The Economics of multinationals:
Theory of Vertical FDI
Lessons 1 and 2
Giorgio Barba Navaretti
Gargnano, June, 11-14 2006
Objectives and background
• OBJECTIVES
– Investigate different forces affecting the choice
of fragmenting production
– Investigate effects of production fragmentation
• BACKGROUND
– Simplified version of Helpman (1984) adding
VFDI to HO => FPE
– Extension in the spirit of Feenstra and Hanson
(1996) => Not necessarily FPE
Setting
• Production is split in two stages: components (c)
and assembly (a).
• Perfect competition
• Two factors, labour and capital, used in both
stages with prices in country i wi and ri
• Constant returns to scale, so unit cost functions
for each stage are c(wi, ri) and a(wi, ri).
• Production of one unit of a uses one unit of c (no
substitution between c and primary factors)
• Trade costs are incurred on shipping final products
and components
Cost functions
Cost of a unit of output delivered to country k if
components are produced in country i and final assembly
takes place in j:
Bijk =  c(wi , r i ) ij + a(w j , r j ) jk
c
a
 iic =  iia = 1 and for i  j, ijc , ija  1
When do firms fragment
production?
•
•
•
•
Countries 1 and 2.
1 is North, has higher wages
1 has advantage in integrated production
Assembly is labour intensive (carried out in
2 if production is fragmented)
• Trade costs same in both directions
Trade costs and production regimes
Assembled
product trade
costs, a
 c( w , r ) 
1
1
c
B111 , B222 :
Self sufficiency.
B111 , B122 :
All compnts country 1.
Assembly in both.

+ a( w2 , r2 )  a =  c( w1 , r1 ) + a(w1 , r1 )
HFDI


VFDI

B121 ,B122 :
All compnts country 1
All assembly country 2
 c( w , r ) 
1
F
Combined
increases in
c and a
1
 c(w1 , r1 ) + a(w1 , r1 ) a =  c(w2 , r2 ) + a(w2 , r2 )
export
B111 , B112 :
All production in
country 1
c

+ a(w2 , r2 ) =  c( w1 , r1 ) + a( w1 , r1 ) a .
Components trade costs, c
Figure 4.1: Assembly labour intensive;
country 1 high wage
Trade costs and effects on trade
Value added.
Value of trade.
Value of trade
Value added in country 1
Value added in country 2
VFDI
 HFDI


Trade costs, c, a
Figure 4.2: Assembly labour intensive;
country 1 high wage
Effects: fragmentation and factor
prices in partial equilibrium
Figure 1. Integrated vs. Fragmented production
w
C
I
II
AA
CC
A’A’
I’I’
C’C’
C’
1 (w1,r1)
A
=> p = a(w,r)+c(w,r)
=> p = a (w,r) + c(w1,r1)
=> p = a (w1,r1) + c(w,r)
=> p’ = a (w,r) + c(w1,r1)
=> p’ = a (w,r) + c(w,r)
=> p = a (w2,r2) + c(w,r)
I’
3(w3,r3)
A
A’
2(w2,r2)
C
A’
I’
C’
I
r
Fragmentation in general
equilibrium
• Extension by Helpman and Helpman and Krugman of the H-O model
to include FDI
• 2 countries, 2 goods, 2 factors model
• Qs:
• Under what circumstances does FDI occur?
• What is the effect of FDI on factor prices?
 a =1 and c=1 (free trade in components) or = 4 (no trade in components)
•
Endowments of factors in countries 1 and 2 L1, K1, L2, K2
•
One sector is manufacturing (divided in components and assembly)
which has fixed factor intensities
•
The rest of the economy is sector Y: employs the entire endowment
minus factors employed in M
Fragmentation in general equilibrium,
other assumptions
Output and mkt clearing factor prices in Y:


M
Yi = Y Li  LM
,
i , Ki  Ki


M
Y Li  LM
i , Ki  Ki
wi =
,
Li


M
Y Li  LM
i , Ki  Ki
ri =
.
K i
•DEMAND:
•Incomes in each country are the sum of the returns to the two factors, wiLi + riKi,
i = 1, 2.
•Consumers have identical homothetic preferences
•Goods have the same price in both countries
=> Trade is only driven by international differences on the supply side
L2
O2
m2
K1 
M
c
c’
y2
c
E
E’
m1
K2
Y
y1
L1 
O1
Figure 4.4: Production and FPE.
Fragmentation and factor price
convergence
How to explain the
Nafta paradox (skill
premium rising in Mex
and US - Feenstra
Hanson)?
Ki - Ki M
Y1
w1/r1
B
I
Y2
IIA
IIB
A
w2/r2
O
Li - Li M
Figure 4.5: Relocation and
factor prices
Fragmentation and factor prices in
general equilibrium
L2
O2
B
(-, -)
K1 
a
(-, +)
(+, -)
(+, +)
M
( 0, 0 )
Y
c
(-, +)
c
(+, +)
(+, -)
a
K2
(-, -)
L1 
O1
Figure 4.6: Change in wage rental
ratio, (country 1, country 2).
Effects on skill structure when firms are
heterogeneous
Barba Navaretti, Bertola Sembenelli, 2006
Main issues
• Vertical investment depend on transport
costs and relative factor costs
• The effects of VFDI on factor prices
depends on the relative factor intensities of
M’s activities and on the relative factor
endowments of countries