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


Introduction

The Bottom Line

Trade Costs and General Demands: Together at Last!


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)


http://www.nobelprize.org/nobel_prizes/economic-sciences/laureates/2008/press.html

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


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)


Introduction

Outline

1 Preliminaries



4 Gains from Trade


6 Conclusion



Preliminaries

Plan of Lectures

1 PreliminariesMonopolistic Competition in the Global Economy



4 Gains from Trade


6 Conclusion



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)


Integrated versus Segmented Markets

Plan of Lectures

1 Preliminaries



4 Gains from Trade


6 Conclusion





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


Globalization versus Colder Icebergs

Plan of Lectures

1 Preliminaries



4 Gains from Trade


6 Conclusion




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



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



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



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



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


Gains from Trade

Plan of Lectures

1 Preliminaries



4 Gains from Trade


6 Conclusion



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


Calibrating Gains from Trade

Plan of Lectures

1 Preliminaries



4 Gains from Trade


6 Conclusion





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


Conclusion

Plan of Lectures

1 Preliminaries



4 Gains from Trade


6 Conclusion



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


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.


Supplementary Material

Plan of Lectures

1 Preliminaries



4 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


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


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).


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


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


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


monopolistic competition in trade iii trade costs and...

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