Monopolistic Competition in Trade III Trade Costs and...
Transcript of Monopolistic Competition in Trade III Trade Costs and...
Monopolistic Competition in Trade IIITrade Costs and Gains from Trade
Notes for Graduate International Trade Lectures
J. Peter Neary
University of Oxford
January 21, 2015
J.P. Neary (University of Oxford) Monopolistic Competition III January 21, 2015 1 / 31
Plan of Lectures
1 Preliminaries
2 Integrated versus Segmented Markets
3 Globalization versus Colder Icebergs
4 Gains from Trade
5 Calibrating Gains from Trade
6 Conclusion
7 Supplementary Material
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Introduction
The Bottom Line
Trade Costs and General Demands: Together at Last!
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Introduction
Motivation
“Traditional trade theory assumes that countries are different and explains whysome countries export agricultural products whereas others export industrialgoods. The new theory clarifies why worldwide trade is in fact dominated bycountries which not only have similar conditions, but also trade in similar products. . . This kind of trade enables specialization and large-scale production,which result in lower prices and a greater diversity of commodities.”
Press Release for Paul Krugman’s Nobel Prize (Emphasis added)http://www.nobelprize.org/nobel_prizes/economic-sciences/laureates/2008/press.html
Note: 3 of the 4 highlighted effects do not hold with CES preferences!
“This is an unsatisfactory result. In another paper [1979] I have developed aslightly different model in which trade leads to an increase in scale of productionas well as an increase in diversity. That model is, however, more difficult to workwith, so that it seems worth sacrificing some realism to gain tractabilityhere.”
Krugman (1980)
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Introduction
In this file
Search for tractability without sacrificing realism
Combine trade costs and additive separability in a simple model
Highlight the importance of demand properties, esp. “subconvexity”
Focus on information needed to calibrate gains from trade
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Introduction
Literature: Monopolistic Competition in GE
Closed economy; additively separable preferences; CES as a special case:
Dixit-Stiglitz (1977)
Trade costs with CES preferences:
Krugman (1980) etc.
Trade costs and gains from trade with CES preferences:
Arkolakis-Costinot-Rodrıguez-Clare (AER 2012), Simonovska-Waugh(2012), Melitz-Redding (2013), Ossa (2013)
Free trade with additively separable preferences:
Krugman (1979)Neary (2009), Zhelobodko-Kokovin-Parenti-Thisse (2012),Dhingra-Morrow (2012), Mrazova-Neary (2013)
Trade costs with non-CES preferences:
Bertoletti-Epifani (2012)Arkolakis-Costinot-Donaldson-Rodrıguez-Clare (mimeo. 2012)Bykadorov-Kokovin (2012)
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Introduction
Outline
1 Preliminaries
2 Integrated versus Segmented Markets
3 Globalization versus Colder Icebergs
4 Gains from Trade
5 Calibrating Gains from Trade
6 Conclusion
7 Supplementary Material
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Preliminaries
Plan of Lectures
1 PreliminariesMonopolistic Competition in the Global Economy
2 Integrated versus Segmented Markets
3 Globalization versus Colder Icebergs
4 Gains from Trade
5 Calibrating Gains from Trade
6 Conclusion
7 Supplementary Material
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Preliminaries Monopolistic Competition in the Global Economy
Equilibrium in the Global Economy
κ+ 1 identical countries; n homogeneous firms in each
Symmetric iceberg trade costs τ ; no fixed costs of trade
L identical worker-consumers per country, additively separable preferences:
U = F
[∫i∈N
u{x(i)}di], F ′ > 0, u′ > 0, u′′ < 0
With symmetry: x(i) = x, x∗(i) = x∗
U = F[n{u(x) + κu(x∗)}
]Market clearing:
Goods-Market Equilibrium: y = L(x+ κτx∗)
Labor-Market Equilibrium: L = n (f + cy)
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Integrated versus Segmented Markets
Plan of Lectures
1 Preliminaries
2 Integrated versus Segmented Markets
3 Globalization versus Colder Icebergs
4 Gains from Trade
5 Calibrating Gains from Trade
6 Conclusion
7 Supplementary Material
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Integrated versus Segmented Markets
Integrated versus Segmented Markets
Integrated: Prices equalized allowing for transport costs:
p∗ = τp
Segmented: Marginal revenues equalized allowing for transport costs:
rx = c, r∗x = τc ⇒ r∗x = τrx
These are the same if and only if preferences are CES: Proof
rx =ε− 1
εp, r∗x =
ε∗ − 1
ε∗p∗
Segmented markets and subconvex demands imply Reciprocal Dumping :
Lower price-cost margins abroad: p∗
τc <pc
Lower τ -inclusive prices abroad: p∗ < τpProof
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Globalization versus Colder Icebergs
Plan of Lectures
1 Preliminaries
2 Integrated versus Segmented Markets
3 Globalization versus Colder Icebergs
4 Gains from Trade
5 Calibrating Gains from Trade
6 Conclusion
7 Supplementary Material
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Globalization versus Colder Icebergs
Profit Maximization
Assume segmented markets
Profit maximization:
r∗x = τrx
⇒ ηx = η∗x∗ + τ
Elasticity of marginal revenue:
η ≡ −xrxxrx
=2− ρε− 1
> 0
x∗ positively related to x:
Decreasing in τ ;Independent of κ
x*
x
> 1
O
= 1
MR=MC
CES: η = η∗ = 1σ ; x∗ = τ−σx
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Globalization versus Colder Icebergs
Free Entry
Zero profits:
π + κπ∗ = f
π = (p− c)Lx = cLxε−1
π∗ = (p∗ − τc)Lx∗ = τcLx∗
ε∗−1
⇒ x
ε− 1+ κτ
x∗
ε∗ − 1=
f
cL
⇒ ωπεηx+ (1− ωπ) ε∗η∗x∗ =
− (1− ωπ) (κ+ τ)
ωπ: Home market profit share
x∗ negatively related to x:
Decreasing in τ and κ
x*
xO
= 0
= 1
> 1
= 1
Lcf)1(
Lcf
)1( *
CES: x+ κτx∗ = (σ − 1) fcL = yL
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Globalization versus Colder Icebergs
Equilibrium Sales
Home and export sales:
επηx = (1− ωπ) [−κ+ (ε∗ − 1) τ ]
επη∗x∗ = − (1− ωπ) κ
− [1 + ωπ (ε− 1)] τ
π-weighted aggregateelasticity:
επ ≡ ωπε+ (1− ωπ) ε∗
Globalization (κ ↑): x ↓ x∗ ↓
Lower τ : x ↓ x∗ ↑
x*
xO
A
B
MR=MC
= 0
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Globalization versus Colder Icebergs
Equilibrium Sales
Home and export sales:
επηx = (1− ωπ) [−κ+ (ε∗ − 1) τ ]
επη∗x∗ = − (1− ωπ) κ
− [1 + ωπ (ε− 1)] τ
π-weighted aggregateelasticity:
επ ≡ ωπε+ (1− ωπ) ε∗
Globalization (κ ↑): x ↓ x∗ ↓
Lower τ : x ↓ x∗ ↑
x*
xO
= 0
A
C
MR=MC
CES: ε = σ, εη = εη∗ = 1
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Globalization versus Colder Icebergs
Implications for Prices, Output, and Firm Numbers
Prices: p = εε−1c, p∗ = ε∗
ε∗−1τc ⇒ p = ε+1−ερε(ε−1) x, p∗ = ε∗+1−ε∗ρ∗
ε∗(ε∗−1) x∗+ τ
Both increasing with sales if and only if demands are subconvex
Intensive margin: y = x+ κτx∗ ⇒ y = ωxx+ (1− ωx) (κ+ τ + x∗)
ωx: Share of home sales in total output
In free trade:
y
∣∣∣∣τ=1
= (1− ω)
(1− 1
εη
)(κ+ τ)
Positive if and only if η > 1ε
. . .
. . . i.e., if and only if demand is subconvex: η − 1ε
= ε+1−ερε(ε−1)
So: “Trade liberalization” ambiguous
Lower τ reduces firm output if and only if demand is subconvex.
Extensive margin: L = n (f + cy) ⇒ n = −ψy Application
ψ ≡ cyf+cy : Share of variable costs in total costs
Inverse measure of returns to scale; ψ = εh−1εh
εh: A sales-weighted harmonic mean of ε and ε∗ Details
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Gains from Trade
Plan of Lectures
1 Preliminaries
2 Integrated versus Segmented Markets
3 Globalization versus Colder Icebergs
4 Gains from Trade
5 Calibrating Gains from Trade
6 Conclusion
7 Supplementary Material
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Gains from Trade
Welfare Change and the Elasticity of Utility
Measure welfare change by the change in equivalent income, Y : Details
Y =
(εzεu
1
ξu− 1
)NY − ωY p− (1− ωY )p∗
ξ ≡ xu′
u : Elasticity of utility Recall properties
Near free trade:
Y
∣∣∣∣τ=1
= (1− ω)
(1− ξξ
κ− τ)
+ψ − ξψξ
n
Direct effect: Always welfare-improving
Indirect effect: Sufficient conditions for a net gain:
ψ = ξ:CES preferences guarantee efficiency: ψ = σ−1
σ= ξ; or
Activist anti-trust policy adjusts n to ensure efficiency.
ψ − ξ and n have the same sign; e.g.:Utility is subconcave: ψ > ξ, varieties are under-supplied; andDemand is subconvex: τ ↓ → y ↓ → n ↑. Recall
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Calibrating Gains from Trade
Plan of Lectures
1 Preliminaries
2 Integrated versus Segmented Markets
3 Globalization versus Colder Icebergs
4 Gains from Trade
5 Calibrating Gains from Trade
6 Conclusion
7 Supplementary Material
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Calibrating Gains from Trade
Calibrating Gains from Trade
ACRC: 2 sufficient statistics:
{home market shareelasticity of import demand
Calibrating home market shares:
ωx = ωπ = ωu either in free trade or with CES preferences
But not in general Details
Calibrating demand elasticities:Calibrated elasticities frequently taken from import demand studies
Broda-Weinstein (2006): Median elasticity of 2.9
Recall: εi ≡ ωiε+ (1− ωi) ε∗ i = x, z, π, Y, u
With subconvexity and x∗ < x:
ε∗ > ε ⇒ ε∗ an upward-biased estimate of εi . . .
. . . which underestimates the gains from trade
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Conclusion
Plan of Lectures
1 Preliminaries
2 Integrated versus Segmented Markets
3 Globalization versus Colder Icebergs
4 Gains from Trade
5 Calibrating Gains from Trade
6 Conclusion
7 Supplementary Material
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Conclusion
Summary
Integrated versus segmented markets:
Different except in CES caseSegmented markets and subconvexity imply reciprocal dumping
Globalization versus colder icebergs:
Globalization reduces spending on all existing varietiesLower trade costs switch spending from home to imported varietiesIsomorphic only in CES case
Calibrating gains from trade:
Many more parameters need to be calibrated than in CES caseHome market shares in output, profits, and welfare differ in generalImport demand elasticities likely to be upward-biased estimates
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Conclusion
Thanks and Acknowledgements
Thank you for listening. Comments welcome!
The research leading to these results has received funding from the European Research Council under the European Union’s
Seventh Framework Programme (FP7/2007-2013), ERC grant agreement no. 295669. The contents reflect only the authors’
views and not the views of the ERC or the European Commission, and the European Union is not liable for any use that may be
made of the information contained therein.
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Supplementary Material
Plan of Lectures
1 Preliminaries
2 Integrated versus Segmented Markets
3 Globalization versus Colder Icebergs
4 Gains from Trade
5 Calibrating Gains from Trade
6 Conclusion
7 Supplementary MaterialReview: Superconvex Demands, Superconcave UtilityProofsShare ParametersChange in Real Income: DetailsJ.P. Neary (University of Oxford) Monopolistic Competition III January 21, 2015 25 / 31
Supplementary Material Review: Superconvex Demands, Superconcave Utility
Review: Superconvexity and Superconcavity
Perceived demand function:
p = p(x) p′ < 0
Elasticity: ε(x) ≡ − p(x)xp′(x)
FOC: ε ≥ 1
Convexity: ρ(x) ≡ −xp′′(x)p′(x)
SOC: ρ < 2
CES: p(x) = βx−1σ
ε = σ, ρ = σ+1σ > 1
Superconvexity:
p(x) more convex than CES
ρ > ε+1ε
ε increasing in sales: εx ≥ 0.
Sub-utility function:
u = u(x) u′ > 0, u′′ < 0
Elasticity: ξ(x) ≡ xu′(x)u(x)
Taste for variety: 0 < ξ < 1
CES: u(x) = σσ−1βx
σ−1σ
ξ = σ−1σ
Superconcavity:
u(x) more concave than CES
ξ > ε−1ε
ξ decreasing in sales: ξx ≤ 0.
Application
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Supplementary Material Proofs
Proofs
Marginal revenue and price: Back to Text
r(x) ≡ xp(x) ⇒ rx = p+ xp′ =
(1 +
xp′
p
)p =
ε− 1
εp
Proof that mark-ups rise with sales if and only if demands are subconvex:Back to Text
p
c=
p
rx=
ε(x)
ε(x)− 1⇒ d log
p
c= − 1
ε(ε− 1)εxdx =
1
ε(ε− 1)
[ε+ 1
ε− ρ]x
So: x∗ < x ⇒ ε(x∗) > ε(x) ⇒ ε(x∗)
ε(x∗)− 1<
ε(x)
ε(x)− 1⇒ p∗
τc<p
c
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Supplementary Material Proofs
Proofs (cont.)
Linking variable cost share ψ ≡ cyf+cy to elasticities of demand: Back to Text
In free trade: ψ = cypy = c
p = p+xp′
p = ε−1ε
With trade costs: ψ = εh−1εh
εh: A sales-weighted harmonic mean of ε and ε∗
Proof:
ψ = c(x+κτx∗)px+κp∗x∗
= ωxcp
+ (1− ωx) τcp∗
= ωxε−1ε
+ (1− ωx) ε∗−1ε∗
= 1− 1εh
, εh ≡[ωxε
−1 + (1− ωx)(ε∗)−1]−1
Alternatively: ψ = c(x+κτx∗)px+κp∗x∗ = c
p
p ≡ ωxp+ (1− ωx) p∗
τ: A sales-weighted average of the net prices
received by the firm in the home and foreign markets (p and p∗
τ).
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Supplementary Material Share Parameters
Shares: Summary
Recap:ωx ≡ x
x+κτx∗ : Share of home sales in total output
ωπ ≡ ππ+κπ∗ : Share of home market profits in total profits
ωu ≡ uu+κu∗ : Share of utility from home goods in total utility
ωz ≡ zz+κz∗ : Share of home goods in total spending (z = npx)
Special Cases:
1 Free trade: ωx = ωπ = ωu = ωz = 11+κ
2 CES: ωx = ωπ = ωu = ωz = 11+κτ1−σ
In general: Back to Text
DemandUtility
Subconcave Superconcave
Subconvex ωπ > ωz > {ωx, ωu} {ωπ, ωu} > ωz > ωxSuperconvex ωx > ωz > {ωπ, ωu} {ωx, ωu} > ωz > ωπ
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Supplementary Material Share Parameters
Shares: Proofs
Rewrite: ωx = 11+κ τx
∗x
, ωπ = 11+κπ
∗π
, ωu = 11+κu
∗u
, ωz = 11+κ z
∗z
Assume τ > 1 and x > x∗ throughout
ωπ > ωz > ωx if and only if demands are subconvex (i.e., ε < ε∗):
p = εcε−1 ⇒ z∗
z = p∗x∗
px = ε∗
ε∗−1ε−1ε
τx∗
x < τx∗
x ⇒ ωz > ωx
π = cLxε−1 = Lpx
ε = Lzε ⇒ π∗
π = εε∗z∗
z < z∗
z ⇒ ωπ > ωz
ωu > ωz if and only if utility is superconcave (i.e., ξ < ξ∗):
ξ ≡ xu′
u ⇒ u∗
u = ξξ∗x∗(u∗)′
xu′ = ξξ∗p∗x∗
px = ξξ∗z∗
z < z∗
z ⇒ ωu > ωz
CES: ε = ε∗ = σ, ξ = ξ∗, x∗ = τ−σx ⇒ ωx = ωπ = ωu = ωz = 11+κτ1−σ
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Supplementary Material Change in Real Income: Details
Change in Real Income: Details
Back to Text
Additive separability: U = F [Nu(x)]
Budget constraint: I =∫i∈N p(i)x(i)di = Npx ⇒ x = I
Np
Taste for variety requires ξ < 1
Proof: Npx = I, p = I = 0⇒ x = −N ⇒ U = (1− ξ)N
Indirect utility function: V (N, p, I) = F[Nu
(INp
)]Define equivalent income Y (N, p) : V
(N, p, I
Y
)= U0
So: Nu(
INpY
)is fixed by U0
With I = wL fixed: N = ξ(N + p+ Y )
⇒ Change in Real Income:
Y =1− ξξ
N − p
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