 1:

(18)

Assume that, in sector M, …rms compete in prices and quality. In view of(3) then, any particular …rm’s price and quality setting rules are15

cx (ws ; wu )
pi

1

#

(19)

= 1

qi pi1 # )= cq (ws ; wu )qi g 0 (qi ):Z(Z

cx (ws ; wu )] xi[pi1) qi p1i #
Z

(#

(20)

Note that these conditions take into account the e¤ect of a change in priceand quality on Z: Under symmetry, these two equations reduce to:1cx (ws ; wu )p[pcx (ws ; wu )] x

#

#

1
n

1

1
n

= 1

(21)

= cq (ws ; wu )qg 0 (q):(22)

The next four equations respective spell, under symmetry, the zero-pro…tcondition, the full-employment conditions and the market-clearing condition
for any variety.

[pcx (ws ; wu )] x

cx (ws ; wu )cq (ws ; wu )g(q) = 0(23)n [cqu (!)g(q) + cxu (!)(x + )] + cyu (!)Y

= Lu

(24)

n [cqs (!)g(q) + cxs (!)(x + )] + cys (!)Y

= Ls

(25)

(ws Ls + wu Lu )
= x:
pn

(26)

Eq. (18) together with (21)-(26) are seven equations having seven variables,
ws ; wu ; p; x; q; n and Y:
16

Unless further structure is imposed, it does not seem possible to compare
the autarky equilibria across North and South. But this is immaterial to theissue of whether FPE and PQE hold in free trade. Therefore, we …rst analyze
FPE and PQE at the present level of generality, and, then consider special
cases illustrating the trade-e¤ects on product quality in each country.

3.2

Free Trade

As countries open up free trade, …rms in each country face competition fromlocal and foreign …rms. Eqs. (19) and (20) still characterize price and quality
setting rules of any particular …rm, except that the term Z include the priceand quality terms of domestic and foreign varieties, i.e.,cx (wsr ; wur )
pr

1
[pr

#

cx (wsr ; wur )] xr(#(ZR1) qr pr1 #ZR= 1

qr p1r # )ZR

where r refers to North or South, and ZR =(27)

= cq (wsr ; wur )qr g 0 (qr ) (28)P

1 #: The zero-pro…tr n r qr p rand the full employment conditions remain the same:[prcx (wsr ; wur )] xr

cx (wsr ; wur )cq (wsr ; wur )g(qr ) = 0(29)

nr [cqu (! r )g(qr ) + cxu (! r )(xr + )] + cyu (! r )Yr = Lur (30)nr [cqs (! r )g(qr ) + cxs (! r )(xr + )] + cys (! r )Yr = Lsr : (31)17Finally, we have the market-clearing condition for any particular variety,expressed as
IR qr= xr ;
p#r ZR(32)

where IR is the world income.
Unlike under monopolistic competition, it is however not a straightfoward
exercise to prove that FPE and PQE hold when both countries incompetely
specialize; this is because the long-run …rm-output is dependent on the relative wage or the product price ratio. A formal –and a rather long –proof isgiven in Appendix B, and thus,
Proposition 2 In free trade equilibrium, as long as each country incompletely specializes, FPE and PQE hold under oligopoly.7
The economic explanation behind product quality equalization underoligopoly is a bit more involved, compared to the monopolistic-competitioncase. Here, quality production depends on relative wage as well as the number of rivals. Note that free trade provides each …rm located in either country
an access to the entire global market. Therefore, each …rm competes withthe same number of …rms. This, together with FPE, implies PQE.
Given that the world economy moves from autarky to the integrated
equilibrium, insofar as the qualitative e¤ects on …rm-output, product price,
7
Following the structure of proving the trade pattern in case of monopolistic competition, it is straightforward to prove that in this model too North is the net exporter ofgood M.

18

product quality and relative wages are concerned, free trade is equivalent
to augmenting a country’s factor endowments to the respective world factor
endowments. The question before us is: how does product quality in eachcountry adjust when there is a regime change from autarky to free trade?
It is however di¢ cult to answer this question at the current level of generality. In what follows, we consider two special cases. In both, the numeraire
good is produced by unskilled labor only so that the unskilled wage is …xed
in terms of this good. For notational simplicity, let the unskilled labor coe¢ cient be one such that the unskilled wage is equal to unity. Since wu is given,
let ws = w denote the relative wage. The special cases di¤er in terms ofassumed factor intensity di¤erence between quantity and quality production
in sector M.
3.2.1

Same Factor Intensities in Producing Quantity and Quality
in Sector M

Suppose that quantity and quality production in sector M are equally skill
intensive, i.e., cx (w)=cq (w) is constant. This implies that a …rm’s quality
choice depends only on product market competition, not on the relative wage.
For notational simplicity choose the unit of q such that cx (w)=cq (w) is equal
to unity. Accordingly, de…ne cx (w) = cq (w)c(w):

In autarky, eqs. (21)-(23) and (25)-(26) reduce topa =na + (# 1) (na 1)c (wa )(# 1) (na 1)

19

(33)

[pa
[pa

c (wa )] xa

c (wa )] xa (nana1)

g(qa )c(wa )

=

(34)
(35)

[ + g(qa )]c (wa ) = 0

na [g(qa ) + xa + ] =Lsc0 (wa )(36)(wa Ls + Lu )= xa :
na pa(37)

These equations solve pa ; qa ; na ; wa and xa .8 The …rst three equations imply

xa =

(#
na

1) (na(na

1)
1)

x(na ); g(qa ) =+na(na 1)(na 1)

q(na ): (38)+Check that both quantity and quality are monotonically increasing functionsof n, showing the pro-competitive e¤ect of an increase in n: Notice that unlike
under monopolistic competition, the long-run output does not depend only
on the …xed-cost parameter, ; and the preference parameter #:Using the expressions in (38), eqs. (36) and (37) are respectively expressedasLs
na [na + (# 1) (na 1)]= 0
na(na 1)c (wa )

(39)

8
The full-employment of unskilled labor essentially determines the output of the numeraire sector, which is independent of how the other variables in the system are determined.

20

w
FF
1

MM
1

n
Figure 1: Determination of w and nna [na + (# 1) (na 1)]=
na(na 1)

wa Ls + Lu:
c (wa )

(40)

Dividing these equations gives
Lu
wa +
Ls

c0 (wa )= 1;c(wa )(41)

which determines wa : As expected, an increase in Lu =Ls implies an increasein wa . Once wa is known; either of (39) and (40) determines na and thereby
output and product quality. In the (w; n) space measuring w along thevertical axis, eq. (39) spells a positive locus, while (41) implies a horizontal
line. These are respectively shown as F F1 and M M1 in Figure 1.

21

Note that while relative wage is a¤ected by relative endowment only, thenumber of …rms, output and product quality are a¤ected by both relative
endowment and absolute endowments. We consider two comparative statics,
which enable us to compare North and South under autarky and compare
free trade to autarky.
1. Suppose the absolute endowment of skilled labor remains unchanged
but its relative endowment increases. Then M M1 curve shifts down, showingthat the relative wage as well as the number of …rms fall. The former e¤ect
is direct, and, as w falls, …rms in sector M adopt a more skill-intensive technique. The total endowment of skilled labor being given, sector M is able tosustain a smaller number of …rms. In turn, less competition implies a lower
output and a lower product quality chosen by a …rm.
2. Suppose the relative endowments are unchanged, but the absoluteendowments increase. Then F F1 shifts to the right, while the M M1 curve
does not shift. As a result, wa is unchanged, while na is higher (i.e. a greater
market size sustains more …rms). More …rms mean more competition andhence a greater output and a higher product quality by a …rm.
Now de…ne North as the country in which both the relative and absoluteendowments of skilled labor are higher. It then follows that under autarky,
waN < waS , while qaN 7 qaS : However, qaN > qaS if the relative endowment di¤erence is small enough or if the sector M is su¢ ciently highly skill
intensive.9 We assume that either of these conditions holds.
9

In the extreme case if sector M uses skilled labor only, the F F1 curve is vertical,
implying qaN > qaS unambiguously.

22

We are now ready to determine the e¤ects of international trade. As
shown earlier, FPE and PQE hold in free trade equilibrium. Furthermore,because North is relatively and absolutely more endowed with skilled labor,
in moving from autarky to free trade it essentially ‘faces’a decrease in therelative endowment and an increase in the absolute endowment of skilledlabor. By similar argument, South faces an increase in the relative andabsolute endowment of skilled labor. By using Figure 1 and applying it to theNorth we …nd that Northern relative wage increases and so does the quality(since the number of …rms in the world economy in free trade exceeds that
under autarky). In the South, the relative wage declines but Figure 1 cannot
unambiguously indicate the direction of change in product quality. However,given that qaN > qaS and product quality improves in the North, PQE implies
that product quality must improve in the South as well.10 Indeed, Southcatches up or erases its ‘quality de…cit’ even in the face of North further
improving its product quality. In summary, as the world economy moves
from autarky to free trade, the relative wage increases in the North and falls
in the South, while product quality improves in both countries, along withquality leapfrogging by the South.
It is worth-emphasizing that oligopoly competition underlies quality leapfrogging. The special case under consideration is able to entirely focus on this by
suppressing the e¤ect of relative wage changes on product quality. Insofar
10International trade is also equivalent to an increase in the absolute endowment of
unskilled labor in each country. But this is immaterial for changes in the variables we areinterested in.

23

as the e¤ect on relative wages is concerned, its decline in the South depends
critically on the assumption of no factor intensity di¤erence between quantityand quality production in sector M. If we had assumed that quality production is more skill intensive, then relative wage would be related to the quality
level and as a consequence leapfrogging can occur together with an increasein the relative wage in both countries. Such a case is considered next.
3.2.2

Quality in Sector M dependent on Skilled Labor Only

This is the case where, in the two extreme ends, the numeraire good is produced by unskilled labor only and the quality production in sector M isundertaken by skilled labor only (with respective input coe¢ cients normalized to one), while quantity production in sector M requires both factors
having a Cobb-Douglas technology. Let cx (w) = w ( < 1) and w denotes
the relative wage.
The following equations characterize the autarky equilibrium:na + (# 1) (na 1) x
c (wa ) = pa(# 1) (na 1)

(42)

[pa

cx (wa )] xa(na 1)
wa g(qa )
=
na

(43)

[pa

cx (wa )] xa

cx (wa )(44)

wa g(qa ) = 0

na [g(qa ) + cxs (wa )(xa + )] = Ls
24

(45)

xa =

(wa Ls + Lu )
:
na pa

(46)

The …rst two equations, the price and quality setting rules, follow from (21)and (22). The next three are respectively the zero-pro…t condition, the fullemployment condition of skilled labor and the market-clearing condition.
Eqs. (42) - (44) imply

xa =

(#
na

1) (na(na

1)
1)

x(na ); g(qa ) =+[na(na 1)(na 1)]b(wa )h(na ; wa );+(47)
where b(w) = cxw(w) : Compared to the earlier special case, note that quality
choice is in‡uenced by the relative wage rate also. Substituting (47) into (45)and (46),
na f

(na

1) + [(#
na
(na

) (na
1)

na [na + (# 1) (na 1)]=
na(na 1)

1) + 1]g= b(wa )Ls

wa Ls + Lu:
cx (wa )

(48)

(49)

These are two equations in two variables, na and wa ; solving the autarky
equilibrium. However, product quality being our focus, it will be convenient
to deal with an equation system having q explicitly as a variable. Towards
this end, we divide the last two equations and obtain

25

w

MM
2

FF
2

q
Figure 2: Determination of Relative Wage and Product Quality(nana + (# 1) (na 1)=
1) + [(#) (na 1) + 1]

wa Ls + Lu
wa Ls

;

(50)

which will be used to evaluate the e¤ect of a relative endowment change.
Next we implicitly invert the function h(n; w) and obtain n = n(g ; w); and++ +view (48) and (50) determining wa and ga : From the de…nition of the g( )function, g and q are one-to-one related. Hence a solution of g is equivalent
to a solution of q.
Appendix B proves that these equations respectively spell a negative relation and a positive relation between wa and qa , shown respectively by F F2
and M M2 curves in Figure 2.
Note that not just the relative endowment but absolute endowments mat26

ter toward the equilibrium relative wage (and quality choice) –because theprice-cost mark-up is not constant. We consider the same two comparative
statics as in the previous special case.
First, suppose that the absolute endowment of skilled labor remains unchanged but its relative endowment increases. Then M M2 shifts to the right.
As a result, wa falls and qa rises. These results are intuitive.
Next, suppose the relative endowments are unchanged, while the absoluteendowments increase. Then F F2 shifts to the right, with the implication thatboth wa and qa increase.
Again, de…ning North as the country in which both the relative and absolute endowments of skilled labor are higher, it then follows that underautarky, qaN > qaS , while waN 7 waS :As before, a movement from autarky to free trade (along with FPE andPQE) means that the North essentially faces a decrease in the relative endowment and an increase in the absolute endowment of skilled labor, while
South faces an increase in the relative and absolute endowment of skilledlabor. In Figure 2, F F2 curve shifts to the right for both countries, while theM M2 curve shifts to the left for the North and to the right for the South.
Thus we obain the following comparison between autarky and free trade: As
the world economy moves from autarky to free trade, in the North the relative wage increases, while product quality may fall or improve, while in theSouth relative wage may increase or decrease but product quality improves.

27Given that qaN > qaS , quality leapfrogging will occur if the North increases it product quality. Observing the shifts of F F2 and M M2 curves it
follows that this will happen if the relative endowment di¤erences are notlarge (implying that the leftward shift of the M M2 curve is relatively small).
Also, in this case, relative wage will rise in the South too, because the e¤ects
due to relative endowment di¤erences are small. Hence, we have following
proposition.
Proposition 3 Quality leapfrogging occurs if (a) the relative endowment difference across countries is small enough or (b) if the skill intensity di¤erence
between quality and quantity production is small enough and the skill intensity
in sector M su¢ ciently exceeds the skill intensity of the numeraire sector.
3.2.3

Relation to the Existing Literature on Trade and Quality
Leapfrogging

There is a literature on quality leapfrogging in the presence of international
trade, meaning a simple catching-up in quality, without the quality leader upgrading its quality further. This is motivated by mutual trade liberalizationor country-speci…c incentives o¤ered to lagging industries in the South.11 For
example, Motta, Thisse and Cabrales (1997) develop a partial-equilibrium
oligopoly model of vertical product di¤erentiation a la Shaked and Sutton(1982), in which one country’s …rm has initial leadership. Their conclusion
is that such leadership is likely to persist in the presence of free international
11

This is di¤erent from quality leapfrogging via basic research in discovering new products or catching up in terms of technology.

28

trade; leapfrogging is possible only if the country sizes are very similar. Herguera and Lutz (1998) consider a similar model and show that leapfrogging
can occur when the lagging country o¤ers special incentives to its industry.12
Compared to this literature, the distinguishing features of our analysis arethat we consider a more general oligopoly with entry and exit and that too
in a general-equilibrium framework in which the costs of producing quality
and quantity change in response to international trade - with the implicationthat the initial leader (the North) may further improve its product quality.
Quality leapfrogging occurs, not in terms of new technology adoption, but
in response to competition under given technologies of producing quality andquantity.

4

Concluding Remarks

The literature on product quality and trade policy is vast. Yet, how free trade
may induce a change in product quality does not seem to have been addressed
adequately. While the partial-equilibrium models are not designed to address
this issue, the existing general-equilibrium models typically classify productbrands according to their quality in an exogenous fashion and analyze whichcountries would have comparative advantage which brands –rather than how
the quality levels of the brands themselves respond to a change in the trade
regime. This paper has developed a baseline, factor-endowment framework,in which the technologies of quantity and quality production are given and
12This paper also cites useful empirical evidences on quality leapfrogging.

29

available to all (both) trading countries. The model is a hybrid one having
both horizontal and vertical product di¤erentiation. Quality choice by …rms
responds to relative wage changes and changes in the degree of competition.
There are two central results. First, factor price equalization (FPE) is shown
to imply product quality equalization (PQE). Second, oligopoly competition
may imply that product quality improves due to trade in both North andSouth and yet South leapfrogs and erases the quality de…cit in the FPE-PQE
equilibrium.
In the oligopoly model in particular, we have assumed that …rms treat
price and quality as their strategies. Other combinations are possible ofcourse. However, the micro structure of demand based on the generalized
Dixti-Stiglitz utility function makes it extremely hard to analytically deal
with other pairs of strategic variables among price, quantity and quality, e.g.
quantity and quality. But oligopoly …rm behavior would yield quality as afunction of relative wage and the degree of competition (the number of …rms)
and therefore the basic insights of our analysis are likely to go through.
The key notion of our model is that of production of quality, not necessarily as a technology innovation but as an outcome of factor combinations. In a
dynamic, endogenous-growth framework, it will be interesting to di¤erentiate
between basic innovation resulting in the form of a jump in potential quality
and actual quality upgrading based on new technology as well as factor useor organization.
Also, while, in order to emphasize the implications of factor endowment30

di¤erences, our model maintains the assumption of identical technologies
of both quantity and quality production, the analytical di¤erence between
these two concepts is applicable to the issue of technology transfer between
North and South –insofar as it leads to a di¤erence between potential quality
achievable and actual quality achieved.

31

References
Copeland, B. and A. Kotwal, ”Product Quality and the Theory of Comparative Advantage,”European Economic Review, 40, 1996, 1745-1760.
Das, S. P., ”Trade and Relative Wages in a Global Economy,” Review ofInternational Economics, 11, 2003, 397-411.
Das, S. P. and S. Donnenfeld, ”Oligopolistic Competition and International Trade: Quantity versus Restrictions,” Journal of International
Economics, 27, 1989, 299-318.
Deming, W. E., Out of the Crisis, MIT Press, Cambridge, MA., 1986.
Dixit, A. and V. Norman, International Trade, 1980, Cambridge: Cambridge University Press.
Flam, H. and E. Helpman, ”Vertical Product Di¤erentiation and NorthSouth Trade,”American Economic Review, 1987, 810-822.
Falvey, R. E., ”The Comparison of Trade within Import-Restricted ProductCategories,”Journal of Political Economy, LXXXVII (1979), 1105-14.
Falvey, R. E. and H Kierzkowski, ”Product Quality, Intra-Industry Tradeand (Im)Perfect Competition” in Protection and Competition in International Trade: Essays in Honour of Max Corden, edited by H.
Kierzkowski, 1987, Basil Blackwell.
Grossman, G. M. and E. Helpman, Innovation and Growth in a Global
Economy, The MIT Press, 1993.
Herguera, H. and S. Lutz, ”Oligopoly and Quality Leapfrogging,” The
World Economy, 21, 1998, 75-94.
Krugman, P., ”Increasing Returns, Monopolistic Competition, and International Trade,”Journal of International Economics, 9, 1979, 469-479.
Motta, M., J.-F. Thisse and A. Cabrales, “On the Persistence of Leadership or Leapfrogging in International Trade,” International Economic
Review, 38, 1997, 809-824.
Murphy, K. M. and A. Shleifer, “Quality and Trade,” Journal of Development Economics, 53, 1997, 1-15.
Rodriguez, C. A., ”The Quality of Imports and the Di¤erential WelfareE¤ects of Tari¤s, Quotas, and Quality Controls as Protective Devices,”
Canadian Journal of Economics, 12, 1979, 439-49.
32

Shaked, A. and J. Sutton, “Relaxing Price Competition Through ProductDi¤erentiation,”Review of Economic Studies, 49, 1982, 3-13.
Zhou, D., Spencer, B. J. and I. Vertinsky, ”Strategic Trade Policy with
Endogenous Choice of Quality and Asymmetric Costs,” Journal of International Economics, 56(1), 2002, 205-232.

33

AppendicesA

The Monopolistic Competition Model

A.1

Relative Supply Curve: Constant-Returns in Quality Production

Given x = x, the zero-pro…t condition in sector Y, namely, (4) and theprice-setting rule in sector M, (5), yield the Stolper-Samuelson expressions:

w
cs =

y
b
up

j j

x

; w
cu =

y
b
sp

j j
x

pb
; j j=
j j

; !
b=

x y
s u

y

x y
u s > 0(A.1)

ywhere xs = wcsxcs , xu = !cuxcu ; ys = wcsycs and yu = wcuycu : Again using x = x,from the quality-setting rule (7), we obtain qb + cbq cbs = 0; implying
qb + ( qs

x
!=0
s )b

(A.2)

If q ; x and y denote the elasticity of factor sustitution respectively in
producing quality in sector M, output in sector M and output in sector Y,
working through the standard Jones’algebra leads tocbxs =x xb;u!

cbqs =

cbxu =

q q
b;
u!

x x
b;
s!

cbqu =

cbas =

q q
b
s!

(A.3)

y y
b;
u!

cbau =

y y
b:
s!

(A.4)

= 0

(A.5)

= 0

(A.6)

Next, totally di¤erentiate the full-emplyment equations (10) and (11) atgiven Ls and Lu . De…ne qu ( qs ) as the proportion of unskilled (skilled) labor
employed in quality production to the total size of unskilled (skilled) labor
0employment in sector M. Also de…ne mj as the share of factor j s employment
yin sector M and similarly j as the share of factor j 0 s employment in sector
Y, where j = s; u. Then we have
m
u

h

n
b+
h
m
b+
s n

q
u
q
s

cbqu + qb + (1cbqs + qb + (1q bxu ) cu34iq bxs ) cs

i

+

y
u

+

y
s

cbyu + Yb
cbys + Ybm yy
De…ne j j = m
u s , which is positive by our factor-intensity assumps ution. Using (A.1), (A.2), (A.3)and (A.4), eqs. (A.5) and (A.6) imply

j j

n
b

pb

Yb

= [ m
s (1
+

q
s)

x x
u+
y y y
s +
u

y y y
u+
s

m
u (1

q
u)

x x
s +

Lqs
Ls

Lqu
Lu

q
s

m q q q
u+
s s
x
s

j j

> 0;

m q q q
s
u u

(A.7)

Lqs
Lx
Lq
Lq
Ly
> u as qs > xs > ys :
Lu
Lu
Lu
Ls
Lu
The sign of the expression in (A.7) proves that the relative supply curve
is upward sloping.
since

A.2

q
s >

x
s;

and

Trade Pattern

It is straightforward to demonstrate that at the trading equilibirum where
FPE and PQE hold, the North is the net exporter of good M.
North’s expenditure on good M equals wsR LsN + wuR LuN . The valueof production of good M in the North is equal to nN pR x. Global market
clearing of any variety is given by x = nRIpRR ;where nR = nN + nS . Hence
North is a net exporter of good M if and only if
wsR LsN + wuR LuN <nN
wsR LsR + wuR LuR :
nR

(A.8)

Here LsR = LsN + LsS and LuR = LuN + LuS :In free trade equilibrium, nN is solved from the equations, cu nN + cyu YN =LuN and cs nN +cys YN = LsN , where cu (cs ) is the unskilled (skilled) labor usedby a …rm in sector M and cyu (cys ) is the unskilled (skilled) labor coe¢ cient insector Y (see (A.11) and (A.12 later). We havecyu LsN cys LuN:(A.9)
cs cyu cu cys
Given our factor-intensity, the numerator and the denominator are both positive. Likewise, nR is solved from (A.13) - (A.14) and has the expression:nN =cyu LsRnR =cs cyu35

cys LuRcu cys(A.10)

Substituting (A.9) and (A.10), (A.8) is equivalent to
LsN! R LsN + LuN<! R LsR + LuR
LsR

k y LuNLsN,
k y LuR
LuN

LsR> 0; where k y
LuR

cys
:
cyu

This is true since the North is relatively more endowed with skilled labor.
It then proves that the North is the net exporter of good M.

A.3

Integrated Equilibrium and Pattern of Specialization

In the integrated equilibrium both goods are produced and consumed in theworld economy. De…necu (!(pR ))cqu (!(pR ))q(!(pR )) + cxu (!(pR ))f (x) ;(A.11)

cs (!(pR ))cqs (!(pR ))q(!(pR )) + cxs (!(pR ))f (x) :(A.12)

Then the equations
cu (!(pR ))nR + cyu (!) YR = LuR(A.13)

cs (!(pR ))nR + cys (!) YR= LsR(A.14)

wu LuR + ws LsR
nR pR= xR ;(A.15)

determine the world price ratio, pR , and the world outputs, nR and YR .
Letting pR ; nR and Y R denote the solutions, !(pR ) ! R is the equilibrium
relative wage.
In Figure 3, if 0N is the origin, then 0S represents the world endowment
point. The rays, km and ky , measure the overall skilled to unskilled labor
empolyment ratio in sector M and Y respectively.13 The points Bm and By
respectively mark the solutions of nR and Y R . Alternatively, if 0S is taken
as the origin, 0N is the world endowment point, and Bm and By respectively
denote the solutions Y R and nR .
13

Since both quantity and quality productions are more skill-intensive compared to the
production of good Y, km is steeper than ka :

36

km

LRu

0S

LRs
nR

Bm

cs ( w R )cu ( w R )c sa ( w R )cua ( w R )

YR
Ba

ka

LRs
0N

LRu

Figure 3: Integrated Equilibrium in the Monopostic-Competition Model37

Now, if the integrated economy is separated into two countries, Northand South, by standard arguments, FPE holds as long as the point representing the endowments of North and South lies within the parallelogram
0N Bm 0S By ; otherwise, complete specialization occurs in equilibrium in atleast one country.

B

Oligopoly Model

B.1

Proof of FPE and PQE

The zero-pro…t condition cy (ws ; wu ) = 1 implicitly gives wu as a monotonically decreasing function of the relative wage: Substituting this function intocx (ws ; wu ) and cq (ws ; wu ) yields cx and cq as functions of ! only and as !
increases, cx and cq increase, since producing quantity and quality in sector
M is relatively more skill intensive than the technology in sector Y. Denotethese functions respectively as cx (!) and cq (!): De…ne b(!) cq (!)=cx (!):
We have b0 (!) > 0; as quality production is more skill intensive than quantity
production.
We now substitute cx (!) and cq (!) for cx (wsr ; wur ) and cq (wsr ; wur ) respectively in eqs. (27) - (29).
>From (27) and (28), eliminate qr p1r # =ZR and obtainb(! r )qr g 0 (qr ) = xr ; where

=(#

1):

(A.16)

Substitute (A.16) into the zero-pro…t condition (29) and obtain
1+

+

xr

=

pr
c (! r )x(A.17)

Write (32) as
qr p r # =xr; whereIR =ZR :(A.18)

Next substitute (A.17) and (A.18) into (27) and eliminate qr pr # and pr =cx (! r ):We
obtainZR#(# 1) xr

+ (1 +) xr= pr :+
xr

38(A.19)

Dividing (A.19) by (A.17) givescx (! r ) =(#ZR1)[ + (1 +)xr ]+ (1 +
)xr
:
+
xr

#

(A.20)

Verify that this equation spells a negative relation between ! r and xr :Next, using g(q) = q 1+ =(1 + ); we write (A.16) as q = [ xr =b(! r )]1=(1+ )and substitute this into the market-clearing condition (A.18). This gives
p# x1=(1+ )

1+=:b(! r )

Now substitute (A.19) into the above and obtain
1
#+
xr 1+

+ (1 +
)xr #
] =
+
xr

[#
1

#

1

#

ZR

1+

[b(! r )] 1+:(A.21)In this equation, check that ! r and xr are positivey related.
We can now prove FPE and PQE. Suppose that in the trading equilibrium
wN > wS : Then (A.20) implies xN < xS , but (A.21) implies xN > xS , acontradiction. Similar contradiction arises if wN < wS : Hence it follows thatwN = wS ; implying xN = xS ; pN = pS and in particular qN = qS :B.2

Slopes of F F2 and M M2 Schedules

For notational simplicity, let us drop the ‘autarky’subscript a. Totally differentiating the h( ) function in (47),
n
b=

(n

1) [n

(n

1)] [bg + (1)w]
b;n
The F F2 schedule graphs the full-employment equation (48).
di¤erentiating this and utilizing (A.22), we obtain+ (#) ] n2(n 1)2gb+ (#) ] (n 1) +(n 1)] f[#(n 1)2 1] + (n 1)2
nf + [+ (#) ] (n 1)g(A.22)
Totallyn 1+ nn 1 [
n

=

(1

[
) [n

39

(A.23)
(1

)g

b
w
b+L
s

The co-e¢ cient of gb is positive, while that of w
b is negative as long as thenumber of …rms, n, is two or higher. This proves that the F F2 schedule isnegatively sloped.
Consider eq. (50), de…ning the M M2 schedule. Since < 1; we havewLs + Lu
>
wLs
,

(n

Lu
(1
>
wLs + Lu# (n 1) + 1
1) + [(#
) (n
) [(#
# (n

1) + 1]) (n 1) + 1]
1) + 1(A.24)

Totally di¤erentiating (50) and using (A.22) once again, we obtain

=

[# (n
(

(1
) (n 1) [n1) + 1] + (n 1) [Lu
wLs + Lu[# (n(n 1)]
gb
+ (#
) ]

(1
)2 (n 1) [n1) + 1] f + (n 1) [(n 1)]
+ (#
) ]g

)

w
b

c
Lu
L
u
wLs + Lu Ls

The coe¢ ent of gb; and, in view of (A.24), the coe¢ cient of w
b are both positive,
proving that the M M2 schedule has a positive slope.

40