lecture 9 - irts and mc (theory)

8/12/2019 Lecture 9 - IRTS and MC (Theory)

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14.581 MIT PhD International Trade Lecture 9: Increasing Returns to Scale and

Monopolistic Competition (Theory)

Dave Donaldson

Spring 2011


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Todays Plan

1 Introduction to New Trade Theory

2 Monopolistically Competitive Models

1 Krugman (JIE, 1979)

2 Helpman and Krugman (1985 book)

3 Krugman (AER, 1980)

3 From New Trade Theory to Economic Geography


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Todays Plan








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New Trade TheoryWhats wrong with neoclassical trade theory?

In a neoclassical world, dierences in relative autarky pricesdue todierences in technology, factor endowments, or preferencesare theonly rationale for trade.

This suggests that:1 Dierent countries should trade more.

2 Dierent countries should specialize in dierent goods.

In the real world, however, we observe that:1 The bulk of world trade is between similar countries.

2 These countries tend to trade similar goods.


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New Trade TheoryWhy Increasing Returns to Scale (IRTS)?

New Trade Theory proposes IRTS as an alternative rationale forinternational trade and a potential explanation for the previous facts.

Basic idea:1 Because of IRTS, similar countries will specialize in dierent goods to

take advantage of large-scale production, thereby leading to trade.

2 Because of IRTS, countries may exchange goods with similar factorcontent.

In addition, IRTS may provide new source of gains from trade if itinduces rms to move down their average cost curves.


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New Trade TheoryHow to model increasing returns to scale?

1 External economies of scale Under perfect competition, multiple equilibria and possibilities of lossesfrom trade (Ethier, Etca 1982).

Under Bertrand competition, many of these features disappear(Grossman and Rossi-Hansberg, QJE 2009).

2 Internal economies of scale Under perfect competition, average cost curves need to be U-shaped,but in this case:

Firms can never be on the downward-sloping part of their average costcurves (so no eciency gains from trade liberalization).

There still are CRTS at the sector level.

Under imperfect competition, many predictions seem possible

depending on the market structure.


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Todays Plan








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Monopolistic CompetitionTrade economists preferred assumption about market structure

Monopolistic competition, formalized by Dixit and Stiglitz (1977), isthe most common market structure assumption among new trademodels.

It provides a very mild departure from imperfect competition, butopens up a rich set of new issues.

Classical examples: Krugman (1979): IRTS as a new rationale for international trade.

Helpman and Krugman (1985): Inter- and intra-industry trade united.

Krugman (1980): Home market eect in the presence of trade costs.


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Monopolistic CompetitionBasic idea

Monopoly pricing:Each rm faces a downward-sloping demand curve.

No strategic interaction:Each demand curve depends on the prices charged by other rms.

But since the number of rms is large, each rm ignores its impact onthe demand faced by other rms.

Free entry:Firms enter the industry until prots are driven to zero for all rms.


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Monopolistic CompetitionGraphical analysis

M R

q

p AC

M C

D


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Krugman (1979)Endowments, preferences, and technology

Endowments: All agents are endowed with 1 unit of labor.

Preferences: All agents have the same utility function given by

U = R n

0 u [c i ]di

where: u (0) = 0, u 0 > 0, and u 00 < 0 (love of variety).

(c ) u 0

cu 00 > 0 is such that 0 0 (by assumption).

n is the number/mass of varieties i consumed.

IRTS Technology: Labor used in the production of each variety i is

l i = f + q i /

where common productivity parameter (rms/plants arehomogeneous).


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Krugman (1979)Equilibrium conditions

1 Consumer maximization:

p i = 1u 0(c i )

2 Prot maximization:

p i = (c

i )

(c i ) 1w

3 Free entry:

p i w

q i = wf

4 Good and labor market clearing:

q i = Lc i L = nf +

Rn

0q i

di


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Krugman (1979)Equilibrium conditions rearranged

Symmetry ) p i = p , q i = q , and c i = c for all i 2 [0, n] .

c and p / w are simultaneously characterized by (see graph):

(PP):

p

w = (c )

(c ) 1 1

(ZP): p

w =

f q

+ 1

= f Lc

+ 1

Given c , the number of varieties n can then be computed usingmarket clearing conditions:

n = 1

f / L + c /


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Krugman (1979)Graphical analysis; PP is upward sloping thanks to assumption that elasticity of substitution is falling

(p/w) 0

c 0

Z

c

p/w P

P

Z


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Krugman (1979)Gains from trade revisited

(p/w) 0

c 1 c 0

Z

Z

c

p/w P

Z

P

Z (p/w) 1

Suppose that two identical countries open up to trade. This is equivalent to a doubling of country size (which would have no

eect in a neoclassical trade model). Because of IRS, opening up to trade now leads to:

Increased product variety : c 1 < c 0 ) 1f / 2L+ c 1 / > 1

f / L+ c 0 /

Pro-competitive/eciency eects : (p / w )1 < (p / w )0 ) q 1 > q 0(thanks to falling elasticity of substitution).


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CES PreferencesTrade economists preferred demand system

Constant Elasticity of Substitution (CES) preferences correspond tothe case where:

U = R n

0 (c i ) 1

di ,

where > 1 is the (constant) elasticity of substitution between anypair of varieties.

What is there to like about CES preferences?

Homotheticity ( u (c ) (c ) 1

is actually the only functional formsuch that U is homothetic).

Can be derived from discrete choice model with i.i.d extreme valueshocks (See Feenstra Appendix B, Anderson et al, 1992).

Is it empirically reasonable? Rejected in eld of IO long ago (independence of irrelevant alternativesproperty, constant markups, and other features we deemed just toounattractive).


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CES PreferencesSpecial properties of the equilibrium

Because of monopoly pricing, CES ) constant markups:p w

= 1

1

Because of zero prot, constant markups) constant output per rm:p w =

f q +

1

Because of market clearing, constant output per rm ) constantnumber of varieties per country:

n = L

f + q / So, gains from trade come only from access to Foreign varieties.

IRTS provide an intuitive reason for why Foreign varieties are dierent. But consequences of trade would now be the same if we hadmaintained CRTS with dierent countries producing dierent goods(the so-called Armington assumption).


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Todays Plan







l d ( )


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Helpman and Krugman (1985)Inter- and intra-industry trade united

Helpman and Krugman (1985), chapters 7 and 8, oer a uniedtheoretical framework in which to analyze inter- and intra-industrytrade.

Basic Strategy:1 Start from the integrated equilibrium, but allow IRTS in some sectors.

2 Provide conditions such that integrated equilibrium can be replicatedunder free trade.

3 Build on the observation that each variety is only produced in onecountry, but consumed in both, to make new predictions about thestructure of trade ows when free trade replicates integratedequilibrium.

H l d K (1985)


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Helpman and Krugman (1985)Back to the two-by-two-by-two world

Compared to Krugman (1979), suppose now that there are: 2 industries, i = X , Y 2 factors of production, f = l , k 2 countries, North and South

Y is a homogeneous good produced under CRTS:

afY w I , r I (constant) unit factor requirements in integrated eq.

X is a dierentiated good produced under IRTS:

afX w I , r I , q I X (average) unit factor requirements in integrated eq.

q I X afX w I

, r I , q I X factor demand per rm in integrated eq.

W.l.o.g, we can set units of account s.t. q I X = 1 for all rms

H l d K (1985)


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Helpman and Krugman (1985)The Integrated Equilibrium Revisited

a X (w I ,r I ,q I X )n X

Slope = w/r

C

v s

v n

k s

l s

k n

O n l n

v

O s

a Y (w I ,r I )Q Y

Taking q I X as given, integrated eq. is isomorphic to HO integrated eq.

Pattern of inter-industry trade (and so net factor content of trade) isthe same as in HO model.

But product dierentiation + IRS lead to intra-industry trade in Y .

H l d K (1985)


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Helpman and Krugman (1985)Trade Volumes

Intra-industry trade has strong implications for trade volumes.

In HO model (with FPE), we have seen that trade volumes do notdepend on country size.

k s

l s

a 1 ( )

k n

O n l n

a 2 ( )

y 2 a 2 ( )

y 1 a 1 ( )

O s

H l d K g (1985)


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Helpman and Krugman (1985)Trade Volumes

In this model, by contrast, countries with similar size trade more(gure drawn for extreme case where both X and Y are dierentiatedgoods):

k s

l s

a Y ( )

k n

O n

l n

a X ( )

a X ( )Q X

a Y ( )Q Y

O s

Should this be taken as evidence in favor of New Trade Theory? If we think of IRS as key feature of New Trade Theory, then no.

Pattern is consistent with any model with complete specialization andhomotheticity, regardless of whether we have CRS or IRS.

A First Look at Gravity


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A First Look at Gravity

Proposition Suppose that countries have identical homothetic preferences and that any good is only produced in one country. Thenbilateral trade ows between countries i and j satisfy gravity

X ij = Y i Y j Y W

Proposition If bilateral trade ows satisfy gravity, then trade volumes are maximized when countries are of equal size

Todays Plan


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Today s Plan



1 Krugman (JIE, 1979)2 Helpman and Krugman (1985 book)



Krugman (1980)


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Krugman (1980)The role of trade costs

Trade costs were largely absent from neoclassical trade models. Solving for the pattern of international specialization in the presence of trade costs is hard.

We now explore the implications of trade costs in the presence of IRTS.

Thanks to Dixit-Stiglitz product dierentiation, solving for internationalspecialization is easy (each rm is deliberately the only rm in the

world to make its own variety), and is not substantially complicated bytrade costs (especially ad valorem trade costs that dont require factorsof production or generate incomeso called iceberg trade costs).

Krugman (1980)


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Krugman (1980)The role of trade costs

Main result : Home-market eect Countries will tend to export those goods for which they have relativelylarge domestic markets.

Basic idea: Because of IRS, rms will locate in only one market.

Because of trade costs, rms prefer to locate in larger markets.

Logic is very dierent from neoclassical trade theory in which largerdemand tends to be associated with imports rather than exports.

Krugman (1980)


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Krugman (1980)Starting point: one factor-one industry-two-country

There are two countries: Home (H ) and Foreign (F ).

There is one dierentiated good produced under IRTS bymonopolistically competitive rms, as in Krugman (1979).

Preferences over varieties are CES:

U = R n

0 (c i ) 1

di ,

There are iceberg trade costs between countries: In order to sell 1 unit abroad, domestic rms must ship > 1 units.

Krugman (1980)


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Krugman (1980)Equilibrium conditions (Home Country)

1 Consumer maximization:

q H , H = w H LH

P H p HH / P H

, q F , H =

w H LH

P H p F , H / P H

(1)

where P H = hnH

p H , H 1 + nF

p F , H 1 i

11 .

2 Monopoly pricing:

p H , H = 1

w H / , p H , F =

1 w H / (2)

3 Free entry:

p H , H w H / q H , H + p H , F w H / q H , F = w H f , (3)

4 Labor market clearing:

LH = nH f + q H , H / + q H , F / (4)

Krugman (1980)


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Krugman (1980)A First Step: Market size and wages

Proposition w H w F if and only LH LF .

Proof: Monopoly pricing and free entry, (2) and (3), imply

q H , H + q H , F = ( 1)f

Combining this with labor market clearing (4), we get

nH = LH / F (5)

Relative wage, w H / w F , is determined by trade balance

nH p H , F q H , F = nF p F , H q F , H (6)


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Krugman (1980)


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Krugman (1980)Home-Market Eect

What would happen if labor supply was perfectly elastic instead?

Suppose that we add a second industry in which a homogeneous goodis produced one-for-one for labor in both countries.

Preferences over two goods are Cobb-Douglas. Suppose, in addition, that homogeneous good is freely traded.

Under these assumptions, wages are equal across countries:w H = w F .

So adjustments across countries may only come from number of varieties nH and nF (labor supply in the dierentiated sector isendogenous).

Krugman (1980)


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ug a ( 980)Home-market eect

Proposition nH / LH nF / LF if and only if LH LF .

Home-market eect : larger market has a disproportionately largeshare of dierentiated good rms (and so will export that good).

Since wages are necessarily equal, rms will only be active in thesmaller market if they face softer competition there.

With a little bit of algebra, one can show that:

nH

nF = LH / LF 1

1 (LH / LF ) 1

Note that nH / nF / 1 > 0 if LH / LF > 1: home-market eectis larger when trade costs are small or elasticity of substitution is large.

From New Trade Theory To Economic Geography


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y g p yBasic Idea

Krugman (JPE 1991) added one additional assumption to Krugman(1980), which was that some workers are perfectly mobile across thetwo countries/regions.

Mobile workers move to where their real wage is highest. These workers are attracted to the already larger region because of thehigher nominal wages they earn there (HME) and the wider array of varieties for sale there (lower price index).

Extent of agglomeration depends (very naturally) on the relativeimportance of the IRTS good in tastes, and the share of workers whoare mobile.

From New Trade Theory To Economic Geography


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y g p yBasic Idea

The result was an extremely inuential model of economicgeography, ie a model in which the distribution of economic activityacross space (ie agglomeration) is endogenous.

Previous modeling approaches had emphasized non-pecuniary,

positive externalities (eg spatially-decaying knowledge spillovers orthick-market search externalities) to explain agglomeration. Krugman(1991) emphasized instead the pecuniary externalities in the Krugman(1980) model.

Time doesnt permit further diversions into this literature in 14.581.But if youre interested, in Spring 2010 we held a Spatial EconomicsReading Group about Krugman (1991) and other key papers in thisliterature and slides from student presentations are here:http://econ-www.mit.edu/faculty/ddonald/spatial.

lecture 9 - irts and mc (theory)

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