Lecture 6 ECONOMIC GEOGRAPHY: THE CORE-PERIPHERY MODEL By Carlos Llano, References for the slides: Fujita, Krugman y Venables: Economía Espacial. Ariel

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

1. Introduction.

2. Core-Periphery Model (FKV, 1999).1. An intuitive view. 2. The model.3. Implications.

3. Aplicacions.

4. Conclusion

Index

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Gobalización, comercio internacional y economía geográfica

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1. Introduction

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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.

1. Introduction

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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.

1. Introduction

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Basic Model:

• 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)

2. The Core-Periphery Model: an intuitive view

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Sector-M (Manufactures)- Dixit-Stiglitz Model monopolistic comp.- Increasing Returns to Scale:Fixed + Variable costs

North & South Mkts

LA

(immobile factor )

LM is moving according to the differences in real wages, w-w* w/P - w*/P*

Z is the freeness of trade:(if T=1, Z=0 , trade is costless; if T=0; Z=1 trade is impossible)

Iceberg transport costs and “the index of freeness of trade varies between 0>Z>1

Sector-A (agriculture)-Walrasian (CRS & Perf. Comp.)-Variable Costs = aA units of L per unit of A-A is the numeraire (pA=1)

LM (mobile factor ) North-South and

South-North Migration

No costs of trade

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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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Backward and Forward Linkagesλ =1/2 (initially)

We consider a “migration shock” dλ >0

Backward (i.e. demand-wages) Linkage

Adjusts in Expenditure

Market Size Effects:The market in the North grows, in the south it decreases.

Adjusts in Production

Due to the costs of trade firms prefer to settle in large markets. This attracts+ LM .

The LM migrated spends its income in the North rather than in the South.


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λ =1/2 (initially)We consider a “migration shock” dλ >0

Forward (i.e. costs-prices) Linkage

Adjusts in Production

Price Index Effect:P-North falls, P* South rises

Adjusts in Production (+ migration)

Ceteris paribus,Smaller costs-of-livingAttract + LM

Now + varieties are produced in the North than in the South

The Northern importVarieties and due to < less costs of trade lower P & higher P*.


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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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• 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).

2. The Core-Periphery Model: the model

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• The agricultural wages equal 1 in both regions:

r

rrωλ

• 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:

rλωγλ rr

1Arw

Average real wage

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. 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). σ1

1

σ1srssr )T(wλG

rrrr μ)φ(1wμλY

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1/σ

s

1-σs

σ1srsr GTYw

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.

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μrrr Gwω

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”.

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2. The Core-Periphery Model: the model2.3. The CP Model: Statement and Numerical Examples• 2 regions * 4 equations= 8 equations for equilibrium:

2

μ1μλwY 11

2

μ1λ)w-μ(1Y 22

σ1

1σ1

2σ1

11 Twλ)(1λwG σ1

1σ1

2σ1

12 λ)w(1TwλG

1/σσ11

1σ22

1σ111 TYGYGYw 1/σ1σ

22σ-11σ

112 GYTGYw

μ111 Gwω μ

22Gwω 2

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“wiggle diagram”

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High transport cost; T=2,1σ= 5; μ=0,4

1/2

0

1λ= percentage that represents manufacturing in region r

2. The Core-Periphery Model: implications

0

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)

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Low transport cost, T=1,5

σ= 5;μ=0,4

1/2

0

1


0

• 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

λ=percentage that represents manufacturing L in region r (remember that we assume (λr=μr)

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Intermediate transport costs; T=1,7

σ= 5;μ=0,4

1/2

0

1

λ=percentage that represents manufacturing in region r


0

• 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)

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T(S)


1,5


“The Tomahawk diagram”•Solid lines: stable equilibriums; Doted lines: unstable eq.•With high transport costs: there is an stable equilibrium (λ=0,5).

0

1

λ

0,5

T

T(B)

Two critical points:• T(S): sustain point in the core-periphery

pattern.• T(B): symmetry break point (equilibrium

is stable).

When are these critical points possible?

1

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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?

1G

μ)/2(1Y

1

1

TG

μ)/2(1Y

2

2

ω1=1

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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:

1/σ1σσ1μ

2 T2

μ1T

2

μ1Tω

• 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

Cost of supplying region 1 from 2.

Cost of supplying region 2 from 1.

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1. What is the relationship between this equation and the sustainability of the core-periphery pattern?

μσ1σμσσ1σ2 T

2

μ1T

2

μ1ω

• 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:

0

σ

2σ1μ

T

ω2

With small level of T, agglomeration is

possible, since ω2 <1= ω1,

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1. What is the relationship between this equation and the sustainability of the core-periphery pattern?

μσ1σμσσ1σ2 T

2

μ1T

2

μ1ω

• 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).

0μσ-1)-(σ “no-black-hole” condition

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ω2

T1

1

1,5

ω 2If the “no-black-hole” condition holds,

T(S)

2. The Core-Periphery Model: implicationsWhen is a core-Periphery Pattern Sustainable?

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.• Ex: If T>1, the expression is >1 and therefore the CP Model doesn’t hold.

The CP pattern is sustainable only when w2<1

▼σ ▼ ρ▲μ

μσ1σμσσ1σ2 T

2

μ1T

2

μ1ω

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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

• Three equations

dw2

μμdλdY

σ1

σ1

σ1

σ1

2G

T1

T1

T1Z

2

2μ

ρZρ)μZ(11

ρ)Z(μρ1μ

ρ

ρ12ZG

dλ

dω

G

dGμdwdwG

G

dG)Z(σσZdYσdw

μ

12

• Income

• Trade Freedom

• Real wages

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T1

0

1,5

ω 2If the “no-black-hole” condition holds,T(B)

2. The Core-Periphery Model: implicationsWhen is the symmetric equilibrium sustainable?

• Free trade:• T=1; Z=0

2

2μ

ρZρ)μZ(11

ρ)Z(μρ1μ

ρ

ρ12ZG

dλ

dω

dλ

dω

• Trade is impossible:• T=∞; Z=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.

• 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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• 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.

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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 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 Geography of Economic Activity”. American Economic Review.

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2. Application• Davis and Wenstein (2002): “Bones, bombs, and break Points: The Geography of

Economic Activity”. American Economic Review.

Documents

Lecture 6 ECONOMIC GEOGRAPHY: THE CORE-PERIPHERY MODEL By Carlos Llano, References for the slides: Fujita, Krugman y Venables: Economía Espacial. Ariel