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Krugman Monopolistic Competition Trade Model
Seyed Ali Madanizadeh
Sharif U. of Tech.
May 3, 2014
Seyed Ali Madanizadeh (Sharif U. of Tech.) Krugman Monopolistic Competition Trade Model May 3, 2014 1 / 23
Introduction
Dixit and Stiglitz (1977): brought monopolistic competition into a GEframework
Krugman (1979,1980, 1985) Monopolistic Competition Trade Model
Economy of scale motive of trade
Seyed Ali Madanizadeh (Sharif U. of Tech.) Krugman Monopolistic Competition Trade Model May 3, 2014 2 / 23
Model
No differences in factor intensities
One factor of production: Call it labor L with wage w
Labor moves across producers but not across countries
Seyed Ali Madanizadeh (Sharif U. of Tech.) Krugman Monopolistic Competition Trade Model May 3, 2014 3 / 23
Model
Same effi ciencies for all the labor and producers z
Production setup requires a fixed cost (additional labor) F
The range of goods to be produced are endogenous
It is determined by the free entry condition
Each producer makes a different good: so it sells it monopolistically.
The space of goods is modeled as a continuum
Index the goods by j
For now consider a closed economy
Seyed Ali Madanizadeh (Sharif U. of Tech.) Krugman Monopolistic Competition Trade Model May 3, 2014 4 / 23
Household
Preferences: Spence-Dixit-Stiglitz (SDS)
A CES over the continuum of goods:
U =(∫
y (j)(σ−1)/σ dj) σ
σ−1
σ > 1
Budget Constraint: ∫p (j) y (j) dj = X = wL+Π
X : Total Spending
Seyed Ali Madanizadeh (Sharif U. of Tech.) Krugman Monopolistic Competition Trade Model May 3, 2014 5 / 23
Household
Demand for good j :
x (j) =(p (j)P
)−(σ−1)X
where
P =(∫
p (j)−(σ−1) dj)−1/(σ−1)
Seyed Ali Madanizadeh (Sharif U. of Tech.) Krugman Monopolistic Competition Trade Model May 3, 2014 6 / 23
Producer
The market structure is monopolistic competition.
Each good is produced by a separate monopolist who takes totalspending X and the price index P in each market as given.
Markets are segmented so that producers can set a different price ineach national market.
Seyed Ali Madanizadeh (Sharif U. of Tech.) Krugman Monopolistic Competition Trade Model May 3, 2014 7 / 23
Producer
Profit maximization⇒Constant Markup m̄ = σσ−1 over price:
p = m̄wz
Revenue of a representative firm
x =(m̄wzP
)−(σ−1)X
Profit in market n :Π =
xσ− wF
Seyed Ali Madanizadeh (Sharif U. of Tech.) Krugman Monopolistic Competition Trade Model May 3, 2014 8 / 23
Market
Suppose J is the measure of producers of goods
Price Index:
P =
(∫ J
0p (j)−(σ−1) dj
)−1/(σ−1)
= J−1/(σ−1)p
= J−1/(σ−1)m̄wz
Seyed Ali Madanizadeh (Sharif U. of Tech.) Krugman Monopolistic Competition Trade Model May 3, 2014 9 / 23
Market Equilibrium
Firm’s revenue in equilibrium:
x =
(m̄wzP
)−(σ−1)X
=
(m̄w
zJ−1/(σ−1)m̄wz
)−(σ−1)X
=XJ
Seyed Ali Madanizadeh (Sharif U. of Tech.) Krugman Monopolistic Competition Trade Model May 3, 2014 10 / 23
Equilibrium Conditions
Income = Expenditure
Jx = X = wL+Π
Free EntryΠ = 0
Unknowns: wP , J
Seyed Ali Madanizadeh (Sharif U. of Tech.) Krugman Monopolistic Competition Trade Model May 3, 2014 11 / 23
Equilibrium Conditions
Π = 0⇒
wσF = x =XJ
=wLJ
Therefore the endogenous number of firms becomes:
J =L
σF
Seyed Ali Madanizadeh (Sharif U. of Tech.) Krugman Monopolistic Competition Trade Model May 3, 2014 12 / 23
Equilibrium Conditions
Real Wage
wP
=w
J−1/(σ−1)m̄wz
=zJ1/(σ−1)
m̄
=z( L
σF
)1/(σ−1)
m̄
Aggregate Welfare
W =wLP
=zLσ/(σ−1)
m̄ (σF )1/(σ−1)
Seyed Ali Madanizadeh (Sharif U. of Tech.) Krugman Monopolistic Competition Trade Model May 3, 2014 13 / 23
Free trade
Consider N similar countries and no trade costs
L→ NL⇒
wP
=z(NL
σF
)1/(σ−1)
m̄
W =z (NL)σ/(σ−1)
m̄ (σF )1/(σ−1)
Total measure of goods = NJ = NLσF ⇒
J =L
σFin each country
Seyed Ali Madanizadeh (Sharif U. of Tech.) Krugman Monopolistic Competition Trade Model May 3, 2014 14 / 23
Costly Trade
Consider 2 similar countries and trade costs dHF = dFH = d
Revenue of a representative firm in i selling to n:
rni =
(m̄wdzP
)−(σ−1)X : (n 6= i)
rii =
(m̄wzP
)−(σ−1)X : (n = i)
Seyed Ali Madanizadeh (Sharif U. of Tech.) Krugman Monopolistic Competition Trade Model May 3, 2014 15 / 23
Costly Trade
Total sales of firms in a country:
R = J
((m̄wzP
)−(σ−1)X +
(m̄wdzP
)−(σ−1)X
)
= J(m̄wz
)−(σ−1) (Pσ−1X + d−(σ−1)Pσ−1X
)= J
(m̄wz
)−(σ−1) (1+ d−(σ−1)
)Pσ−1X
Seyed Ali Madanizadeh (Sharif U. of Tech.) Krugman Monopolistic Competition Trade Model May 3, 2014 16 / 23
Costly Trade
Total Profits of firms in a country:
Π =Rσ− JwF
Seyed Ali Madanizadeh (Sharif U. of Tech.) Krugman Monopolistic Competition Trade Model May 3, 2014 17 / 23
Costly Trade
Price index in a country:
P =
(∫ J
0p (j)−(σ−1) dj
)−1/(σ−1)
=
(J(m̄wz
)−(σ−1)+ J
(m̄wdz
)−(σ−1))−1/(σ−1)
=1
J1/(σ−1)m̄wz
(1+ d−(σ−1)
)−1/(σ−1)
Seyed Ali Madanizadeh (Sharif U. of Tech.) Krugman Monopolistic Competition Trade Model May 3, 2014 18 / 23
Costly Trade Equilibrium Conditions
R = wL+ΠΠ = 0
⇒
JwF =Rσ
=wLσ
⇒J =
LσF
Seyed Ali Madanizadeh (Sharif U. of Tech.) Krugman Monopolistic Competition Trade Model May 3, 2014 19 / 23
Costly Trade Equilibrium Conditions
P =1( L
σF
)1/(σ−1)m̄wz
(1+ d−(σ−1)
)−1/(σ−1)
orwP=
(L
σF
)1/(σ−1)z(1+ d−(σ−1)
)1/(σ−1)
Seyed Ali Madanizadeh (Sharif U. of Tech.) Krugman Monopolistic Competition Trade Model May 3, 2014 20 / 23
Costly Trade
Gains from trade: Moving from Autarky to costly trade
(w/P)d
(w/P)A=(1+ d−(σ−1)
)1/(σ−1)
Seyed Ali Madanizadeh (Sharif U. of Tech.) Krugman Monopolistic Competition Trade Model May 3, 2014 21 / 23
Costly Trade
Trade Elasticity:
XFHXF
= JH
(m̄wHdFHzPF
)−(σ−1)
Seyed Ali Madanizadeh (Sharif U. of Tech.) Krugman Monopolistic Competition Trade Model May 3, 2014 22 / 23
References
Eaton Kortum Book chapter 3.
Krugman 1979, 1980
Krugman & Helpman (1985)
Seyed Ali Madanizadeh (Sharif U. of Tech.) Krugman Monopolistic Competition Trade Model May 3, 2014 23 / 23