when the threat is stronger than the execution: trade...

When the Threat is Stronger than the Execution:Trade Liberalization and Welfare under Oligopoly

Dermot Leahy

Maynooth University

J. Peter Neary

Oxford, CEPR and CESifo

ESEM 2016, GenevaAugust 24, 2016

Leahy and Neary (Maynooth and Oxford) Trade Liberalization under Oligopoly ESEM: August 24, 2016 1 / 34

Introduction

Aron Nimzowitsch

Aron Nimzowitsch, 1886–1935

“The threat is stronger than the execution”


Introduction

Introduction

Trade policy: Gains from trade liberalization

The magnitude of the gains is still a central issue in international trade.Recent work sheds light on the quantitative extent of gains underperfect competition and monopolistic competition with heterogeneousfirms.Less work has been done on trade liberalization under oligopoly.

Despite growing evidence that trade is dominated by large firms.Mayer and Ottaviano (2008), Freund and Pierola (2015)

IO: Oligopoly with cost asymmetries

Who gains and who loses as best-practice technology disseminates?


Introduction

Our Contribution

We compare trade liberalization under Cournot and Bertrandoligopoly in a unified framework with product differentiation.

Common perception that the results of oligopoly trade models arehighly sensitive to the mode of competition.We show that many of the predictions are qualitatively robust towhether firms compete on quantity or price.But: There are important differences between the two cases.

Details:

We use duopoly with linear demands to obtain explicit solutions.Then extend the analysis to oligopoly and more general functionalforms: results are qualitatively robust.

Take-Home:

Firms compete more aggressively under Bertrand than under Cournot.This affects outcomes even when there is no trade under Bertrand.


Introduction

Background Literature

Quantity versus price competition:

Singh and Vives (1984), Vives (1985)

Oligopoly with cost asymmetries:

Lahiri and Ono (1988), Neary (1994)

Welfare effects of trade liberalization under oligopoly:

Use the reciprocal-markets model first developed by Brander (1981)and Brander and Krugman (1983).

Extended by Bernhofen (2001) - Product differentiation.

Clarke and Collie (2003) - Bertrand.

Brander and Spencer (2015), Collie and Le (2015).

For a survey see: Leahy and Neary (2011).

A simultaneous-move game, not about entry deterrence:

Spence (1977), Dixit (1980), Fudenberg-Tirole (1985), Neary (2002)


Introduction

Outline

1 The Model

2 Equilibria with Trade

3 The Nimzowitsch Region

4 General Demands

5 Conclusion


The Model

Outline

1 The ModelUtility and DemandTechnology and Firm Behavior



4 General Demands

5 Conclusion


The Model Utility and Demand

The Model

A symmetric two-country model, with segmented markets.

A home and foreign firm compete in both home and foreign markets.

Demand:

A representative consumer in the home country with quasi-linear utility:

U = z0 + u(x, y)

We first assume a quadratic sub-utility function:

u(x, y) = a(x + y)− b2(x2 + 2exy + y2)

Maximization of utility subject to the budget constraint yields linearinverse demand functions:

p = a− b(x + ey) and p∗ = a− b(y + ex)


The Model Technology and Firm Behavior

Technology and Firm Behavior

Costs:

Marginal costs are constant and we ignore fixed costs.

Profits: Home market profits of the home and foreign firm are:π = (p− c)xπ∗ = (p∗ − c− t)y

Symmetric multilateral trade liberalization under:1 Quantity/Cournot competition2 Price/Bertrand competition

The symmetric case, where the home and foreign firms facesymmetric demands, the same production cost functions, and thesame trade cost.


Equilibria with Trade

Outline

1 The Model

2 Equilibria with TradeQuantity CompetitionPrice CompetitionBertrand vs. Cournot


4 General Demands

5 Conclusion


Equilibria with Trade Quantity Competition

Quantity Competition: Outputs and Profits

Home market outputs:

Free trade: xCF = yCF = Ab(2+e) A ≡ a− c

Prohibitive trade cost: y = 0 → tC = 2−e2 A

⇒ xC = xCF(

1 +e2

ttC

)and yC = yCF

(1− t

tC

)

Profits of home firm:

Due to symmetry, home exports x∗ equal home imports y, → homefirm’s profits on its exports are π∗ = (p∗ − c− t)x∗ = (p∗ − c− t)y.

Effect of a multilateral change in trade costs on total profits:

d (π + π∗)dt

=2(ex− 2x∗)

4− e2

{< 0 when t = 0 (so x = x∗)> 0 when t = tC (so x∗ = 0)

So: Profits are U-shaped in t.



Quantity Competition: Outputs and Profits


Free trade: xCF = yCF = Ab(2+e) A ≡ a− c

Prohibitive trade cost: y = 0 → tC = 2−e2 A

⇒ xC = xCF(

1 +e2

ttC

)and yC = yCF

(1− t

tC

)Profits of home firm:

Due to symmetry, home exports x∗ equal home imports y, → homefirm’s profits on its exports are π∗ = (p∗ − c− t)x∗ = (p∗ − c− t)y.

Effect of a multilateral change in trade costs on total profits:

d (π + π∗)dt

=2(ex− 2x∗)

4− e2

{< 0 when t = 0 (so x = x∗)> 0 when t = tC (so x∗ = 0)

So: Profits are U-shaped in t.



Cournot Profits

Trade is locally bad for profits, in the neighbourhood of autarky.

Must it be globally bad? Anderson, Donsimoni, and Gabszewicz(1989) showed that it is when goods are perfect substitutes.

However, trade liberalization is less bad for firms when e is lower.

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

0.0 0.2 0.4 0.6 0.8 1.0

t

e

t^C

t‐min

t‐eq

Loci of t and e that yield Autarky, Minimum Profits, and Autarky Profits



Welfare under Cournot

Consumer surplus rises monotonically as trade costs fall. (Prices ofboth goods fall)Hence, the range of t where welfare is lower than autarky is smallerthan that where profits are lower.Welfare is also U-shaped in t. It falls below the autarky level betweenthe upper and lower loci reaching a minimum along the middle locus.

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

0.0 0.2 0.4 0.6 0.8 1.0

t

e

t^C

t‐min

t‐eq

Loci of t and e that yield Autarky, Minimum Profits, and Autarky Welfare


Equilibria with Trade Price Competition

Bertrand Competition

To compare Bertrand and Cournot competition we use the samedemand and cost functions.

To solve for Bertrand equilibrium we use direct demand functions:

x =1

b (1− e2)[(1− e)a− (p− ep∗)] y =

1b (1− e2)

[(1− e)a− (p∗ − ep)]


Free trade: xBF = yBF = Ab(2+e−e2)

Prohibitive trade cost: y = 0 → tB = (1−e)(2+e)2−e2 A

⇒ xB = xBF(

1 +e

2− e2t

tB

)and yB = yBF

(1− t

tB

)


Equilibria with Trade Bertrand vs. Cournot

Bertrand vs. Cournot

Straightforward to show that: tB < tC

Profits and welfare also behave similarly to quantity competition fortrade costs between zero and tB.As shown by Vives (1985): price competition is more competitive thanquantity competition in symmetric equilibrium: price competitionleads to lower prices and higher outputs and thus higher welfare.

With linear demands, even with asymmetric firms, price competitionalways leads to higher welfare for t ≤ tB:

WB −WC =1b

e2

(1 + e) (4− e2)2

{(4− e2 − 2e

)A(A− t) +

(4 + e2)

2(1− e)t2

}


Equilibria with Trade Bertrand vs. Cournot

Bertrand vs. Cournot WelfareQualitatively similar as trade costs fall, but also differences:

W

t

WB-WA

WC-WA

Effects of Trade Liberalization on Welfare in Cournot and Bertrand Competition


The Nimzowitsch Region

Outline

1 The Model


3 The Nimzowitsch RegionThe Nimzowitsch Region: Home Best ResponseWelfare in the Nimzowitsch Region

4 General Demands

5 Conclusion




A region of trade costs too high for trade in Bertrand, but low enoughto allow the threat of trade.

Between tB and tC no trade occurs under price competition.

Yet (with linear demands) the pro-competitive threat of trade raiseswelfare above the Cournot level.The threat of trade raises welfare more than actual trade underCournot.We call the region of parameter space in which this outcome holds the“Nimzowitsch Region”.



Trade under Price and Output Competition

t

e

N

M

CB

Regions of Trade

B: yB > yC ; C: yC > yB > 0; N: Nimzowitsch Region; A: Autarky


The Nimzowitsch Region The Nimzowitsch Region: Home Best Response


At tB there is no trade under Bertrand but the domestic firm’s price isbelow the monopoly level.

The home firm does not raise its price, since its rival would then makepositive sales lowering the home firm’s domestic profits.When t reaches tC the home firm can act as an unconstrainedmonopolist.When tB ≤ t ≤ tC, the home firm chooses a price at which the foreignfirm is just unable to produce.Domestic output is: x = A−t

be which falls in t.Since x falls in t in the region tB ≤ t ≤ tC and y = 0, welfare is fallingin t in that region.Hence under price competition, unlike under quantity competition,trade liberalization starting from autarky initially raises welfare


The Nimzowitsch Region The Nimzowitsch Region: Home Best Response

Bertrand vs. Cournot Outputs

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

0.0 0.2 0.4 0.6

xC

yC

xB

yB

XC

XB


The Nimzowitsch Region Welfare in the Nimzowitsch Region

Welfare in the Nimzowitsch Region

Welfare under price and output competition:

W

t

WB-WA

WC-WA

Nimzovitsch Region



Strategic Interactions in the Nimzowitsch Region

*p

p

)(~ pp*

);(~ tpB*

tc );( tpB*

(a) ForeignBest-Response Function

*p

p

)(~ *pp)( *pB )(~

*pB

Btc ˆ

Ctc ˆ

Mp

(b) HomeBest-Response Function

*p

p

)(~*pB

);(~ tpB*

(c) Equilibrium in theNimzowitsch Region



Minimum versus Maximum Import Constraints

Contrast:1 Here: Imports are non-negative: y ≥ 02 Krishna (JIE 1989): Import quota: y ≤ y

Both extend classic results to product differentiation:1 Low-cost firm prices at marginal cost of high-cost

2 No pure-strategy equilibrium with capacity constraints [Edgeworth]

In both, home firm’s best response is a choice between two options:When import constraint binds, a high price yields monopoly profits

When it does not, a low price leads to a standard Bertrand equilibrium

For both options, profits given p∗ are concave in p1 Here: Maximum profits is the lower envelope

Which is itself concave

2 Krishna: Maximum profits is the upper envelopeSo: no equilibrium in pure strategies



The Nimzowitsch Region: The Home Firm

c+tBc+t

c+tC

pM p

y=0p

p*

y>0M B

y=0

Price Competition: The Home Firm’s Perspective


General Demands

Outline

1 The Model



4 General DemandsFree Trade and AutarkyThe Volume of TradeWelfare

5 Conclusion


General Demands

General Demands

Do these results continue to hold with general demands?

p(x, y) for the home good and p∗(y, x) for the foreign?

We assume that the demand functions are twice differentiable andstrictly decreasing in own price, px < 0 and p∗y < 0.

We also assume that p∗(0, x) < ∞ so that foreign demand has a chokeprice and a prohibitive trade cost exists.

We assume that the demand system can be inverted to get:

x(p, p∗) for the home good and y(p∗, p) for the foreign.


General Demands Free Trade and Autarky

Free Trade and Autarky

We impose a few additional mild restrictions such as:

Marginal revenue is always downward-slopingHome marginal revenue falls in a symmetric equilibrium following anequal increase in the outputs of both goodsWe do not restrict quantities to be strategic substitutes under Cournotnor prices to be strategic complements under Bertrand

Given these we are able to show:

1 At t = 0, the volume of trade is higher under Bertrand than Cournot.Prices at t = 0 are lower under Bertrand than Cournot. (This result isimplicit in Vives (1985) who did not look at trade)

2 tB < tC


General Demands The Volume of Trade

The Volume of Trade

The volume of trade under price and output competition:

Here a single intersection but in general there could be many.

Showing that xB > xC

c

r

r(xB)+β(xB)=cr(xC)=c

r(xC)

r,c

x

r(xB)

xC xB

ttCtB

yC(0)

yB(0)

Figure 1

4

Volume of Trade under Quantity and Price Competition


General Demands Welfare

Welfare

Welfare change dW = dχ + dΠ can be written as:

dW = (p− c)dx + (p∗ − c− t)dy− ydt

1 At t = 0 this is dWdt = (p− c)( dx

dt +dydt )− y < 0 under both quantity

and price competition. So at free trade an increase in trade costs isbad. This generalises the result under linear demands.

2 At tC under Cournot we have dx/dt > 0 (if outputs are strategicsubtitutes) so dW

dt = (p− c) dxdt > 0. A small fall in trade costs is bad.

Unlike the linear demand case these results can only be stated atparticular points.



Welfare in the Nimzowitsch Region

The Nimzowitsch Region: {tB, tC}Consider Bertrand competition only:

Equilibrium has y = 0.Hence p∗(0, x)− c− t = 0, implying that x must decrease in t

dx/dt = 1/p∗x(0, x) < 0So a decrease in t between tB and tC raises welfare.At tB a small fall in trade costs under Bertrand lowers welfare (ifdx/dt > 0 ).

This allows us to sign the following derivatives:

dWB

dt

∣∣∣∣tC ,−

< 0dWB

dt

∣∣∣∣tB ,−

> 0dWB

dt

∣∣∣∣tB ,+

< 0



Welfare with General Demands: Summary

W

t

WB-WA

WC-WA(1)

(2)

(3) (4)

(5)

(6)

With general demands, we can only sign the end-pointsBut the results confirm qualitatively the results with linear demands:

(1)dWB

dt

∣∣∣∣t=0,+

< 0 (2)dWC

dt

∣∣∣∣t=0,+

< 0

(3)dWB

dt

∣∣∣∣tB ,−

> 0 (4)dWB

dt

∣∣∣∣tB ,+

< 0 (5)dWB

dt

∣∣∣∣tC ,−

< 0 (6)dWC

dt

∣∣∣∣tC ,−

> 0


Conclusion

Outline

1 The Model



4 General Demands

5 Conclusion


Conclusion

Conclusion

We have compared trade liberalization under Cournot and Bertrand ina unified reciprocal-markets framework using general demands:

The trade cost that chokes off trade is higher under Cournot.The critical level of trade costs below which the possibility of tradeaffects the domestic firms’ behavior is the same under Cournot andBertrand competition.The pro-competitive effects of trade are stronger under Bertrandcompetition despite the fact that for trade costs close to the criticallevel the volume of trade is higher under Cournot competition.

Tighter results if we assume linear demands:

At any trade cost, welfare is higher under Bertrand than under CournotTrue even in the Nimzowitsch Region, where Bertrand trade is zero


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