A Decomposition of the Home-Market EﬀectToru Kikuchi∗
Graduate School of Economics, Kobe University, Kobe 657-8501, JapanandNgo Van Long
Department of Economics, McGill University, Montreal H3A 2T7, CanadaMay 6, 2010

Abstract
Although the home-market eﬀect has become one of the most important concepts in both trade theory and the new economic geography,
it lacks a compelling graphical representation. The purpose of thisnote is to oﬀer such a representation. We will decompose the homemarket eﬀect into two steps: a short-run response to population shift,creating entry-stimulating excess proﬁts (in the short run) for ﬁrms ofthe country that experiences a population gain, and a further round ofentries into the monopolistic sector of the expanding country induced
by exits in the foreign industry.
JEL classiﬁcation: F12
Keywords: Monopolistic Competition; Home-Market Eﬀect; EntryExit Process∗E-mail addresses: kikuchi@econ.kobe-u.ac.jp (Kikuchi), ngo.long@mcgill.ca (Long).

1

1

Introduction

The monopolistic competition model, characterized by increasing returns
and diﬀerentiated products, is a major workhorse of the “New Trade Theory.” Originally conceived by Joan Robinson and Edward Chamberlin in the1930’s, it became highly useful after the mathematical formulation by Dixitand Stiglitz (1977). In their seminal contributions, Krugman (1980) andHelpman and Krugman (1985, ch. 10.4) demonstrate that under monopolistic competition, country size determines the net trade ﬂows in diﬀerentiatedproducts when trade is subject to trade costs. The key idea is what is called
the home-market eﬀect: if two countries diﬀer only in size, in the presenceof trade costs, the larger country will end up with a more-than-proportional
share of the production of diﬀerentiated products.1
The home-market eﬀect has become one of the most important concepts
in both trade theory and the new economic geography.2

Still, it lacks acompelling graphical representation. The purpose of this note is to oﬀer
such a representation. We will decompose the home-market eﬀect into twosteps: a short-run response to population shift, creating entry-stimulatingexcess proﬁts (in the short run) for ﬁrms of the country that experiences apopulation gain, and a further round of entries into the monopolistic sectorof the expanding country induced by exits in the foreign industry. Our experience indicates that this graphical approach helps the reader to gain, almost
eﬀortlessly, a clear understanding of the home-market eﬀect.
The next section presents the basic model. The nature of the trading1

In a review of the scientiﬁc contribution of Paul Krugman, Neary (2009, p. 233) argues

that this was to prove perhaps the most innovative of his contributions.
2See, for example, Brakman, Garretsen, and van Marrewijk (2009, ch. 1), Combes,Mayer and Thisse (2008, ch. 4), and Feenstra (2004, ch. 5). Applications of economic
geography to open-economy macroeconomics include Alesina and Barro (2002).

2

equilibrium is considered in Section 3, followed by concluding remarks inSection 4.

2

The Model

Suppose that there are two countries: Home and Foreign. Home (resp. Foreign) is endowed with L (L∗ ) units of labor, which is the only primary factorof production. The countries have identical technologies.
Each country produces two consumption goods, Good X (diﬀerentiatedproducts) and Good Y (homogeneous goods). Good Y is sold in a perfectlycompetitive market, while Good X is sold in a monopolistically competitivemarket. Good Y is produced under constant returns using only labor; units
are chosen such that one unit of labor produces one unit of output. Wagerates are normalized to unity. International trade of Good X incurs “iceberg”
transport costs, meaning that for every τ units of Good X shipped fromabroad, only one unit arrives. This raises the price to consumers of animported variety from p∗ to τ p∗ , where p∗ is the mill price and τ > 1 isthe transport cost factor.
In each country, agents have the following utility function:u = X µ Y 1−µ , 0 < µ < 1,(1)where Y is the consumption of Good Y and X is an aggregator of the consumption of the diﬀerentiated products,
X=[ n∑i=1]1/ρ∗ρ(ci ) +n∑(c∗i )ρ

, 0 < ρ < 1.

(2)

i=1

Consumption of each variety is given by ci , σ ≡ 1/(1 − ρ) > 1 is the elasticityof substitution between every pair of Good X varieties, and n (resp. n∗ ) is
the numeber of Home (resp. Foreign) varieties, respectively.
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The price index for Good X (which is dual to the aggregator X) is represented by
PX =[ n∑](ρ−1)/ρ

∗ρ/(ρ−1)

(pi )

+i=1n
∑

(τ p∗i )ρ/(ρ−1)

(3)

i=1

Home consumers’ demand for a Home product isc = p−σ (PX )σ−1 µL.

(4)

Similarly, the derived demand (i.e. including units lost by iceberg transportcosts) for a Foreign product from Home consumers isc̃ = τ (τ p∗ )−σ (PX )σ−1 µL.

(5)

The production of a diﬀerentiated product involves a constant marginal
cost β and α units of labor as a ﬁxed cost. With the total number of products available to consumers being very large, each producer sets its price byapplying a constant markup factor on marginal costp = p∗ =σβ.
σ−1(6)

Free entry ensures that proﬁt is zero in the long-run, hence the long-run
equilibrium output of each variety, x, is a constant, independent of the levelof trade costs:α(σ − 1).
(7)
βBefore moving to the trade equilibirum, it is important to note the entryx=exit process. If in the short-run, the demand for a diﬀerentiated productexceeds the long-run equilibrium output x, there are positive proﬁts, which
creates an incentive for new ﬁrms to enter the industry. Conversely, if theshort-run demand is smaller than x, some ﬁrms will exit. This entry-exit
process plays an important role in determining the degree of the home-market
eﬀect.
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3

Trade Equilibrium

Turning to the trade equilibrium with positive trade costs, the product market equilibrium requires that supply equal demand for each Home product:x = c + c̃∗ ≡ C(8)

By substituting (4) for c, the Foreign counterpart of (5) for c̃∗ , into equation(8) and denoting φ ≡ τ 1−σ < 1 we obtain the following aggregate demand
for a Home product (C) and its Foreign counterpart (C ∗ ):
()

µL
L∗
C =,+p n + φn∗ n + (n∗ /φ)
()
LµL∗
∗
C =+.
p (n/φ) + n∗ φn + n∗

(9)
(10)

Figure 1 depicts the relationship between the number of varieties in eachcountry, n and n∗ , and the level of demand for each variety, C and C ∗ .
Aggregate demands are depicted as the curve CC in panel (a) (i.e., the spacen, C), and curve C ∗ C ∗ in panel (b) (i.e. the space n∗ , C ∗ ), respectively. The
long-run equilibrium output level x is represented as the intersection of thehorizontal line ZZ with the vertical axis. The initial equilibria are depictedby points E and E ∗ . Along the curve CC (resp. C ∗ C ∗ ), we treat n∗ (resp.
n) as an exogenous variable.
∂C∂n∂C∂n∗[]µLφ2 L∗= −+< 0,p (n + φn∗ )2 (φn + n∗ )2][µφL∗
L= −+< 0.
p (n + φn∗ )2 (φn + n∗ )2(11)(12)Equation (11) implies that the curve CC is decreasing in n, while (12) indicates that the curve CC is shifted downward when there is an increase inn∗ .
5Now suppose that an exogenous labor movement from Foreign to Home
occurs: in Home, the labor force becomes L+∆L, while in Foreign, the laborforce becomes L∗ − ∆L. We can decompose the movement toward the newequilibrium into two steps.
Step 1: Firstly, suppose that in the short run, the number of varieties
in each country is ﬁxed: The increase in L, combined with the decreasein L∗ , shifts the curve CC is upward (dotted C 0 C 0 ) because φn∗ < n∗ /φ,while the curve C ∗ C ∗ is shifted downward (dotted C ∗0 C ∗0 ). The new shortrun equilibrium is obtained as point E 0 (resp E ∗ ’). Thus each Home (resp.
Foreign) ﬁrm experiences an increase (resp. decrease) in demand relative toits long-run output level x. Since the price stays put at βσ/(σ − 1) while
average ﬁxed cost falls in Home, proﬁt rises for each Home ﬁrm. Similarly,
proﬁt falls for each Foreign ﬁrm. These changes trigger the entry of newﬁrms in Home, while exits begin to occur in Foreign, which are shown asarrows in each panel. (If exits did not occur in Foreign, the new equilibrium
number of Home ﬁrm would be indicated by the intersection of the dotted
C 0 C 0 curve and the line ZZ.)
Step 2: The above entry-exit process gives rise to a second round of curve
shifting, and thus a second round of entries and exits. C 0 C 0 is shifted furtherup by a reduction in n∗ (to C 00 C 00 ), while C ∗0 C ∗0 is shifted further down by anincrease in n (to C ∗00 C ∗00 ). Thus the new long-run equilibrium is obtained as
the point E 00 (for Home) and E ∗00 (for Foreign). It is important to note thatthe second round constitutes the main source of the “home-market eﬀect.”
Expenditure shifting between countries triggers an entry-exit process in eachcountry, which reinforces the ﬁrst entry-exit process. This demonstrates thata change in the relative size of a country’s market has a magniﬁed eﬀect on
the relative size of its Good X sector.

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Proposition 1 (Krugman): If two countries diﬀer only in terms of size,
the larger country will end up with a more-than-proportional share of world
output of diﬀerentiated products.
Finally, we can point to the “home-market magniﬁcation.” Freer trademagniﬁes the degree of relocation that comes from a given shift of population.
In other words, industry becomes more footloose, not less footloose, as trade
gets freer.

4Concluding Remarks

We have decomposed the home-market eﬀect into two steps: a short-run
response to population shift, creating entry-stimulating excess proﬁts (in theshort run) for ﬁrms of the country that experiences a population gain, and afurther round of entries into the monopolistic sector of the expanding country
induced by exits in the foreign industry. Our diagrammatic representation
illustrates the process in an intuitive way. A similar diagrammatic approach
can be used to show how freer trade magniﬁes the home-market eﬀect.

References[1] Alesina, Alberto and Robert J. Barro (2002): Currency Unions, Quarterly
Journal of Economics, Vol. 117 (2), pp 409-436.
[2] Brakman, Steven, Harry Garretsen, and Charles van Marrewijk (2009)
The New Introduction to Geographical Economics, Cambridge, Cambridge University Press.

7[3] Combes, Pierre-Philippe, Thierry Mayer, and Jacques-Francois Thisse(2008) Economic Geography: The Integration of Regions and Nations,Princeton, NJ: Princeton University Press.
[4] Dixit, Avinash K., and Joseph Stiglitz (1977) “Monopolistic Competitionand Optimum Product Diversity,” American Economic Review, Vol. 67,
pp. 297–308.
[5] Feenstra, Robert C. (2004) Advanced International Trade: Theory andEvidence, Princeton, NJ: Princeton University Press.
[6] Helpman, Elhanan and Paul Krugman (1985) Market Structure and Foreign Trade, Cambridge, MA: MIT Press.
[7] Krugman, Paul (1980) “Scale Economies, Product Diﬀerentiation, andthe Pattern of Trade,” American Economic Review, Vol. 70, pp. 950–959.
[8] Neary, J. Peter (2009) “Putting the ‘New’ into New Trade Theory: PaulKrugman’s Nobel Memorial Prize in Economics,” Scandinavian Journalof Economics, Vol. 111, pp. 217–250.

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Figure 1(b)

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