ECONOMIC GEOGRAPHY:

1
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

2
Index

1. Introduction.
2. Core-Periphery Model (FKV, 1999).
3. An intuitive view.
4. The model.
5. Implications.
6. Aplicacions.
7. Conclusion
   

3
1. Introduction
4
1. Introduction

• The Dixit-Stiglitz model is the starting point of
  the monopolistic competition models (DS, 1977).
• 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.

5
1. Introduction

• Conclusions of the Dixit-Stiglitz-spatial model

• 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).
• 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.

6
Basic Model
2. The Core-Periphery Model an intuitive view

• 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)

7
Sector-A (agriculture) -Walrasian (CRS Perf.
Comp.) -Variable Costs aA units of L per unit
of A -A is the numeraire (pA1)
North South Mkts
LA (immobile factor )
No costs of trade
Iceberg transport costs and the index of
freeness of trade varies between 0gtZgt1
Sector-M (Manufactures) - Dixit-Stiglitz Model
monopolistic comp. - Increasing Returns to
Scale Fixed Variable costs
Z is the freeness of trade (if T1, Z0 , trade
is costless if T0 Z1 trade is impossible)
North-South and South-North Migration
LM is moving according to the differences in real
wages, w-w ? w/P - w/P
8
Build Intuition Study model with symmetric
nations
2. The Core-Periphery Model an intuitive view

• 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 ?
• T transport cost
• ? of the industry in the North.
• In the beginning it will be ? 1/2 . Then it can
  tend to concentration.
• The proportion of the industry and its employment
  in a region is the same.

9
2. The Core-Periphery Model an intuitive view
Backward and Forward Linkages
Backward (i.e. demand-wages) Linkage
? 1/2 (initially) We consider a migration
shock d? gt0
10
2. The Core-Periphery Model an intuitive view
Forward (i.e. costs-prices) Linkage
? 1/2 (initially) We consider a migration
shock d? gt0
11
Dispersion Forces
2. The Core-Periphery Model an intuitive view

• 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 gt flight from the agglomeration.

12
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)
• Fr (phi) exogenous share of the agricultural
  labor force in region r.
• ?r (lambda) share of manufacturing labor force
  (LM) in region r.
• To simplify, it is assumed that the initial share
  of manufacturing employment is (LMµ LA 1- µ).

13
2. The Core-Periphery Model the model

• The agricultural wages equal 1 in both regions

• 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

Average real wage
The variation in the share of manufacturing
workers in region r depends on the difference
between the wage and the average
14
2. The Core-Periphery Model the model

• 2. Instantaneous equilibrium on instant t.
• Simultaneous solution of 4 equations

15
2. The Core-Periphery Model the model
16
2. The Core-Periphery Model the model

• 4. Real wages nominal wage deflated by the
  cost-of-living index in region r.
• The differences between regions only depend on
  the manufacturing workers real wage and the
  price indexes in those regions.
• Agricultural workers always earn and the price
  of its products is 1 (perfect competition).

• Solution of the basic C-P model.
• We analyze the solution when R2.
• 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.

17
2. The Core-Periphery Model the model

• 2.3. The CP Model Statement and Numerical
  Examples
• 2 regions 4 equations 8 equations for
  equilibrium

18
wiggle diagram
2. The Core-Periphery Model implications
High transport cost T2,1 s 5 µ0,4

• W1-W2gt0 if ?gt0,5
• When manufacturing is concentrated in r
  (?gt0,5), 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)

1
1/2
0
? percentage that represents manufacturing in
region r
19
2. The Core-Periphery Model implications

• W1-W2ltgt0 for any ?
• The share of manufacturing agglomeration
  forces due to
• BL the gt local market, gt nominal wages.
• FL the gt variety of locally produced goods, lt
  price index.
• Tendency towards agglomeration. Unstable
  Equilibrium even when ?0,5

Low transport cost, T1,5 s 5µ0,4
0
0
1/2
1
?percentage that represents manufacturing L in
region r (remember that we assume (?rµr)
20
wiggle diagram
2. The Core-Periphery Model implications
Intermediate transport costs T1,7 s 5µ0,4

• 5 equilibriums 3 stable 2 unstable
• 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 (?0,5)

0
1
0
1/2
?percentage that represents manufacturing in
region r
21
wiggle diagram
2. The Core-Periphery Model implications

• The Tomahawk diagram
• Solid lines stable equilibriums Doted lines
  unstable eq.
• With high transport costs there is an stable
  equilibrium (?0,5).

?
1

• Two critical points
• T(S) sustain point in the core-periphery
  pattern.
• T(B) symmetry break point (equilibrium is
  stable).

0,5
T(B)
0
T(S)
1,5
T
1
When are these critical points possible?
22
wiggle diagram
2. The Core-Periphery Model implications
23
wiggle diagram
2. The Core-Periphery Model implications

• 1. When is the core-Periphery Pattern Sustainable
  (agglomeration)?
• 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 (?1).
• We are questioning when ?1lt ?2. 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 ?1 if all the industry
  agglomerates in 1?

?11
24
wiggle diagram
2. The Core-Periphery Model implications

• 1. When is a core-Periphery Pattern Sustainable?
• If w11, we have to find out when w2ltgt1
• Thus, we substitute in the w2 equation

Cost of supplying region 1 from 2.
Cost of supplying region 2 from 1.

• Nominal wage at which a firm located in 2 breaks
  even (or exactly covers the costs)
• There is a backward effect via demand from the
  concentration of production to the nominal wage
  rate firms can afford to pay in r 1.

• FL the price index in r2 is T times higher than
  manufactured goods since they have to be imported
  supporting positive transport costs.
• Therefore it islt1

25
wiggle diagram
2. The Core-Periphery Model implications
1. What is the relationship between this equation
and the sustainability of the core-periphery
pattern?

• When T1 (with no transport costs), ?2 1,
• Localization is irrelevant.
• With a small transport cost increase (and by
  totally differentiating and evaluating the
  derivative at T1, ?2 1), we find that

With small level of T, agglomeration is possible,
since ?2 lt1 ?1,
26
wiggle diagram
2. The Core-Periphery Model implications
1. What is the relationship between this equation
and the sustainability of the core-periphery
pattern?
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, s (see next graph).

27
2. The Core-Periphery Model implications
When is a core-Periphery Pattern Sustainable?
?2
? 2
The CP pattern is sustainable only when w2lt1
If the no-black-hole condition holds,
1
T(S)
T
1
1,5

• The stability of T(S) increases the lower s , ?
  are
• Love for varieties capacity for product
  differentiation.
• The stability of T(S) depends in the importance
  of manufacturing (µ )
• If manufacturing is not very important (µ0), not
  enough centripetal forces are generated to
  sustain an agglomeration in region 1 (BL y FL).
  It tends to symmetry.
• Ex If Tgt1, the expression is gt1 and therefore
  the CP Model doesnt hold.

28
wiggle diagram
2. The Core-Periphery Model implications

• 2. When is the symmetric equilibrium broken
  T(B)?
• The symmetric equilibrium T(B) is established
  when T is large.
• How to estimate that breaking point?
• It occurs when ?1-?2 is horizontal in the
  symmetric equilibrium.
• To estimate it, we have to differentiate totally
  respect to de ? d(?1-?2 )/d?

• Income

• Trade Freedom

• Three equations

• Real wages

29
2. The Core-Periphery Model implications
When is the symmetric equilibrium sustainable?
? 2
If the no-black-hole condition holds,
T(B)
0

• Trade is impossible
• T8 Z1

• Free trade
• T1 Z0

T
1
1,5

• With T1, the reallocation of work force (d?)
  does not affect wage differences (d?). Thus,
  (d?/d?0)
• It is equally expensive to consume local
  varieties than to import them.

• With intermediate T , the wages in the central
  region increase (d?/d?gt0).
• The symmetric equilibrium is unstable.

• With high T (autarky), wages in the central
  region decrease (d?/d?lt0), because the
  manufacturing supply increases since they cant
  be exported.

30
wiggle diagram
2. The Core-Periphery Model implications

• The breaking points associated to T are unique
  with the no-black-hole condition, T(B) appears
  when Tgt1,
• The breaking points grow
• The larger manufacturing is (µ).
• The lower s , ? 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.

31
wiggle diagram
2. Applications

• Davis and Wenstein (2002) Bones, bombs, and
  break Points The 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 citiesa 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."'

32
wiggle diagram
2. Application

• Davis and Wenstein (2002) Bones, bombs, and
  break Points The Geography of Economic
  Activity. American Economic Review.

33
wiggle diagram
2. Application

• Davis and Wenstein (2002) Bones, bombs, and
  break Points The Geography of Economic
  Activity. American Economic Review.