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Multi-Product Firms and Flexible Manufacturingin the Global Economy

J. Peter Neary

University of Oxfordand CEPR

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Evidence on Multi-Product Firms

Multi-product firms (MPFs) …

Bernard, Redding, Schott (2006)

- are present in all industries- typically coexist with single-product firms- account for

• 41% of the total number of firms• 91% of total output

- are very active in varying their product mix(50% both add and drop products, 30% drop only, 8% add only

during average 5 year interval)

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Literature on Multi-Product Firms

• Existence, Market Structure, and Diversification:Brander-Eaton (1984); Klemperer (1992); Eaton-

Schmitt (1994); Baldwin-Ottaviano (2001); Johnson-Myatt (2003, 2006); Grossmann (2005)

• Free Entry Models based on Fixed Costs:Ottaviano-Thisse (1999); Baldwin, Gu (2005);

Allanson-Montagna (2005)

• MPFs and Trade: Evidence and TheoryBernard-Redding-Schott (2005, 2006); Nocke-

Yeaple (2005)

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Our Contribution

• Develop a new model of multi-product firms (MPFs) based on flexible manufacturing

• Explore intra-firm adjustments within MPFs in partial and general oligopolistic equilibrium (GOLE)

• Show how the existence of MPFs alters predictions of conventional trade models

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Overview of the Model

• General Oligopolistic Equilibrium (GOLE)[Neary (2002)]

• Continuum of identical industries [0,1], k identical countries, MPFs in all[D.P. has asymmetric countries and industries: similar results]

• Globalization:– Increase in the number of countries– Both a market-size and a competition effect

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Outline• Consumers and Firms• Industry Equilibrium

– Scale and Scope of MPFs– Comparative Statics

• General Equilibrium– The Global Economy– Adjustment to Globalization

• Extensions– Country/Firm Asymmetries– Free Entry

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Outline

• Consumers and Firms• Industry Equilibrium

– Scale and Scope of MPFs– Comparative Statics

• General Equilibrium– The Global Economy– Adjustment to Globalization

• Extensions– Country/Firm Asymmetries– Free Entry

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Preferences and Demand

1

0

( )U u q z u q z dz

Continuum Quadratic Preferences:

2zN

0

21

zN

0

221

zN

0

diziqbediziqe1bdiziqazqu

,,,

zeYzixe1bazip ,,

Neary (JEEA 2003), Ottaviano-Tabuchi-Thisse (IER 2002)

Inverse World Market Demand:

kL

bb

aa

''

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Costs and Technology of Multi-Product Firms

Demand: eYixe1baip

fdiixicipj

jjjj

0

Profits:

Firm Output: j

diixX jj

0

F.O.C. Scale: YXebicaixe'b jjj 12

F.O.C. Scope: 0jjx

Flexible Manufacturing: c c c i c i w ij j j j j( ) , ' ( ) ( ) ( )0 00

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Flexible Manufacturing

ic

i

"Core Competence"

Product Range

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First Order Condition: Scale

eYba

YXeba

ix

eYixe1baip

ic

"Cannibalization Effect"

ixMR

ip

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First Order Condition: Scope

YXeba

i

Xe1b2

"Core Competence"

Product Range

ic

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Equilibrium Output Profile

ix

i

0

iix

"Core Competence"

Product Range

x ib e

a w i b e km X( )' ( )

[ ( ) ' ( ) ]

1

2 11

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Multi-Product Firms (cont.)

• Prices vary across varietiesCompare models with fixed costs: e.g., Nocke-Yeaple

• Higher prices and lower profit margins on goods further from a firm’s core competence

Prices: p i a w i km b eX( ) [ ' ( ) ( ) ' ] 1

21

Price-Cost Margins: p i w i a w i km b eX( ) ( ) [ ' ( ) ( ) ' ] 1

21

[“km” is the competition effect; “-1” is the cannibalization effect]

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Scale and Scope Combined

Firm Scope:

Industry Output: Y=kmX

Firm Scale: x ib e

a w i b e km X( )' ( )

[ ( ) ' ( ) ]

1

2 11

X

b

a w

e e kmi di

1

2 1 1

10'

( ' )

( ) ( )' ( )

x w a b e km X( ) ( ) ' ( ) 0 1

i.e., 2 equations in X and

Combine: 2 10

b e X w i di' ( ) ( ) ( ) ( ) ( )

[ ( ) ' ]

(): Cost savings from flexible manufacturing

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First Order Condition: Scope

YXeba

i

Xe1b2

"Core Competence"

Product Range

Cost savings from

flexible manufacturing

ic

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Outline

• Consumers and Firms• Industry Equilibrium

– Scale and Scope of MPFs– Comparative Statics

• General Equilibrium– The Global Economy– Adjustment to Globalization

• Extensions– Country/Firm Asymmetries– Free Entry

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FOC: Scope

X

Scope: (X)

w a b e km X ( ) ' ( ) 1

Industry Output: Y=kmX

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FOC Scale

Scale: X()

X

X

b

a w

e e kmi di

1

2 1 1

10'

( ' )

( ) ( )' ( )

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Figure 3: Industry Equilibrium

Scale: X()

X

Scope: (X)

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Market-Size Effect of Globalization

Scale: X()

X

Scope: (X)

w a b e km X ( ) ' ( ) 1

0)(

1'

)1()1(2

)'(

'

1dii

kmee

wa

bX

'b

bkL

k L

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Market-Size Effect on Output Profile

ix

i

Product Range

)]()([)1('2

])1(')([)1('2

1)(

ieb

w

Xkmebiwaeb

ix

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Competition Effect of Globalization

Scale: X()

X

Scope: (X)

w a b e km X ( ) ' ( ) 1

X

b

a w

e e kmi di

1

2 1 1

10'

( ' )

( ) ( )' ( )

k m

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Competition Effect on Output Profile

ix

i

Product Range

])1(')([)1('2

1)( Xkmebiwa

ebix

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Full Effect of Globalization

Scale: X()

X

Scope: (X)

w a b e km X ( ) ' ( ) 1

X

b

a w

e e kmi di

1

2 1 1

10'

( ' )

( ) ( )' ( )

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Intra-Firm Adjustment

ix

i

x

k

( ) 0

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Intra-Firm Adjustment

ix

i

x

k

( ) 0

X rises, so infra-marginal products must increase

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Intra-Firm Adjustment

ix

i

Outputs rise Outputs fall

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Impact on ProductivityProof here for X; also holds for a price-weighted Divisia Index

Output:

Xw

b ei di

( )

' ( )( ) ( ) ( )

2 1 0

0

diixilMPF

x ib e

a w i b e km X( )' ( )

[ ( ) ' ( ) ]

1

2 11

lw

b ei i diMPF

( )

' ( )( ) ( )[ ( ) ( )]

2 1 0

X

l MPF

( )

( )

Labour Demand:

Productivity:

This is decreasing in

So: globalization encourages “leaner” firms

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Impact on Product Variety

Low Flexibility 0nN

chigh

High Flexibility 0nN

clow

N km

N

km km

k

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Partial Equilibrium ResultsProposition 1: In partial equilibrium, an increase in

competition reduces δ and X but raises Y. An increase in the size of the market increases both X and Y but leaves δ unaffected.

Proposition 2: Firm productivity depends negatively on and on nothing else. Hence it rises when competition increases but is independent of the size of the market.

Proposition 3: In partial equilibrium, the impact of globalization on N depends on the degree of flexibility in manufacturing. If flexibility is low, N rises as k increases, otherwise N falls. A necessary condition for a fall in N is that costs are concave in varieties.

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Outline• Consumers and Firms• Industry Equilibrium

– Scale and Scope of MPFs– Comparative Statics

• General Equilibrium– The Global Economy– Adjustment to Globalization

• Extensions– Country/Firm Asymmetries– Free Entry

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Overview of GE Model

3 Equations:

Firm Scope: ( , )X w

Firm Scale: X X w ( , )

Labour Market Equilibrium: w w X ( , )

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Scale and Scope in General Equilibrium

Firm Scope:

Recap:

Firm Scale:

Xb

a w

e e km

1

2 1 1'

( ' )

( ) ( )

w a b e km X ( ) ' ( ) 1

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Industry Equilibrium

X

w IE: X(w)

Xb

a w

e e km

1

2 1 1'

( ' )

( ) ( )

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Labour MarketLD Multi-product Firms:

0

diixilMPF

Labour Market Equilibrium: L mf m i x i di

( ) ( )0

Combine with FOC (scale):

L

mf

b ei a w i b e km X di

1

2 11

0' ( )( ) ( ) ' ( )

Combine with FOC (scope):

2 10

b eL

mf w i i di' ( ) ( ) ( ) ( )[ ( ) ( )]

a b e km X w ' ( ) ( )1

x ib e

a w i b e km X( )' ( )

[ ( ) ' ( ) ]

1

2 11

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Labour-Market Equilibrium

X

w

LL: w(X)

L

mf

b ei a w i b e km X di

1

2 11

0' ( )( ) ( ) ' ( )

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Figure 5: General Equilibrium

X

w

LL: w(X)

IE: X(w)

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Adjustment to Globalization in GE: Summary

• Market-size and competition effects as in PE

• Responses of X and as in PE

• Wage rate may rise or fall (presumptively rises in linear case)

• Product range more likely to fall when w rises

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Outline

• Consumers and Firms• Industry Equilibrium

– Scale and Scope of MPFs– Comparative Statics

• General Equilibrium– The Global Economy– Adjustment to Globalization

• Extensions– Country/Firm Asymmetries– Free Entry

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Multi-product firms with longer product lines and more flexible technology tend to respond more to shocks

Industry Equilibrium: Heterogeneous Firms

hh

jj

h

j

d

d

wheree

e eand cj

j

jj j

jj:

( )

( )[ ( )]

2

2 11

)1('2

)(

')(

)1(2)(

1 eb

wXXY

w

eYba

e

e

jj

j

km

j

jj

jj

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In free-entry equilibrium, profits are:

• Decreasing in m: Negative competition effect

• Increasing in L: Positive market-size effect

• Increasing in k: Market-size effect dominates

Hence: Rise in k encourages entry, reinforcing earlier results:

• Firm output may fall, but national output mX must rise

• falls, so productivity rises

Free Entry

0

0j

j j j jp i c i x i di f

Profits:

0

' 1 ( )b e x i eX x i di f

2 2

0' (1 )b e x i di eX f

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i.e., Effect on diversity is qualitatively the same as in no-entry case, but magnified in absolute value

Free Entry (cont.)

Effect on Product Diversity:

ln ln ln1

ln ln ln

d N d d mN km

d k d k d k

ln ln ln ln1

ln ln ln ln

d m d m

k m d k d k

ln ln ln1 1

ln ln ln

d N d m

d k k d k

Effect on diversity with no entry

ln ln:

ln lnBUT

k m

Recall: No market-size effect on diversity with no entry

Magnification effect

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Conclusion• Globalization can have a considerable impact on both scale

and scope of multi-product firms Introduces a new margin of adjustment: Intra-firm extensive margin

• “Cannibalization effect” crucial→ Oligopoly important

• Impact on scope depends on wage effects→ General equilibrium important

• New source of gains from trade: productivity increases, as firms become “leaner”: concentrate on their core competence

• New source of losses from trade: Variety may fall

• Impact on variety depends on flexibility→ Fall in diversity possible even with symmetry & w/out entry

Entry (inter-firm extensive margin) reinforces intra-firm effect

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Thank you!