1. THE CORE-PERIPHERY MODEL
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 Introduction. Core-Periphery Model (FKV, 1999). Aplicacions.
An intuitive view.
The model.
Implications.
Aplicacions.
Conclusion

3. Gobalización, comercio internacional y economía geográfica
1. Introduction
Gobalización, comercio internacional y economía geográfica

4. Gobalización, comercio internacional y economía geográfica
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.
Gobalización, comercio internacional y economía geográfica

5. Gobalización, comercio internacional y economía geográfica
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.
Gobalización, comercio internacional y economía geográfica

6. 2. The Core-Periphery Model: an intuitive view
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)
Gobalización, comercio internacional y economía geográfica

7. Gobalización, comercio internacional y economía geográfica
Sector-A (agriculture)
-Walrasian (CRS & Perf. Comp.)
-Variable Costs = aA units of L per unit of A
-A is the numeraire (pA=1)
North & South Mkts LA
(immobile
factor )
No costs of trade
Iceberg transport costs and “the index of freeness of trade varies between 0>Z>1
Sector-M (Manufactures)
- Dixit-Stiglitz Model monopolistic comp.
- Increasing Returns to Scale:
Fixed + Variable costs
Z is the freeness of trade:
(if T=1, Z=0 , trade is costless; if T=0; Z=1 trade is impossible)
LM (mobile factor )
North-South and South-North Migration
LM is moving according to the differences in real wages, w-w*  w/P - w*/P*
Gobalización, comercio internacional y economía geográfica

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 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.
Gobalización, comercio internacional y economía geográfica

9. 2. The Core-Periphery Model: an intuitive view
Backward (i.e. demand-wages) Linkage
Backward and Forward Linkages
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 Expenditure
The LM migrated spends
its income in the North rather than in the South.
Adjusts in Production
Market Size Effects:
The market in the North grows, in the south it decreases.

10. 2. The Core-Periphery Model: an intuitive view
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
Now + varieties are produced in the North than in the South
Adjusts in Production
(+ migration)
Price Index Effect:
P-North falls, P* South rises
The Northern import
Varieties and due to
< less costs of trade
lower P & higher P*.

11. 2. The Core-Periphery Model: an intuitive view
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 => 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):
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).
Gobalización, comercio internacional y economía geográfica

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:
1. Income: Since WA=1 for every r; the income 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 regions to r (those with low transport costs to r) increases.
Thus, due to the concentration of industry in one region, prices decreases in the later and rises in the others (Forward linkage effect).

15. 2. The Core-Periphery Model: the model
3. Nominal wages: it shows the level of wages at which manufacturing in region r breaks even:
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.

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 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).
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”.

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. 2. The Core-Periphery Model: implications
“wiggle diagram”
High transport cost;
T=2,1
σ= 5; μ=0,4
W1-W2>0 if λ>0,5
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.
Similar scenario to the movement of factor L without trade (Krugman y Obstfeld, 2007, Chapter 7) 1
1/2
λ= percentage that represents manufacturing in region r
Gobalización, comercio internacional y economía geográfica

19. 2. The Core-Periphery Model: implications
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
Low transport cost,
T=1,5
σ= 5;μ=0,4
1/2 1
λ=percentage that represents manufacturing L in region r (remember that we assume (λr=μr)

20. 2. The Core-Periphery Model: implications
“wiggle diagram”
Intermediate transport costs; T=1,7
σ= 5;μ=0,4
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 (λ=0,5) 1
1/2
λ=percentage that represents manufacturing in region r

21. 2. The Core-Periphery Model: implications “The Tomahawk diagram”
“wiggle diagram”
“The Tomahawk 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:
T(S): sustain point in the core-periphery pattern.
T(B): symmetry break point (equilibrium is stable).
0,5
T(B)
T(S) 1
1,5 T
When are these critical points possible?

22. 2. The Core-Periphery Model: implications
“wiggle diagram”

23. 2. The Core-Periphery Model: implications
“wiggle diagram”
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 (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?
ω1=1

24. 2. The Core-Periphery Model: implications
“wiggle diagram”
1. When is a core-Periphery Pattern Sustainable?
If w1=1, we have to find out when w2<>1
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 r=2 is T times higher than manufactured goods since they have to be imported supporting positive transport costs.
Therefore it is<1

25. 2. The Core-Periphery Model: implications
“wiggle diagram”
1. What is the relationship between this equation and the sustainability of the core-periphery pattern?
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:
With small level of T, agglomeration is possible, since ω2 <1= ω1,

26. 2. The Core-Periphery Model: implications
“wiggle diagram”
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, σ (see next graph).

27. 2. The Core-Periphery Model: implications
When is a core-Periphery Pattern Sustainable? ω2
The CP pattern is sustainable only when w2<1
ω 2
If the “no-black-hole” condition holds,
▼σ ▼ ρ ▲μ 1
T(S) T 1
1,5
The stability of T(S) increases the lower σ , ρ 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 (µ=0), not enough centripetal forces are generated to sustain an agglomeration in region 1 (BL y FL). It tends to symmetry.
Ex: If T>1, the expression is >1 and therefore the CP Model doesn’t hold.
Gobalización, comercio internacional y economía geográfica

28. 2. The Core-Periphery Model: implications
“wiggle diagram”
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 ω1-ω2 is horizontal in the symmetric equilibrium.
To estimate it, we have to differentiate totally respect to de λ: d(ω1-ω2 )/dλ
Income
Trade Freedom
Three equations
Real wages
Gobalización, comercio internacional y economía geográfica

29. 2. The Core-Periphery Model: implications
When is the symmetric equilibrium sustainable?
ω 2
If the “no-black-hole” condition holds,
T(B)
Trade is impossible:
T=∞; Z=1
Free trade:
T=1; Z=0 T 1
1,5
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.
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.

30. 2. The Core-Periphery Model: implications
“wiggle diagram”
The breaking points associated to T are unique: with the “no-black-hole” 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.

31. Gobalización, comercio internacional y economía geográfica
2. Applications
“wiggle diagram”
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 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 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."'
Gobalización, comercio internacional y economía geográfica

32. Gobalización, comercio internacional y economía geográfica
2. Application
“wiggle diagram”
Davis and Wenstein (2002): “Bones, bombs, and break Points: The Geography of Economic Activity”. American Economic Review.
Gobalización, comercio internacional y economía geográfica

33. Gobalización, comercio internacional y economía geográfica
2. Application
“wiggle diagram”
Davis and Wenstein (2002): “Bones, bombs, and break Points: The Geography of Economic Activity”. American Economic Review.
Gobalización, comercio internacional y economía geográfica