Footloose Capital and
Productive Public
Services
Pasquale Commendatore
Ingrid Kubin
Carmelo Petraglia
Forthcoming in: “Geography, Structural
Change and Economic Development:
Theory and Empirics”, Salvadori N.,
Commendatore P. and Tamberi M. (Eds),
Edward Elgar Publishing
2
Outline






Motivation and Aim
Basic Framework
Short-run equilibrium
Capital movements and long-run
equilibrium
The impact of public services on
industrial location
Conclusions
3
Motivation and Aim

European Cohesion Policy is inconsistent
since it sometimes seems to target
agglomerations of industrial activities in core
regions, but more often stimulates their
relocation in the periphery (Brakman et al.
2005). Such a criticism provides a motivation
to analyse policy issues in New Economic
Geography (NEG) models, which mainly focus
on the determinants of the spatial location of
the manufacturing industry
4
Motivation and Aim





We aim to study the impact of such policies on the
spatial distribution of economic activities within a
NEG model
What are the agglomeration and dispersion effects
induced by policy measures aimed to make
backward regions more attractive to foreign firms?
Does the result depend on the financing scheme of
such policies?
In Commendatore et al (forthcoming Èconomie
Internationale) focus on long-run equilibrium location
In this paper: focus also on the dynamic process
5
Basic Framework




2 trading regions (r = 1,2)
2 sectors in each region:
• Agriculture (A): perfect competition
• Manufacturing (M): monopolistic competition (“i”
varieties of a composite good)
2 factors of production:
• K is inter-regionally mobile (K owners are immobile)
• L is inter-regionally immobile (intra-regionally
mobile)
A central government provides public services which
enhance labour productivity in M
6
Agriculture


Constant return to scale sector
1 unit of labour = 1 unit of output
7
Manufacturing sector


1 unit of capital & βr units of labour = 1 unit of
output
Decreasing average costs:
TCr ( xi )  F  wM  r xi


n=K
number of (firms=) varieties in regions 1 & 2:
n1,t  t n  t K
n2,t  (1  t )n  (1  t )K
8
Transport costs


Agricultural good traded costless across
regions
Transport costs for manufacturers in “iceberg”
form:
•
1 unit shipped, 1/T arrives, where T≥1
Trade Freeness
Prohibitive tc
 T
 0
1
No tc
 1
9
Government


1 unit of agricultural good = 1 unit of H
Hrβr
  f (H )
r


r
; f ’ <0, f ’’>0
H financed taxing residents’ income
Balanced budget constraint: TB = H
TB  s H TB  (1  s )H
1
F
2
F
sF = share of public expenditures financed by residents in region 1
10
Consumption and Expenditure
Utility function (household j; j = 1 .. L)
1  
A
M
where
1 11  
N

11   
CM   xi

; σ>1

U C
C



i

Total expenditure in manufactured goods:
M   w L  w L    H 
A
A
M
M
11
Regional Expenditure
Regional expenditures in manufactured goods:

Given:
sK = share of capital owned by capitalists living in region 1
sL = share of workers located in region 1
M  s w L  w L   s   TB 
1
L
A
A
M
M
K
1
M 2  (1  sL )wA LA  wM LM   (1  sK )  TB2 
M1
sE 
M
 region 1’s relative market size
12
Short-run equilibrium


regional allocation of private capital (λ) is given
Perfect mobility of workers between sectors:
wA  wM  w

Agriculture:
pA  w  1

Manufacturing sector:

pr 
r
 1
 pr depends on the allocation of H
13
Short-run equilibrium

The higher H1 (given H2), the cheaper
manufactured goods in region 1:
p1  p 
p2  ph
where
 2 f ( H 2 ) and h
h

0
H
1 f ( H1 )
1
14
Short-run equilibrium

Demand = supply in region 1 and region 2:

1  sE    1 M

sE
q1,t  d1,t  


 t  1  t   z t  1  t  z  p K
q2,t  d 2,t

 1 M
sE 
1  sE






1



z



1


z




t
t
t
 t
 pz 1 K
zh
1
and
z
0
H1
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Short-run equilibrium

Short-run equilibrium profits in regions 1 and 2:

1  sE    1 M

sE
 1,t  


 t  1  t   z t  1  t  z   K
 2,t

z M
sE
1  sE



 t  1  t   z t  1  t  z   K
16
Capital movements and long-run
equilibrium

The incentive to move capital is based on
relative profitability:
R  t 
 1,t

 2,t
17
Capital movements and long-run
equilibrium
if
 0

t 1  Z  t    F  t  if
 1
if

F  t   0
0  F  t   1
F  t   1
where
R  t   1
F  t   t  t 1  t 
t R  t   1  t 
18
Capital movements and long-run
equilibrium


In the long-run, profits across regions equalize
Interior fixed point 0 <λ*<1:
1
(1   )(1   ) 
1 (1  z )( z   ) 
  z
sE 


2
(1  z )( z   ) 
2 (1   )(1   ) z 
*

Boundary (CP) fixed points 0 and 1
19
z 1
z  0.98
1
sE 
2
20
The impact of public services
on industrial location
 *
  ( z 2  1)(1   2 )  z
12
sE

1
sE 
z
2 
2
H1
(1   z ) 
(z  )
 H1 (1   z )( z   ) H1
>0
<0
?
“Productivity effect”
Positive sign: ↑ H1  region 1 is more attractive because
of the lower labour input requirement relative to region 2
“Demand effect”
the sign depends on how H1 impacts on the relative
market size of region 1 (sE = M1/M)
21
The impact of public services
on industrial location
The impact on H1 on sE depends on
the distribution of the tax burden across
the two Regions:
sF = sL  the demand effect = 0
sF > sL  the demand effect is negative
sF < sL  the demand effect is positive
22
The impact of public services
on industrial location
sL = 0.5 ; sK = 0.25 ; σ = 4 ; μ = 0.5 ; Ф = 0.2 ; sE < 0.5
region 1's share of capital
λ*
1
sF  0.5
sF = sL
sF > sL
sF  0.55
0.5
sF  1
0
0
sF = 1
0.5
provision of public services in region 1
H1
1
23
  0.3
  0.23
1
sE 
2
24
Conclusions

The overall effect of an increase in productive public
services on industrial location has been
decomposed into two effect:
• Firms attracted by lower input requirements
(productivity effect), while higher taxation tend
to shrink the local market, leading firms to
relocate elsewhere (demand effect)
• The demand effect is nil only if tax payers of
the richer region contribute on the basis of their
capacity
25
Conclusions

Further results
• dynamics of capital movements (stability of
industrial location equilibria under alternative
degrees of economic integration)
• policy analysis extended to a dynamic context
26