Multi-Product Firms and Trade Liberalization

TL;DR: This paper developed a general equilibrium model of international trade that features selection across multiple products, products and countries, where firms' export decisions depend on a combination of product productivity and country consumer tastes.

Abstract: This paper develops a general equilibrium model of international trade that features selection across …rms, products and countries. Firms’export decisions depend on a combination of …rm “productivity”and …rm-product-country “consumer tastes”, both of which are stochastic and unknown prior to the payment of a sunk cost of entry. Higher-productivity …rms export a wider range of products to a larger set of countries than lower-productivity …rms. Trade liberalization induces endogenous reallocations of resources that foster productivity growth both within and across …rms. Empirically, we …nd key implications of the model to be consistent with U.S. trade

Summary

1. Introduction

• Firms producing multiple products dominate domestic production and international trade.
• The introduction of endogenous product scope creates a new margin of firm adjustment, which generates novel firm and industry dynamics in response to trade liberalization.
• As a result, some of the increase in the ex post profitability required for the expected value of entry to equal the new higher sunk cost of entry is achieved through an expansion of product scope, implying a dampened decline in the zero-profit productivity cutoff.
• Even though product scope contracts for all firms, declining trade costs result in an increase in both the share of products exporters sell abroad as well as their level of exports in each product.
• 6 Nocke and Yeaple (2006) develop a theory of multi-product firms in which firms vary in terms of a single dimension, "organizational capability", and in which a firm's productivity for all of its products declines with the number of products manufactured.

2. Empirical Motivation

• The authors model and its assumptions are motivated by a series of stylized facts about multi-product firms reported by Bernard, Redding and Schott (2006b) and Bernard, Jensen and Schott (2005), henceforth BRS and BJS, respectively.
• These facts document the importance of multi-product firms for aggregate production and trade as well as the substantial heterogeneity of products within firms.
• Column two of Table 1 reports an analogous decomposition of U.S. firm-product exports in 2000 using trade data from BJS.
• One of the distinguishing features of the model that the authors develop below is a positive correlation between firms' extensive and intensive margins.
• The authors find that product fixed effects account for 30 percent of the variation in the firm-product shipments of multi-product firms and 28 percent of the variation for all firms.

3. The Model

• The authors consider a framework where firms can choose whether to participate in multiple product markets and compete with one another in supplying horizontally differentiated varieties within those product markets.
• Products are imperfect substitutes in demand and require specific production expertise.
• The model can be interpreted as capturing an economy consisting of many products or as capturing an industry (e.g. consumer electronics) with many products (e.g. DVD-players, Televisions and MP3-players) of which firms supply distinct varieties (e.g. Sony, JVC and Panasonic).

3.1. Preferences

• The representative consumer derives utility from the consumption of a continuum of products which the authors normalize to the interval [0, 1].
• There is a constant elasticity of substitution across products so that the utility function takes the following form: EQUATION where i indexes products.
• Within each product market, a continuum of firms produce differentiated varieties of the product, so that C i is a consumption index which also takes the constant elasticity of substitution form: EQUATION ) where ω indexes varieties.

3.2. Production Technology

• The specification of entry and production follows Melitz (2003).
• The two distributions g (ϕ) and z (λ) are independent of one another and common to all firms, and the product expertise distribution is independently and identically distributed across products.
• 14 Once the sunk cost has been paid, and firm ability and product expertise are observed, firms decide whether to enter and in which product markets to participate.
• While their formulation captures these features in an intuitive and tractable way, one could also generate idiosyncratic variation in firm-product productivity from a pairwise interaction between firm and product characteristics.
• 15 We analyze a setting with two factors of production, skilled and unskilled labor, in Section 9. firm ability and product expertise.the authors.the authors.

3.3. Firm-Product Profitability

• Demand for a product variety depends upon the own variety price, the price index for the product and the price indices for all other products.
• At the same time, the price of firm's variety in one product market only influences the demand for its varieties in other product markets through the price indices.
• 17 This optimization problem yields the standard result that the equilibrium price of a product variety is a constant mark-up over marginal cost: EQUATION where the authors choose the wage for the numeraire and so w = 1.
• From equation ( 9), the ratio of revenue for two varieties of the same product depends solely on their relative productivities: EQUATION 17 The structure of their model eliminates strategic interaction within or between firms.
• The zero-profit cutoff for product expertise for a firm with ability ϕ * is defined by: EQUATION ).

3.4. Firm Profitability

• A firm with a particular ability draw ϕ decides whether or not to enter based on a comparison of the fixed headquarters cost and total profits across those products where its product expertise draw λ i is greater than the zero-profit cutoff λ * (ϕ).
• With a continuum of identical products and independent draws for product expertise, the law of large numbers implies that a firm's expected revenue across the continuum of products equals its expected revenue for an individual product.
• Total profits across products equal expected profits for an individual product minus fixed headquarters costs.
• The lower the ability of a firm ϕ, the higher the zero-profit cutoff for product expertise λ * (ϕ), and so the lower the probability of drawing a product expertise sufficiently high to profitably manufacture a product.
• For sufficiently low draws of firm ability, the excess of revenue over fixed production costs in the small range of profitable products falls short of the fixed headquarters cost.

3.5. Free Entry

• Firms from the competitive fringe decide whether or not to enter based on a comparison of the expected value of entry and the sunk entry cost.
• The authors assume that there is a constant exogenous probability of firm death (δ), as a result of force majeure events beyond the manager's control, which generates ongoing firm entry and exit.
• The expression for average firm profits conditional on entry π is analogous and takes expectations over values for ability in equation ( 14).

3.6. Goods and Labor Markets

• The steady-state equilibrium is also characterized by stationary distributions of firm ability and product expertise that are determined by the zero-profit cutoffs ϕ * and λ * (ϕ) and that are again the same across products.
• Therefore, the mass of firms manufacturing an individual product is the following fraction of the mass of firms: EQUATION.
• With a constant mass of firms producing in steady-state, the mass of firms that draw an ability sufficiently high to enter must equal the mass of firms that die, implying the following steady-state stability condition: EQUATION.
• Finally, labor market clearing implies that the demand for labor in production and entry equals the economy's aggregate supply of labor: EQUATION where the subscripts q and e respectively denote labor used in production and entry.

4.1. Multi-Product Firms

• The authors begin by determining the zero-profit cutoff for expertise for every firm as a function of its ability and the zero-profit cutoff for ability ϕ * .
• In contrast, an increase in the zero-profit cutoff for ability ϕ * raises a firm's zero-profit cutoff for expertise λ * (ϕ) because it raises the average productivity of rival firms' products, and so intensifies product market competition, and hence increases the value for expertise at which sufficient revenue is generated to cover fixed production costs.
• Intuitively, a higher fixed production cost raises the equilibrium level of product revenue needed for zero profits to be achieved.
• Similarly, increases in the elasticity of substitution reduce the revenue of low-expertise products relative to that of higher expertise products.
• The relationship between a firm's product scope and its ability is illustrated graphically in Figure 1 .

4.2. Free Entry

• Intuitively, a higher value of ϕ * implies a higher average ability of a firm's competitors and so lower average prices of competing varieties, which reduces average firm revenue and average firm profits.
• Similarly, a higher value of λ implies a higher average product expertise of the varieties manufactured by competitors and hence lower average prices of competing varieties.
• The free entry condition in equation ( 24) implicitly defines a unique zero-profit cutoff for ability as a function of model parameters alone.
• As the product fixed production cost (f p ) rises, so does the zero-profit cutoff for ability (ϕ * ), since a higher productivity is required in each product to generate sufficient revenue to cover the fixed production cost, and greater ability raises productivity in all products.
• Increases in either the fixed headquarters cost (f h ) or the sunk entry cost (f e ) reduce the zeroprofit cutoff for ability via the same logic discussed above: as the fixed headquarters cost rises, the ex post profits of firms across all products decline, thereby depressing entry and diminishing product market competition.

4.3. Goods and Labor Markets

• Therefore, aggregate revenue equals the economy's aggregate supply of labor, R = L, and the labor market clears.
• The authors are now in a position to determine the price index for each product, which depends on average variety prices and the mass of firms producing each product in equation ( 18).
• Average variety prices have already been determined above.
• The mass of firms producing any product equals aggregate revenue divided by average firm revenue, M = R/r, where the authors have solved for both aggregate and average firm revenue.
• The constant fraction of firms that produce each product depends solely on the zero-profit cutoff for firm ability ϕ * and the zero-profit cutoffs for expertise λ * (ϕ) for which the authors have already solved.

5. Properties of the Closed Economy Equilibrium

• On the one hand, the firm charges a lower price for products where it has higher productivity and as a result enjoys higher sales.
• A given increase in firm ability leads to a larger increase in firm size than it would with exogenous product scope because of firms' endogenous expansion along their extensive margins.
• As a result, the zero-profit cutoff for ability below which firms exit is higher when product scope is endogenous than when all firms manufacture the same exogenous range of products.
• Therefore, as shown formally in the proof of Proposition 2, the reduction in firm weighted-average productivity from expanding into lower expertise products cannot outweigh the increase caused by enhanced productivity in existing products, which implies that firm weighted-average productivity is monotonically increasing in ability.
• Intuitively, as the sunk entry cost rises, entry declines and product market competition is diminished.

6. Open Economy

• The authors denote domestic market variables with a superscript d and export market variables with a superscript x.
• There are fixed costs of operating across national borders, such as the costs of mastering customs procedures and building distribution networks.
• There are also fixed costs of entering export markets that are specific to individual products, such as costs of market research, advertising and conforming to foreign regulatory standards.
• As more products are exported, total fixed exporting costs rise, but average fixed exporting costs fall because the headquarters costs of becoming an exporter are spread over a larger number of products.

6.1. Consumption and Production

• The combined revenue from a product depends upon whether or not it is exported: EQUATION ) Consumer love of variety and fixed production costs imply that no firm ever exports a product without also selling it in the domestic market.
• The combined profit from a product is therefore: EQUATION.

6.2. Firm-Product Profitability

• Manipulating the zero-profit condition for expertise for firms with different abilities ϕ yields the same expressions for the equilibrium range of products manufactured as in equations ( 22) and ( 23).
• The zero-profit cutoffs for firm ability (ϕ * ) and product expertise (λ * (ϕ)) will differ between the closed and open economies and thus induce differences in equilibrium product scope.
• The intuition underlying this relationship in the export market is analogous to the intuition underlying the similar relationship in the domestic market (equation ( 22)).
• As the exporting cutoff for ability ϕ * x increases, the average productivity of the product varieties supplied to the export market by rival firms increases, which intensifies export market competition, and so raises the exporting cutoff for product expertise.
• Since revenue in the export market is proportional to revenue in the domestic market, there is an equilibrium relationship between the exporting and zero-profit cutoffs for expertise.

6.3. Firm Profitability

• The authors noted earlier that no firm ever exports a product without also selling it in the domestic market.
• 25 As in the closed economy, with a unit continuum of identical products, firm profits from domestic sales equal expected profits from domestic sales in an individual product market minus fixed headquarters costs.
• Only firms who draw an ability equal to or greater than ϕ * enter, and the zero-profit cutoff for ability varies between the closed and open economy, as established below.
• For sufficiently low draws of ability, the excess of revenue over fixed exporting costs in the small range of products that the firm could profitably sell abroad falls short of the exporting headquarters cost.
• Such products are supplied to the domestic market but not exported.

6.5. Goods and Labor Markets

• The steady-state equilibrium is also characterized by stationary distributions of firm ability and product expertise in domestic and export markets, which are determined by the zero-profit cutoffs ϕ * and λ * (ϕ) and the exporting cutoffs ϕ * x and λ * x (ϕ), and are the same across products.
• Using the equilibrium pricing rule (25) and the symmetry of the two countries, the aggregate price index for each product may be written as a function of the mass of firms manufacturing the product for domestic and export markets.
• Therefore, the expression for the mass of firms supplying the domestic market in a product remains as in equation ( 19) for the closed economy, while the expression for the mass of firms supplying the export market in a product is analogous: EQUATION ).
• Finally, labor market clearing requires that the demand for labor in production for the domestic market, in production for the export market and in entry equals the economy's aggregate supply of labor.

7.1. Multi-Product Exporters

• The authors substitute for product revenue from export sales using the relationship between relative variety revenues in equation ( 10) and the exporting cutoff condition for expertise in equation ( 29).
• Since the exporting cutoff for expertise determines the fraction of products that a firm exports (which equals [1 − Z (λ * x (ϕ))] ), equations ( 30) and ( 37) together determine the equilibrium range of products exported for each value of firm ability.
• The comparative statics of the range of products exported parallel those of the range of products manufactured.
• The third comparative static is again a property of general equilibrium.
• As the exporting headquarters cost rises, the total ex post profits of exporting firms decline, thereby reducing the expected value of entry, depressing entry, and diminishing product market competition.

7.3. Goods and Labor Markets

• Together these variables determine the ex post distributions of firm ability and product expertise in both domestic and export markets.
• Combining the steady-state stability, free entry and labor market clearing conditions, it can again be shown that aggregate revenue equals the economy's aggregate supply of labor (R = L).
• The mass of firms producing any product equals aggregate revenue divided by average revenue, M = R/r, where the authors have determined both aggregate and average revenue above.
• The price index for each product in equation ( 35) follows immediately from the mass of firms producing each product, M p , and the mass of firms exporting each product, M px , as well as average variety prices in the domestic and export market for which the authors have already solved.

8. Properties of the Open Economy Equilibrium

• Multi-product firms' decisions about endogenous product scope introduce an additional adjustment margin along which economies can respond to trade liberalization.
• Additional intuition for these findings can be gained from comparing the free entry conditions in the closed and open economies (equations ( 24) and ( 39)).
• Following reductions in trade costs, all firms experience increases in average productivity, but firms that switch from non-exporting to exporting experience an additional source of productivity growth.
• New exporters not only drop lower-expertise products, but also expand output of newly exported products, which shifts the composition of firm output towards higher-expertise products.
• 30 The expansion of multi-product firms along the extensive margin of the number of products exported helps to explain the extreme inequality that is observed in the distribution of export shipments across firms.

9. Multi-Product Firms and Comparative Advantage

• Two-country and two-industry heterogeneous firm framework of Bernard, Redding and Schott (2006a).the authors.
• 31 While the factor intensity of production varies across industries, all products within an industry are modelled symmetrically and therefore have the same factor intensity.
• The relative price indices for the two industries vary across countries because of the combination of comparative-advantage-based specialization and trade costs.
• These differences in the degree of competition in turn imply that variable profits in the export market are greater relative to variable profits in the domestic market in the comparative-advantage industry than in the comparative disadvantage industry.
• Hence, the opening of trade causes a larger increase in average industry productivity in the comparative-advantage industry because of both stronger firm-level productivity growth and greater across-firm reallocations of resources.

10. Conclusions

• Although multi-product firms dominate world production and trade they have received relatively little theoretical attention among international trade economists.
• While their framework is necessarily an abstraction, the introduction of endogenous product scope to a heterogeneous firm model with entry and exit represents an important step towards greater understanding of multiple-product firms and their responses to trade liberalization in general equilibrium.
• For each firm in each Census year, the authors record the set of products in which the firm produces.
• For further details about the construction of the dataset, see Bernard, Redding and Schott (2006b).
• For export value, exports per product and the count of exported products the authors use the Linked/Longitudinal Firm Trade Transaction Database from Bernard, Jensen and Schott (2005) which links individual trade transactions to firms in the United States.

Figures

Figure 2: Trade Liberalization and Product Scope

Table 2: Correlation of U.S. Firms’ Extensive and Intensive Margins

Table 3: Common and Idiosyncratic Components of Firm-Product Shipments

Table 1: Regression Decompositions of U.S. Firm Shipments and Exports

Figure 1: Product Scope and Firm Ability

Full text

CEP Discussion Paper No 769
December 2006
Multi-Product Firms and Trade Liberalization
Andrew B. Bernard, Stephen J. Redding
and Peter K. Schott

Abstract
This paper develops a general equilibrium model of multi-product firms and analyzes their behavior during trade
liberalization. Firm productivity in a given product is modeled as a combination of firm-level “ability” and firm-
product-level “expertise”, both of which are stochastic and unknown prior to the firm’s payment of a sunk cost
of entry. Higher firm-level ability raises a firm’s productivity across all products, which induces a positive
correlation between a firm’s intensive (output per product) and extensive (number of products) margins. Trade
liberalization fosters productivity growth within and across firms and in aggregate by inducing firms to shed
marginally productive products and forcing the lowest-productivity firms to exit. Though exporters produce a
smaller range of products after liberalization, they increase the share of products sold abroad as well as exports
per product. All of these adjustments are shown to be relatively more pronounced in countries’ comparative
advantage industries.
Keywords: heterogeneous firms, endogenous product scope, love of variety, core competency
JEL Classification: F12, F13, L11
This paper was produced as part of the Centre’s Globalisation Programme. The Centre for Economic
Performance is financed by the Economic and Social Research Council.
Acknowledgements
Andrew B. Bernard and Peter Schott thank the National Science Foundation (SES-0241474 and SES-0550190)
and Stephen Redding thanks the Centre for Economic Performance (CEP) and Princeton University for research
support. We thank Jonathan Eaton, Gordon Hanson, Marc Melitz, Guy Michaels, Peter Neary, Henry G.
Overman, Esteban Rossi-Hansberg and seminar participants at the NBER, LSE, Penn State, University of
Pennsylvania, University of British Columbia, UC Davis and UC San Diego for helpful comments and
discussion. The research in this paper was conducted while Bernard and Schott were Special Sworn Status
researchers of the U.S. Census Bureau at the Boston and New York Research Data Centers. Research results and
conclusions expressed are those of the authors and do not necessarily reflect the views of the Census Bureau, the
NBER, or any other institution to which the authors are affiliated.
Andrew B. Bernard is an Associate Professor of Business Administration at Tuck School of Business
in the US Email: andrew.b.Bernard@dartmouth.edu. Stephen Redding is a member of the Centre for Economic
Performance and a lecturer in Economics at the London School of Economics. Email: s.j.redding@lse.ac.uk.
Peter K. Schott is an Assistant Professor of Economics at Yale School of Management. Email:
peter.schott@yale.edu.
Published by
Centre for Economic Performance
London School of Economics and Political Science
Houghton Street
London WC2A 2AE
All rights reserved. No part of this publication may be reproduced, stored in a retrieval system or transmitted in
any form or by any means without the prior permission in writing of the publisher nor be issued to the public or
circulated in any form other than that in which it is published.
Requests for permission to reproduce any article or part of the Working Paper should be sent to the editor at the
above address.
© A. B. Bernard, S. J. Redding and P. K. Schott, submitted 2006
ISBN 0 7530 1986 8

Multi-Produc t Firms and Trade Liberalization 2
1. In troduction
Firms producing multiple products dominate domestic production and international
trade. In the U nited States, firm s manufacturing more than one product account for
more than 90 percent of total man u fa cturin g shipm ents, while firmsthatexportmultiple
products represen t more than 95 percent of total exports.
1
Despite the overwh elming
empirical importance of m ulti-product firms, comp aratively little theoretical researc h
examines how firm s’ product scope (i.e., the number of goods produced or exported) is
determined or ho w it is influe nced by globalization.
This paper dev e lops a general equilibrium m odel of in tern ation a l trade in which firms
that are heterogeneous in both firm -specific ability and firm -product-specificexpertise
choose endogenous ranges of products to manufacture and sell abroad. The model is
motivated by a series of stylized facts about m ulti-product firms that have emerged
recently, most notably a positive correlatio n between the number of products firms
produce and their outpu t per product. The frame work captures these stylized facts and
returns a number of novel theoretical implications that can be tak en to the data.
A key prediction of the model is that trade liberalization induces adjustments along
firm s’ extensive (n umber of goods) and intensive (sales per product) margins as well
as entry and exit. As trade costs fall, reallocations of r esou rc es occur both within
fir ms, as surviving firms drop their marginally productiv e products, and across firm s,
as firms with the lowest overall productivit y exit. Though exporters are among the
firm s dropping their least-productiv e products, the share of products they export as
well as their sales per exported product rise. Significan tly, productivity increases both
within firm s and within industries as trade costs fall. As a result, the model provid es
an in tuitive micro-foundation for the m uch-discussed idea that in ternational trade spurs
firm s to rationalize production, but one that does not imply money being left on the
table prior to liberalization.
2
Our framework represen ts a significant departure from existing models of heteroge-
nous firms (e.g., Jo vanov ic 1982, Hopenha y n 1992, Ericson and Pak es 1995, Melitz 2003
and Bernard, Redding and Scho tt 2006a) which restrict firm s to production of a single
product. The in troduction of endogenous product scope creates a new margin of firm
adjus tm e nt, which generates nov el firm and industry dynamics in response to trade lib-
eraliza tion . As in existing heterogen eou s firm models, the firms considered in this paper
vary in terms of productivity. Here, how ever, firm “productivity” in a give n product is a
combination of two capabilitie s: firm - level “abilit y ” and firm-product-level “expertise”.
We assume these two components of overall fir m productiv ity to be stochastic, indepen-
1
These figures come from Bernard, Redding and Schott (2006b) and Bernard, Jensen and Schott
(2005) and are discussed further below. They define products as five-digit SIC and ten-digit Harmonized
System categories, respectively.
2
The hypothesis that trade liberalization raises firm productivit y by reducing X-inefficiency has a
long tradition, but theories of this form face the challenge of explaining X-inefficiency as an equilibrium
phenomenon (see for example the discussion in Lawrence 2000).

Multi-Product Firms and Trad e Liberalization 3
dent, and unknow n prior to firms pa ying a sunk cost of entr y. Th ese assumption s are
meant to capture the idea that ev en though some firms are successful in a broad range
of activities (e.g., General Electric), even the most successful firm ma y not be the most
efficient producer of any giv en product. Though w e assume that firm abilit y and product
expertise are uncorrelated, and that a firm’s expertise across products is uncorrelated, a
firm ’s productivity across products is nevertheless positively correlated because higher
firm ability raises productivity in all products.
3
The model w orks as follow s. After a firm incurs the sunk entry cost, and after firm
ability as w e ll as product expertise in all products are rev ealed, the firm decides which (if
an y) of a con tinuum of products to manufacture. Firms that decide to en ter at least one
product mark et must pay a fixed headquarters cost which is independent of the range of
products man ufactured, as w ell as fixed production costs for eac h product market they
enter. Mar gin al costs of production vary across products, declining with firm abilit y
and product expertise. Abilit y var ies across firms and expertise varies across products
for a firm with a particular ability. Firm s with higher abilities hav e a lower zero-pr ofit
cutoff for product expertise, i.e., the lev el of product expertise at which variable profit
exceeds the fixe d production costs. As a result, firms with greater abilit y can profitably
man ufacture a larger range of products, extending their product scope. Though firms
with high ability enjo y higher ave rage produc tivity than firms with lo wer ability, the
percen tage differen c e in av erage productiv ity is smaller than the percentage difference
in ability as a result of their end ogenous expansion into lo wer-expertise products.
The equilibriu m of the model exhibits con ven tion al self-selection of the most produc-
tive firms into production. Here, self selection across firms is driven by the interaction
of stochastic fir m ab ility and fixed headqu arter s costs. Firms drawing low ability are
unable to generate enough variable profittocoverfixed headquarters costs from the
small number of products in which they have high expertise. They have low average
productivity and exit immediate ly.
With endogenous product scope, the model also features self-selection within firms.
Firms’ product selection is explained by the in teraction of stochastic product expertise
and fixed production costs for each product. Firms that become active in a product have
systematically higher productivity in that product than in the products they choose not
to produce. They also hav e systematically higher productivity in that product than
firm s that decide not to produce it.
Stochastic variation in firm ability yields a positive correla tion bet ween firms’ inten-
sive and extensiv e margins: more productive firms are on average larger not only because
they sell more of a giv en product but because they man ufacture more products. T his
positive correlation bet ween intensiv e and extensive margins magnifies ineq u a lity in the
firm-size distribution and has general equilib riu m implicatio ns for firms’ en try and exit
3
An example of a firm ability that influences productivity across all products is proficiency in the
organization of production, including the use flexible manufacturing methods and other productivity-
enhancing techniques: see for example Milgrom and Roberts (1990).

Multi-Product Firms and Trad e Liberalization 4
decisions. As higher-ability firms expand along the extensive margin in to lower-expertise
products, demand for labor rises, w ag es increase and the profitab ilit y of lower-ability
firm s declines. Relativ e to a setting with exogenous product scope, this mec hanism
drives up the zero-profit thresho ld for ability above which firm entry is profitable.
One manifestation of the influence of endogenous product scope is the role it plays
in dampenin g firm entry and exit responses to exogenous shock s to mark et structure. In
con ventional heterogeneous-firm models, an increase in sunk costs of en try, for example,
reduces the zero-profit productivity cutoff necessary for survival, allo w in g firms with
previously unprofitable levels of productivit y to enter the market. As the sunk entry
cost rises above the expected value of entry, entry from the fringe declines, competition
is diminished and the ex post profitab ility of production increa se s . As a result the
zero-profit productivity cutoff falls until the expected value of en try is equal to the new
higher sunk entry cost. When product scope is endogenous, the reduction in competition
induced b y the higher sunk en try cost allo ws firms to expand along their extensive
margin s into lower-expertise products. As a result, som e of the increase in the ex p ost
profitability required for the expected value of en try to equal the new higher sunk cost of
entry is achieved throug h an expansio n of product scope, implying a dampened decline
in the zero-profit productivity cutoff. While there is less reallocation through firm entry
and exit than in a model with exogenous product scope, firm en try and exit is only
part of overall reallocation which now also includ e s reallocation across products within
firm s.
4
The open economy equilibrium permits examin ation of a wide range of firm responses
to globalization . W hen intern ation al trade with fixed and variable trade costs is pos-
sible, the model reproduces the con ventional result that only the highest-productivity
firm s are profitable enough to ov ercom e trade costs and become exporters. With en-
dogenous product scope, however, exporters ship only a relativ ely small fraction of their
o verall output abroad. While exporters’ high-expertise products are profitable enough
to overcome trade costs and are sen t abroad, their lo wer-expertise goods are confined to
the domestic mark e t. In equilibrium the same product might be both exported and sold
dom estic ally b y some firms and only sold locally by others.
A key result of the model is that trade liberalizat ion pressures firms to focus on
their “core competencies”.
5
When product scope is endogenous, symmetric reductions
in countries’ fixed or variable trade costs cause all firms to drop their lo west-expertise
products. This result is driv en by the general equilibrium influence of grow ing export
opportunities on labor markets. As trade costs fall, exporters’ foreign markets expand,
4
For empirical evidence on firm entry and exit as a source of reallocation and productivity growth,
see Dunne et al. (1989), Baily et al. (1992) and Foster et al. (2001) among man y others. For evidence
on the role of reallocation across products within firms, see Bernard, Redding and Schott (2006b).
5
The concept of core competencies appears in both the theory of the firm and the business strategy
literature (see for example Aghion and Tirole 1995, Ossa 2006, Porter 1998 and Sutton 2005). As
formalized here, core competencies refer to the products where firms have the greatest expertise.

Frequently asked questions

Q1. What are the contributions in this paper?

This paper develops a general equilibrium model of multi-product firms and analyzes their behavior during trade liberalization. 

Q2. What percentage of the total exports of goods are produced by firms that produce more than one product?

In the United States, firms manufacturing more than one product account for more than 90 percent of total manufacturing shipments, while firms that export multiple products represent more than 95 percent of total exports. 

Q3. What is the effect of the zero-profit cutoff for product expertise?

As competition declines, firms with lower product-expertise draws can generate sufficient profits to cover fixed production costs, and so the zero-profit cutoff for product expertise falls. 

Q4. What is the exporting cutoff for expertise for a firm?

An increase in the fixed exporting cost for a product (fx) or the elasticity of substitution (σ) raises the exporting cutoff for expertise (λ∗x (ϕ)) for firms of all abilities, since a higher value for expertise is required to generate sufficient revenue to cover the fixed exporting cost. 

Q5. What is the role of the extensive margin in accounting for variation in firm-product sales?

Since log firm sales in the model are proportional to log productivity, variation in firm-product sales can be similarly decomposed. 

Q6. What is the effect of the increase in labor demand on the zero-profit cutoff ability?

This increase in labor demand bids up wages, and so reduces the profitability of low-ability firms, which leads to a smaller reduction in the zero-profit-cutoff ability compared to when product scope is exogenous. 

Q7. What is the alternative explanation for variation in export shares?

30Another complementary explanation for variation in export shares involves single-product firms and fixed exporting costs that are specific to individual export markets, so that only higher-productivity firms find it profitable to serve destinations with higher fixed exporting costs (see for example Eaton, Kortum and Kramarz 2005). 

Q8. What is the exporting cutoff for expertise for a firm with a lower ability?

To determine the exporting cutoff for expertise for the lowest ability exporter, λ∗ix (ϕ ∗ x), the authors combine the requirement that zero profits are made from export sales by a firm with ability ϕ∗x in equation (33) with the expression for firm profits from export sales in equation (32). 

Q9. What is the zero-profit cutoff for expertise for a firm with ability?

From equation (23) it can be seen that an increase in the fixed production cost or the elasticity of substitution raises λ∗ (ϕ∗), which in turn raises the zero-profit cutoff for expertise for firms of all abilities, λ∗ (ϕ). 

Q10. What is the effect of the opening of trade on the equilibrium product scope?

the opening of trade leads to a contraction in equilibrium product scope, as firms focus on their “core competencies” in a narrower range of higher-expertise products. 

Q11. What is the value of the zero-profit cutoff for expertise?

Since product revenue is increasing in expertise, the higher level of product revenue needed for zero profits implies a higher value of the zero-profit cutoff for product expertise λ∗ (ϕ).