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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

- Introduction.
- Core-Periphery Model (FKV, 1999).
- An intuitive view.
- The model.
- Implications.
- Aplicacions.
- Conclusion

1. Introduction

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.

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.

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)

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

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.

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

2. The Core-Periphery Model an intuitive view

Forward (i.e. costs-prices) Linkage

? 1/2 (initially) We consider a migration

shock d? gt0

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.

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).

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

2. The Core-Periphery Model the model

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

2. The Core-Periphery Model the model

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.

2. The Core-Periphery Model the model

- 2.3. The CP Model Statement and Numerical

Examples - 2 regions 4 equations 8 equations for

equilibrium

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

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)

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

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?

wiggle diagram

2. The Core-Periphery Model implications

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

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

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,

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).

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.

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

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.

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.

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."'

wiggle diagram

2. Application

- Davis and Wenstein (2002) Bones, bombs, and

break Points The Geography of Economic

Activity. American Economic Review.

wiggle diagram

2. Application

- Davis and Wenstein (2002) Bones, bombs, and

break Points The Geography of Economic

Activity. American Economic Review.