Lecture: The Core-Periphery model
Two approaches for location and concentration
Inherent differences in locations
Random events that enforce themselves
Destiny vs. good luck (which can change over time)
Different views on role of government
Different views on role of history (and random events).
Forces that determine concentration
In equilibrium there is a balance between these forces.
Types of agglomeration economies
At level of individual firms
o Internal returns to scale
At level of the sector
o Economies of localization (Marshall)
At level of group of sectors
o Economies of urbanization (Jacobs)
Factors influencing agglomeration
Local demand (potentially including path-dependency)
Fixed costs
Transport costs
Comparative advantage (partly human-made)
The core-periphery model was the starting point of ‘The New Economic Geography’.
The mechanism behind agglomeration; the model lies in explaining agglomeration as
something that arises endogenously:
The 2 regions are identical.
Symmetric equilibria are possible, however
Sometimes: asymmetric equilibria arise, not clear which region is going to be
the center or periphery
o Path dependency.
Intuitive insights: agglomeration can be the result of the interaction of economic
actors in a market environment → Homogeneous space becoming heterogeneous.
Some regions grow, but none of them has natural (dis)advantage.
,Summary of the model
Because of economies of scale, producers have an incentive to concentrate
production of each good or service in a limited number of locations.
Because of the cost of transacting across distance, the preferred location of each
individual producer are those where demand is large or supply of inputs is convenient
– which in general are the locations chosen by other producers. Thus concentration
of industry, once established, tends to be self-sustaining.
Economic theory has for a long time focused on perfect competition, which is
incompatible with endogenous agglomerations, because production can be efficient
at an arbitrary small scale.
Important aspects of the CP model
Increasing returns to scale
o Dixit Stiglitz model of imperfect competition.
Iceberg transportation costs; part of the goods melt away when transporting.
Need for simulations; there is no closed form solution of the equations.
Building blocks of the Core-Periphery model
Traditional elements of economic theory
o Utility maximizing consumers
Cobb Douglas utility function over two types of goods
One of the goods is a composite manufacturing good
Some manufacturing goods have a CES-subutility function.
Typical two-stage optimization problem
o Profit maximizing producers
Modern elements of economic theory
o Increasing returns to scale
o Monopolistic competition
Spatial elements of economic theory
o Iceberg transportation costs
,Two Stage Budgeting
1. The consumer determines the allocation of budget over manufacturing an
agricultural goods, and
2. Determines the demand for varieties of the manufacturing goods.
The first stage needs information from the second stage, so it’s not really a
sequential procedure.
Demand for Food and Manufacturing Goods
Budget shares are determined by the higher level Cobb-Douglas utility function for
food F and the composite manufacturing good M . The price-index I is the price for
this composite good. The price for food is the numeraire:
U =F 1−δ M δ F+ I ⋅ M =Y
The maximization of this utility function under the budget constraint lead to demand
functions:
F=( 1−δ ) Y ; M =δ ⋅
Y
I ( )
Expenditure on manufacturing goods is δY and the price elasticity of the demand for
the manufacturing good M with respect to I is -1 (Y denotes individual income).
Demand for Manufacturing Goods
Sub-utility function
(∑ )
N 1
ρ ρ
M= c i , 0< ρ< 1
i=1
M =¿subutility,
c i=¿ amount consumed of variety i,
N=¿ total number of varieties,
ρ=¿ a parameter.
ρ indicates how easy it is to substitute one variety for another;
o for ρ=1this is easy,
o for ρ → 0 it is difficult.
ρ is closely related to the price elasticity of demand ϵ=1/(1−ρ).
Indicates love-of-variety
Maximize this sub-utility function under the constraint
N
∑ pi c i=δY
i=1
Solution of the demand equations:
( )
1
ρ−1 N ρ
p
c i= i
δY , A=∑ p ρ−1
j
A j=1
We take the value of A as given when we discuss properties of the demand curve. If
the number of varieties is large, the error is small.
Price elasticity of demand has absolute value – ϵ (demand is downward sloping):
−ϵ =
∂ c i pi
∂ pi ci
= ( )
∂ log ci
∂ log pi
, Properties of the demand equations:
1. Fixed budget shares for food and manufacturing are unrealistic
2. Iso-elastic demand functions are also specific.
Aggregate Demand
Sum of all individual demands and erivation is essentially adding up.
Total labor force is L
A fraction γ works in the manufacturing sector, where they earn a wage W
o Income Y =W
The others work in the food sector where they earn a wage 1
o Income Y =1
A fraction ϕ of the workers in the food sector and a fraction λ of the workers in
the manufacturing sector live in region 1, the others in region 2.
For example,
The total number of workers in the food sector in region 2 is: ( 1−ϕ )( 1−γ ) ⋅ L
The number of varieties produced in region 1 is n1 and in region 2 n2 , so
n1 +n 2=N
The price of variety i in region 1 is pi ,1, the price of variety i in region 2 is pi ,2 .
Total demand for variety i in region 1 is
p−ϵ
i,1
x i ,1= δ Y1,
∑ p1−ϵ
j,1
j
where Y 1 is total income in region 1.
Transportation Costs
Iceberg transportation costs: a given share of the production melts away during
transportation. There exist no transportation costs within regions.
Producers
Produce at one location.
Have a linear cost function and take wage as given
Maximize profits by setting the price.
Production is equal to demand plus total transportation cost.
Optimal Price Setting
Fixed cost α and variable cost β
Labor is the only input → C ¿
o Wage is region specific and production is variety specific.
Revenues: R=p i ,1 x i ,1 + pi , 2 x i ,2
If a firm is located in region 1, total production is x i=x i ,1 +T ⋅ x i ,2
Profits π=( pi , 1−β W 1 ) x i ,1 + ( pi , 2−β W 1 T ) x i ,2 −α W 1
Short-run Equilibrium
In the short run the location of workers in the manufacturing sector is given. Firms are
assumed to locate where the workers are. The number of varieties produced in the
two regions are: n1 =λN , n2=( 1−λ ) N .
Lecture: The Empirical Status of the New Economic Geography
Two approaches for location and concentration
Inherent differences in locations
Random events that enforce themselves
Destiny vs. good luck (which can change over time)
Different views on role of government
Different views on role of history (and random events).
Forces that determine concentration
In equilibrium there is a balance between these forces.
Types of agglomeration economies
At level of individual firms
o Internal returns to scale
At level of the sector
o Economies of localization (Marshall)
At level of group of sectors
o Economies of urbanization (Jacobs)
Factors influencing agglomeration
Local demand (potentially including path-dependency)
Fixed costs
Transport costs
Comparative advantage (partly human-made)
The core-periphery model was the starting point of ‘The New Economic Geography’.
The mechanism behind agglomeration; the model lies in explaining agglomeration as
something that arises endogenously:
The 2 regions are identical.
Symmetric equilibria are possible, however
Sometimes: asymmetric equilibria arise, not clear which region is going to be
the center or periphery
o Path dependency.
Intuitive insights: agglomeration can be the result of the interaction of economic
actors in a market environment → Homogeneous space becoming heterogeneous.
Some regions grow, but none of them has natural (dis)advantage.
,Summary of the model
Because of economies of scale, producers have an incentive to concentrate
production of each good or service in a limited number of locations.
Because of the cost of transacting across distance, the preferred location of each
individual producer are those where demand is large or supply of inputs is convenient
– which in general are the locations chosen by other producers. Thus concentration
of industry, once established, tends to be self-sustaining.
Economic theory has for a long time focused on perfect competition, which is
incompatible with endogenous agglomerations, because production can be efficient
at an arbitrary small scale.
Important aspects of the CP model
Increasing returns to scale
o Dixit Stiglitz model of imperfect competition.
Iceberg transportation costs; part of the goods melt away when transporting.
Need for simulations; there is no closed form solution of the equations.
Building blocks of the Core-Periphery model
Traditional elements of economic theory
o Utility maximizing consumers
Cobb Douglas utility function over two types of goods
One of the goods is a composite manufacturing good
Some manufacturing goods have a CES-subutility function.
Typical two-stage optimization problem
o Profit maximizing producers
Modern elements of economic theory
o Increasing returns to scale
o Monopolistic competition
Spatial elements of economic theory
o Iceberg transportation costs
,Two Stage Budgeting
1. The consumer determines the allocation of budget over manufacturing an
agricultural goods, and
2. Determines the demand for varieties of the manufacturing goods.
The first stage needs information from the second stage, so it’s not really a
sequential procedure.
Demand for Food and Manufacturing Goods
Budget shares are determined by the higher level Cobb-Douglas utility function for
food F and the composite manufacturing good M . The price-index I is the price for
this composite good. The price for food is the numeraire:
U =F 1−δ M δ F+ I ⋅ M =Y
The maximization of this utility function under the budget constraint lead to demand
functions:
F=( 1−δ ) Y ; M =δ ⋅
Y
I ( )
Expenditure on manufacturing goods is δY and the price elasticity of the demand for
the manufacturing good M with respect to I is -1 (Y denotes individual income).
Demand for Manufacturing Goods
Sub-utility function
(∑ )
N 1
ρ ρ
M= c i , 0< ρ< 1
i=1
M =¿subutility,
c i=¿ amount consumed of variety i,
N=¿ total number of varieties,
ρ=¿ a parameter.
ρ indicates how easy it is to substitute one variety for another;
o for ρ=1this is easy,
o for ρ → 0 it is difficult.
ρ is closely related to the price elasticity of demand ϵ=1/(1−ρ).
Indicates love-of-variety
Maximize this sub-utility function under the constraint
N
∑ pi c i=δY
i=1
Solution of the demand equations:
( )
1
ρ−1 N ρ
p
c i= i
δY , A=∑ p ρ−1
j
A j=1
We take the value of A as given when we discuss properties of the demand curve. If
the number of varieties is large, the error is small.
Price elasticity of demand has absolute value – ϵ (demand is downward sloping):
−ϵ =
∂ c i pi
∂ pi ci
= ( )
∂ log ci
∂ log pi
, Properties of the demand equations:
1. Fixed budget shares for food and manufacturing are unrealistic
2. Iso-elastic demand functions are also specific.
Aggregate Demand
Sum of all individual demands and erivation is essentially adding up.
Total labor force is L
A fraction γ works in the manufacturing sector, where they earn a wage W
o Income Y =W
The others work in the food sector where they earn a wage 1
o Income Y =1
A fraction ϕ of the workers in the food sector and a fraction λ of the workers in
the manufacturing sector live in region 1, the others in region 2.
For example,
The total number of workers in the food sector in region 2 is: ( 1−ϕ )( 1−γ ) ⋅ L
The number of varieties produced in region 1 is n1 and in region 2 n2 , so
n1 +n 2=N
The price of variety i in region 1 is pi ,1, the price of variety i in region 2 is pi ,2 .
Total demand for variety i in region 1 is
p−ϵ
i,1
x i ,1= δ Y1,
∑ p1−ϵ
j,1
j
where Y 1 is total income in region 1.
Transportation Costs
Iceberg transportation costs: a given share of the production melts away during
transportation. There exist no transportation costs within regions.
Producers
Produce at one location.
Have a linear cost function and take wage as given
Maximize profits by setting the price.
Production is equal to demand plus total transportation cost.
Optimal Price Setting
Fixed cost α and variable cost β
Labor is the only input → C ¿
o Wage is region specific and production is variety specific.
Revenues: R=p i ,1 x i ,1 + pi , 2 x i ,2
If a firm is located in region 1, total production is x i=x i ,1 +T ⋅ x i ,2
Profits π=( pi , 1−β W 1 ) x i ,1 + ( pi , 2−β W 1 T ) x i ,2 −α W 1
Short-run Equilibrium
In the short run the location of workers in the manufacturing sector is given. Firms are
assumed to locate where the workers are. The number of varieties produced in the
two regions are: n1 =λN , n2=( 1−λ ) N .
Lecture: The Empirical Status of the New Economic Geography
