Transcript Tema 5-

Lecture 6
ECONOMIC GEOGRAPHY:
THE CORE-PERIPHERY MODEL
By Carlos Llano,
References for the slides:
• Fujita, Krugman y Venables: Economía Espacial. Ariel Economía, 2000.
• Materiales didácticos de diferentes autores: Baldwin; Allen C. Goodman; Bröcker; J. Sánchez
Index
1. Introduction.
2. Core-Periphery Model (FKV, 1999).
1. An intuitive view.
2. The model.
3. Implications.
3. Aplicacions.
4. Conclusion
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1. Introduction
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1. Introduction
1. The Dixit-Stiglitz model is the starting point of the
monopolistic competition models (DS, 1977).
2. FKV-99 present a spatial version of the DSM:
• 2 regions; 1 mobile productive factor (L= labor).
• 2 products:
• Agriculture: residual sector, perfect competition, constant
returns to scale.
• Manufacturing: product differentiation (n varieties); economies
of scale; monopolistic competition;
• Goods mobility (transport costs) but not factors
• Iceberg transport cost for both goods.
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1. Introduction
Conclusions of the Dixit-Stiglitz-spatial model:
1. Price Index Effect (Forward Linkage): the region with a larger
manufacturing sector will have a lower price index for manufactured
goods, since a small part of manufacturing consumption in this region is
carrying the transport costs. (the region is self-sustainable).
2. Home market Effect (Backward Linkage): an increase in the
manufacturing demand (dY/Y) causes:
•
If labor supply is perfect elastic: a more than proportional increase in
production and employment (dL/L). A country/region with an idiosyncratic
demand of a product become a net exporter rather than a net importer.
•
If the labor supply is positive : part of the home market advantages results in
higher wages rather than in exports causing the agglomeration of low-qualified
labor.
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economía geográfica
2. The Core-Periphery
Model: an intuitive view
Basic Model:
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• Assumptions of the Core-Periphery Model (FKV, 1999):
– 2 countries (north-south)
– 2 sectors (A agriculture. & M manufacturing)
– 1 factor labor. 2 specializations: agricultural L and manufacturing L.
• Only LM is mobile
• Migration is based exclusively in the wage differences in LM.
– There are only transport costs in M: in the form of iceberg costs (Trs)
• The short run model:
• LM is only used in producing M (DS sector)
• L is only used in A (Walrasian model or perfect competition)
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LA
(immobile
factor )
Sector-A (agriculture)
-Walrasian (CRS & Perf. Comp.)
-Variable Costs = aA units of L per unit of A
-A is the numeraire (pA=1)
Sector-M (Manufactures)
- Dixit-Stiglitz Model monopolistic comp.
- Increasing Returns to Scale:
Fixed + Variable costs
LM
(mobile
factor )
LM is moving according to the differences
in real wages, w-w*
 w/P comercio
- w*/P*
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No costs
of trade
North
&
South
Mkts
Iceberg transport
costs and “the
index of freeness of
trade varies
between 0>Z>1
Z is the freeness of trade:
(if T=1, Z=0 , trade is
costless; if T=0; Z=1 trade
is impossible)
North-South and
South-North
Migration
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2. The Core-Periphery Model: an intuitive view
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Build Intuition: Study model with symmetric nations
• This model describes 3 localization forces:
– 2 agglomeration forces (symmetry de-stabilizers)
• Relationships between costs & demand (agglomeration forces)
– 1 dispersion force (symmetry stabilizer)
• Local competition (dispersion force),
• Two key variables : T y λ
– T= transport cost;
– λ = % of the industry in the North.
– In the beginning it will be λ= 1/2 . Then it can tend to concentration.
– The proportion of the industry and its employment in a region is the
same.
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2. The Core-Periphery Model: an intuitive view
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Backward(i.e.
anddemand-wages)
Forward Linkages
Backward
Linkage
λ =1/2 (initially)
We consider a “migration shock” dλ >0
Due to the costs of trade firms
prefer to settle in large markets.
This attracts+ LM .
Adjusts in Production
Adjusts in Expenditure
The LM migrated spends
its income in the North
rather than in the South.
Market Size Effects:
The market in the North grows, in the south it decreases.
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2. The Core-Periphery Model: an intuitive view
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Forward (i.e. costs-prices) Linkage
λ =1/2 (initially)
We consider a “migration shock” dλ >0
Ceteris paribus,
Smaller costs-of-living
Attract + LM
Adjusts in Production
(+ migration)
The Northern import
Varieties and due to
< less costs of trade
lower P & higher P*.
Adjusts in Production
Price Index Effect:
P-North falls, P* South rises
Now + varieties are
produced in the North
than in the South
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2. The Core-Periphery Model: an intuitive view
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Dispersion Forces
• These two centrifugal forces (BL and FL)
opposes to a stabilizer force: “Local
competition”
• Ceteris Paribus , firms will tend lo settle
where there is a smaller number of
competitors.
• Results => flight from the agglomeration.
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2. The Core-Periphery Model: the model
• Labor forces: LA agricultural workers y LM manufacturing
workers,
• The LA is given. LM is initially given, but then will move looking
for higher wages. Therefore, the geographical distribution is
exogenous (first) but endogenous (afterwards):
• Φr (phi): exogenous share of the agricultural labor force in
region r.
• λr (lambda): share of manufacturing labor force (LM) in region r.
• To simplify, it is assumed that the initial share of manufacturing
employment is: (LM=µ ; LA= 1- µ).
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2. The Core-Periphery Model: the model
• The agricultural wages equal 1 in both regions:
wrA  1
• The manufacturing wages may differ.
• The migration of the workers between N-S is determined by
the differences in wages:
– If the real wage is below the average real wage, people migrate:
   λ r ωr
Average real wage
r
λ r  γωr   λ r
The variation in the share of manufacturing
workers in region r depends on the difference
between the wage and the average
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2. The Core-Periphery Model: the model
2. Instantaneous equilibrium: on instant t.
– Simultaneous solution of 4 equations:
1. Income: Since WA=1 for every r; the income Yr  μλ r w r  (1  μ)φ r
for every region r depends on its corresponding
share of manufacturing workers and its
corresponding wage.
2. Price index: expression from the DS. Model :
– The price index in r tends to be lower when
the share of manufacturing (λs) in the nearest
1
regions to r (those with low transport costs to

 1σ
1 σ
r) increases.
G r   λ s (w s Tsr ) 


– Thus, due to the concentration of industry in
one region, prices decreases in the later and
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rises in the others (Forward linkage effect).
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2. The Core-Periphery Model: the model
3. Nominal wages: it shows the level of
1/σ
wages at which manufacturing in region r

1σ
σ -1 
breaks even:
w r   Ys Tsr G s 
 s

– If the price indexes in all regions were
similar, the nominal wage in region r
tends to be higher if the income in the
other nearest regions (low Trs) is high.
– Firms pay >w if they have access to a
larger market. Backward linkages.
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2. The Core-Periphery Model: the model
4. Real wages: nominal wage deflated by the cost-ofliving index in region r.
• The differences between regions only depend on the
manufacturing worker’s real wage and the price
indexes in those regions.
• Agricultural workers always earn = and the price of its
products is =1 (perfect competition).
ω r  w r G r μ
Solution of the basic C-P model.
• We analyze the solution when R=2.
• We wonder if manufacturing tends to concentrate, inducing:
– Differences in prices, income and wages.
– A pop-up of a manufacturing “core” vs an agricultural “periphery”.
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2. The Core-Periphery Model: the model
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2.3. The CP Model: Statement and Numerical Examples
• 2 regions * 4 equations= 8 equations for equilibrium:
1 μ
Y1  μλw 1 
2


1
1 σ 1 σ
G 1  λw 11σ  (1  λ)w 2 T 

w 1  Y1G
σ 1
1

σ 1
1σ 1/σ
2
1
 Y2 G Y T
ω1  w 1 G
μ
1
Y2  μ(1 - λ)w 2 

G 2  λw1T 
1σ

1 μ
2
 (1  λ)w
σ 1 1- σ
1
w 2  Y1G T  Y2G

1
1σ 1σ
2

σ 1 1/σ
2
ω 2  w 2G 2 μ
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2. The Core-Periphery Model: implications
High transport cost;
W1“wiggle
-W2>0 if diagram”
λ>0,5
T=2,1
σ= 5; μ=0,4
1  2
• When manufacturing is + concentrated in r (λ>0,5), its
labor force earn – (+ competition, less ec. scale, expensive
production)
• Workers migrate to the other one.
• It tends to the symmetric equilibrium in manufacturing.
0
• Similar scenario to the
movement of factor L
without trade
(Krugman y Obstfeld,
2007, Chapter 7)
0
λ=
1/2
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manufacturing in region r18
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2. The Core-Periphery Model: implications
Low
transport
cost,
T=1,5
σ= 5;μ=0,4
• W1-W2<>0 for any λ
• The + share of manufacturing + agglomeration forces due to:
–
–
BL: the > local market, > nominal wages.
FL: the > variety of locally produced goods, < price index.
• Tendency towards agglomeration. Unstable Equilibrium even when λ=0,5
1  2
0
0
1/2
1
λ=percentage that represents manufacturing L in region r (remember that we assume19 (λr=μr)
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2. The Core-Periphery Model: implications
Intermediate
transport
costs; T=1,7
σ= 5;μ=0,4
• 5 equilibriums: 3 stable; 2 unstable
“wiggle diagram”
• The equilibrium is locally stable:
–
–
If the initial share is unequal, it tends towards concentration (C-P).
If the initial share is equal, industry allocates equally (λ=0,5)
1  2
0
0
1/2
1
λ=percentage that represents manufacturing in region r
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2. The Core-Periphery Model: implications
“The “wiggle
Tomahawk
diagram”
diagram”
• Solid lines: stable equilibriums; Doted lines: unstable eq.
• With high transport costs: there is an stable equilibrium (λ=0,5).
λ
1
Two critical points:
0,5
T(B)
0
T(S)
1
1,5
• T(S): sustain point in the core-periphery
pattern.
• T(B): symmetry break point (equilibrium
is stable).
T
When are these critical points possible?
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2. The Core-Periphery Model: implications
“wiggle diagram”
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2. The Core-Periphery Model: implications
1. When is the core-Periphery
Pattern
Sustainable (agglomeration)?
“wiggle
diagram”
• It breaks when there are incentives to migrate, this is, when the
wages in the North are not higher enough than in the south.
• Then, the Core-Periphery Pattern is not self-sustainable
How would we express this model analytically?
• We assume that all the manufacturing labor force are in region 1 (λ=1).
• We are questioning when ω1< ω2. This is, when the real wages in the
region with + industry are lower than in the periphery (with no industry).
• What will be the value of ω1 if all the industry agglomerates in 1?
Y1  (1  μ)/2
Y2  (1  μ)/2
G1  1
G2  T
ω1=1
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2. The Core-Periphery Model: implications
1. When is a core-Periphery Pattern Sustainable?
“wiggle diagram”
If w1=1, we have to find out when w2<>1
• Thus, we substitute in the w2 equation:
1  μ 1σ 1  μ σ 1 
ω2  T 
T 
T 
2
 2

μ
Cost of supplying
region 1 from 2.
1/σ
Cost of supplying
region 2 from 1.
• FL: the price index in r=2 • Nominal wage at which a firm
located in 2 breaks even (or exactly
is T times higher than
covers the costs):
manufactured goods since
• There is a backward effect via
they have to be imported
demand from the
supporting positive
concentration of production to
transport costs.
the nominal wage rate firms
• Therefore it is<1
can afford to pay in r =1.
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2. The Core-Periphery Model: implications
1. What is the relationship“wiggle
betweendiagram”
this equation and the
sustainability of the core-periphery pattern?
1  μ 1σ μσ 1  μ σ 1μσ
ω 
T

T
2
2
σ
2
• When T=1 (with no transport costs), ω2 =1,
• Localization is irrelevant.
• With a small transport cost increase (and by totally differentiating and
evaluating the derivative at T=1, ω2 =1), we find that:
ω 2 μ 1  2σ 

0
T
σ
With small level of T, agglomeration is
possible, since ω2 <1= ω1,
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2. The Core-Periphery Model: implications
1. What is the relationship“wiggle
betweendiagram”
this equation and the
sustainability of the core-periphery pattern?
1  μ 1σ μσ 1  μ σ 1μσ
ω 
T

T
2
2
σ
2
(σ - 1) - μσ  0
“no-black-hole” condition
• If T is very large, the first term becomes small and there are two
possibilities for the second term:
• If the “no-black-hole” condition does not hold, then the
agglomeration is stable: everyone in New York
• If the “no-black-hole” condition holds then the second term is
large, and the agglomeration depends on the values of T, μ, σ
(see next graph).
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2. The Core-Periphery Model: implications
When is a core-Periphery Pattern Sustainable?
The CP pattern
is sustainable
only when w2<1
ω2
ω σ2 
ω2
1
1  μ 1σ μσ 1  μ σ 1μσ
T

T
2
2
If the “no-blackhole” condition
holds,
T(S)
▼σ ▼ ρ
▲μ
1
1,5
T
1. The stability of T(S) increases the lower σ , ρ are:
•
Love for varieties; capacity for product differentiation.
2. The stability of T(S) depends in the importance of manufacturing (μ ):
•
•
If manufacturing is not very important (µ=0), not enough centripetal forces are generated to
sustain an agglomeration in region 1 (BL y FL). It tends to symmetry.
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Ex: If T>1, the expression is >1 and therefore
the
CP
Model
doesn’t
hold.
economía geográfica
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2. The Core-Periphery Model: implications
2. When is the symmetric “wiggle
equilibrium
broken [T(B)]?
diagram”
• The symmetric equilibrium T(B) is established when T is large.
• How to estimate that “breaking point”?:
–
–
It occurs when ω1-ω2 is horizontal in the symmetric equilibrium.
To estimate it, we have to differentiate totally respect to de λ: d(ω1-ω2 )/dλ
• Three equations
μ
dw
2

1  T 1σ 

2G 1σ
• Income
dY  μdλ 
• Trade Freedom
1  T 1σ
Z
1  T 1σ
• Real wages
σdw  2 ZdY  (σσ1 )Z
G μ dw  dw  μ
2





dω
1

ρ
μ
1

ρ

Z(μ
 ρ) 
μ
 
 2ZG 
2 
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dλ
ρ
1

μZ(1

ρ)

ρZ



economía geográfica
dG
G
dG
G
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2. The Core-Periphery Model: implications
When is the symmetric equilibrium sustainable?
dω
dλ
2
dω
μ  1  ρ   μ 1  ρ   Z(μ  ρ) 
 
 2ZG 
2 
dλ
 ρ   1  μZ(1  ρ)  ρZ 
ω2
T(B)
If the “no-blackhole” condition
holds,
0
• Trade is impossible:
• T=∞; Z=1
• Free trade:
• T=1; Z=0
1
• With T=1, the reallocation
of work force (dλ) does not
affect wage differences
(dω). Thus, (dω/dλ=0)
• It is equally expensive to
consume local varieties
than to import them.
T
1,5
• With intermediate T , the
wages in the central region
increase (dω/dλ>0).
• The symmetric equilibrium
is unstable.
• With high T (autarky), wages in
the central region decrease
(dω/dλ<0), because the
manufacturing supply increases
since they can’t be exported.
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2. The Core-Periphery Model: implications
“wiggle diagram”
• The breaking points associated to T are unique: with the “no-blackhole” condition, T(B) appears when T>1,
• The breaking points grow :
–
The larger manufacturing is (μ).
–
The lower σ , ρ are: the highest product differentiation is and the highest
the price index margin is respect to the costs.
–
The higher the intensity of the BL and FL is.
• The sustain points T(S) are always produced with high values of T.
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2. Applications
• Davis and Wenstein (2002):
“Bones,
bombs, and break Points: The
“wiggle
diagram”
Geography of Economic Activity”. American Economic Review.
• It analyzes the concentration of the Japanese population and
industry in 303 Japanese cities, since -6000 b.c. until 1998.
• Shock: “The Allied strategic bombing of Japan in World War II
devastated the targeted 66 cities. The bombing destroyed
almost half of all structures in these cities—a total of 2.2
million buildings. Two-thirds of productive capacity vanished.
300.000 Japanese were killed. Forty percent of the population
was rendered homeless. Some cities lost as much as half of
their population owing to deaths, missing, and refugees."'
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2. Application
• Davis and Wenstein (2002):
“Bones,
bombs, and break Points: The
“wiggle
diagram”
Geography of Economic Activity”. American Economic Review.
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economía geográfica
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2. Application
• Davis and Wenstein (2002): “Bones, bombs, and break Points: The Geography of
Economic Activity”. American “wiggle
Economic diagram”
Review.
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