Lecture 8: Increasing Returns and Monopolistic
Competition
Elhanan Helpman
Harvard
Fall 2016
Elhanan Helpman (Harvard)
Lecture 8: Increasing Returns and Monopolistic Competition
Fall 2016
1 / 12
Increasing Returns: Motivation
Some uncomfortable features about neoclassical trade theory:
stresses country asymmetries, while the bulk of trade ‡ows between similar
countries, and it involves little net factor trade (70% of trade is intraindustry
trade; see Grubel and Lloyd, 1974);
hard (though not impossible) to generate predictions for bilateral trade ‡ows,
while the evidence suggests robust patterns (gravity equation);
misses important aspects of the e¤ects of trade liberalization (within industry
reallocations; Balassa, 1964);
hard to think about …rms (intra…rm trade, multinational activity).
We will discuss models with scale economies, imperfect competition and
product di¤erentiation, which have proved to be very useful for dealing with
these caveats.
These models do not attempt to replace neoclassical trade theory— e¤ort to
embed new features in the factor proportions framework (see Helpman and
Krugman, 1985).
A natural …rst step: study external (or Marshallian) economies of scale, which
are consistent with perfect competition and homogenous products.
Elhanan Helpman (Harvard)
Lecture 8: Increasing Returns and Monopolistic Competition
Fall 2016
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External Economies of Scale
The unit cost function is
ci w k , ξ ,
(1)
where ξ is a vector of external e¤ects that a¤ect the productivity of …rms in
sector i and country k.
An important distinction is between national external e¤ects vs. international
external e¤ects.
We will come back to this distinction in the discussion of growth.
The standard assumption is ξ = Xik and ∂ci w k , Xik /∂Xik < 0, which
implies positive domestic and within-industry external e¤ects.
Because (in…nitessimal) …rms do not internalize the e¤ect of their output
levels on ξ, these …rms perceive the cost function in (1) as featuring constant
returns to scale.
The equilibrium conditions under autarky and free trade are then analogous
to those in the neoclassical model, except for the fact that both the cost
functions and unit factor requirements depend on ξ A and ξ T .
Elhanan Helpman (Harvard)
Lecture 8: Increasing Returns and Monopolistic Competition
Fall 2016
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External Economies: Some Implications
With local external e¤ects:
replication of the integrated equilibrium requires that an industry with external
e¤ects be concentrated in one country;
as a result, the FPE set may look quite di¤erent from the standard shape and
may not include the 45o degree line (see …gure below);
equilibrium is not unique (even when FPE is attainable);
countries with identical relative factor endowments may feature positive trade
‡ows and the H-O theorem may fail even in the 2 2 2 case;
gains from trade are not ensured unless every country’s GDP (evaluated at
post-trade prices) is higher under the vector ξ T than under the vector ξ A .
Still, when FPE (or conditional FPE) is attained, the Vanek equations hold:
Antweiler and Tre‡er (2002) use this fact to estimate the size of economies of
scale from the Vanek equations.
Elhanan Helpman (Harvard)
Lecture 8: Increasing Returns and Monopolistic Competition
Fall 2016
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External Economies: Integrated Equilibrium
K
V3
V2
E
C
V1
L
When the external economies are worldwide, but sector-speci…c, the FPE set
consists of the entire hectagon.
Elhanan Helpman (Harvard)
Lecture 8: Increasing Returns and Monopolistic Competition
Fall 2016
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External Economies of Scale: Antweiler and Tre‡er (2002)
µ
1
They specify sectoral productivity levels, γi (Xi ) = Xi i , and embody them
into Vanek equations. This allows them to estimate µi , with µi > 1
representing external economies of scale.
The results are reported in the following table:
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Lecture 8: Increasing Returns and Monopolistic Competition
Fall 2016
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Monopolistic Competition: Introduction
Balassa (1964) proposed monopolistic competition as a setup for explaining
the observed trade ‡ows within the European common market.
These types of models gained prominence in the 1980s, because they can
explain trade between similar countries and intraindustry trade:
even within industries, …rms may produce varieties of the industry’s product;
if consumers value “variety” or tastes over varieties are heterogeneous, many
brands are consumed;
with increasing returns, production of an individual variety is concentrated in
one location and therefore brands are internationally traded.
These features lead naturally to intra-industry trade, and can generate large
volumes of trade between similar countries.
Elhanan Helpman (Harvard)
Lecture 8: Increasing Returns and Monopolistic Competition
Fall 2016
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Monopolistic Competition
With internal economies of scale there cannot be perfect competition.
Chamberlain (1933) proposed monopolistic competition as the market
structure:
1
2
3
Every …rm has some market power; it faces a downward sloping demand curve.
There is a large number of …rms so that a price change by a single …rm has no
e¤ect on the level of demand faced by the other …rms.
There is free entry so that …rms’pro…ts are driven down to zero (the large
group case).
With product di¤erentiation a …rm has an incentive to di¤erentiate its brand.
Elhanan Helpman (Harvard)
Lecture 8: Increasing Returns and Monopolistic Competition
Fall 2016
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Product Di¤erentiation
Where does the downward sloping demand come from?
Several approaches to product di¤erentiation have been proposed. The most
popular is the “love-of-variety” approach of Dixit and Stiglitz (1977) (see
also Spence, 1976; and Lancaster, 1979).
Let there be I sectors or goods and denote by Ωi the set of varieties of good
i; denote by ω 2 Ωi a particular variety of good i.
Preferences of a representative consumer are of the form
U = U [u1 ( ) , u2 ( ) , ..., uI ( )] .
In the constant elasticity of substitution (CES) case with a continuum of
varieties:
ui =
Elhanan Helpman (Harvard)
Z ni
0
1 /αi
xi ( ω ) α i d ω
, 0 < αi < 1.
Lecture 8: Increasing Returns and Monopolistic Competition
(2)
Fall 2016
9 / 12
Product Di¤erentiation (continued)
The elasticity of substitution across varieties is constant and given by
σi = 1/ (1 αi ).
as αi ! 1, σi ! ∞ and varieties become perfect substitutes [ui linear in
xi (ω )];
as αi ! 0, σi ! 1 and we get the Cobb-Douglas case;
αi < 0 is ruled out for reasons that will become clear.
Notice the “love-of-variety” feature. Under perfect symmetry, xi (ω ) = xi for
all ω, and we have
(1 αi )/αi
ui = ni1 /αi xi = ni
(ni xi )
| {z }
.
“real” spending
This approach has also been used to represent production; producers may
prefer a larger variety of inputs (e.g., more specialized inputs) because they
yield higher productivity.
How do you solve this demand system? Use two-stage budgeting:
1
2
Rn
choose xi (ω )s to maximize ui subject to 0 i pi (ω ) xi (ω ) d ω
choose Ei to maximize U ( ) subject to ∑Ii =1 Ei
E.
Elhanan Helpman (Harvard)
Lecture 8: Increasing Returns and Monopolistic Competition
Ei ;
Fall 2016
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An Example: Krugman (1980)
Consumers have identical CES preferences as in (2) over varieties of a single
good.
Technology:
there is a constant marginal cost of production equal to 1/ϕ units of the
unique factor of production, labor;
there is a …xed cost of production f in terms of labor.
Market structure in the single sector is characterized by monopolistic
competition with a continuum of …rms of endogenous measure n.
Solving the utility maximization problem yields demand for each variety:
xi ( ω ) =
where
P=
Z n
0
E
P
p ( ω )1
p (ω )
P
σ
,
(3)
1 / (1 σ )
σ
dω
(4)
is the ideal price index (minimum cost of obtaining one unit of utility).
Elhanan Helpman (Harvard)
Lecture 8: Increasing Returns and Monopolistic Competition
Fall 2016
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Closed Economy
Each …rm maximizes pro…ts π (ω ) = p (ω ) x (ω ) (1/ϕ) wx (ω ) wf
subject to (3).
Because …rms take E and P as given (continuum assumption), we get the
standard constant-markup pricing formula of a monopolist facing a constant
price elasticity of demand:
σ w
p (ω ) =
.
σ 1ϕ
Now we can write the free-entry (or zero-pro…t) condition as
1
σ p ( ω ) x ( ω ) = wf , or simply:
x (ω ) = (σ
1) f ϕ.
(5)
Labor market clearing implies, however, that (f + x /ϕ) n = L, yielding:
n=
L
.
σf
Scale E¤ects: Note that the resulting welfare is n1 /α (x /L), which is
proportional to L1 /(σ 1 ) , i.e., larger economies produce more varieties and
achieve higher welfare.
Elhanan Helpman (Harvard)
Lecture 8: Increasing Returns and Monopolistic Competition
Fall 2016
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