Outline Market Size, Trade, and Productivity Introduction … · 2012-08-19 · Market Size, Trade, and Productivity Peter Eppinger Outline Introduction Motivation Contribution Closed

Market Size,Trade, and

Productivity

Peter Eppinger

Outline

Introduction

Motivation

Contribution

Closed Economy

Demand Side

Supply Side

Free Entry &Equilibrium

Open Economy

Demand & Supply

Free Entry

Equilibrium

Impact of Trade

TradeLiberalization

References

Market Size, Trade, and ProductivityMelitz, M. J. & G. I. P. Ottaviano

Peter Eppinger

University of Munich

July 22, 2011

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Productivity

Peter Eppinger

Outline

Introduction

Motivation

Contribution

Closed Economy

Demand Side

Supply Side


Open Economy

Demand & Supply

Free Entry

Equilibrium

Impact of Trade

TradeLiberalization

References

Outline

IntroductionMotivationContribution

Closed EconomyDemand SideSupply SideFree Entry & Equilibrium

Open EconomyDemand & SupplyFree EntryEquilibriumImpact of Trade

Trade Liberalization

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Productivity

Peter Eppinger

Outline

Introduction

Motivation

Contribution

Closed Economy

Demand Side

Supply Side


Open Economy

Demand & Supply

Free Entry

Equilibrium

Impact of Trade

TradeLiberalization

References

Motivation

My Bachelor Thesis: Ottaviano et al. (2009)apply the model to study gains from the euro

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Productivity

Peter Eppinger

Outline

Introduction

Motivation

Contribution

Closed Economy

Demand Side

Supply Side


Open Economy

Demand & Supply

Free Entry

Equilibrium

Impact of Trade

TradeLiberalization

References

Contribution

I Melitz and Ottaviano (2008) set up a model similar toMelitz (2003) featuring

I monopolistic competitionI firm heterogeneity

I In addition, they modelI a linear demand system (with a homogenous good)I endogenous markups, which respond to the ‘toughness

of competition’ in the market (feedback channel)

I This new, ‘highly tractable’ frameworkI allows market size differences to play a roleI incorporates all (conventional) channels for welfare gainsI allows for analysis of various trade liberalization

scenarios between several asymmetric countries

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Productivity

Peter Eppinger

Outline

Introduction

Motivation

Contribution

Closed Economy

Demand Side

Supply Side


Open Economy

Demand & Supply

Free Entry

Equilibrium

Impact of Trade

TradeLiberalization

References

Closed Economy IPreferences

L consumers in each country share preferences

U = qc0 +α

∫i∈Ω

qci di − 1

2γ

∫i∈Ω

(qci )2 di − 1

2η

(∫i∈Ω

qci di

)2

over a continuum of differentiated varieties qi , i ∈ Ω and ahomogenous good q0 (numeraire with qc0 > 0 byassumption).

I γ > 0 is the degree of product differentiation betweenvarieties, so if γ → 0 consumers only care about totalconsumption of all varieties Qc =

∫i∈Ωq

ci di

I α, η > 0 govern substitutability between qi & q0,α ↑ or η ↓ =⇒ relative increase in demand for Qc

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Productivity

Peter Eppinger

Outline

Introduction

Motivation

Contribution

Closed Economy

Demand Side

Supply Side


Open Economy

Demand & Supply

Free Entry

Equilibrium

Impact of Trade

TradeLiberalization

References

Closed Economy IIDemand

Each consumer maximizes U s. t. the budget constraint=⇒ inverse demand: pi = α− γqci − ηQc for all qci > 0

Hence, we arrive at the linear market demand system:

qi ≡ Lqci =αL

ηN + γ− L

γpi +

ηN

ηN + γ

L

γp , ∀i ∈ Ω∗ ,

I where N is the measure of consumed varieties (Ω∗ ⊂ Ω)

I and p = 1N

∫i∈Ω∗pi di is the average price.

In contrast to CES preferences, the price elasticity ofdemand ε = |(∂qi/∂pi)(pi/qi )| = [(pmax/pi )− 1]−1 is notexclusively determined by product differentiation γ.

pmax is the upper price bound, where demand for qi equals 0.

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Productivity

Peter Eppinger

Outline

Introduction

Motivation

Contribution

Closed Economy

Demand Side

Supply Side


Open Economy

Demand & Supply

Free Entry

Equilibrium

Impact of Trade

TradeLiberalization

References

Closed Economy IIIWelfare

Plugging qci into U yields the following expression for welfare(indirect utility):

U = I c +1

2

(η +

γ

N

)−1(α− p)2 +

1

2

N

γσ2p ,

I I c denotes the income of the consumer

I σ2p is the variance of prices

Welfare U rises with

I decreases in the average price p

I increases in the variance of prices σ2p

I increases in N =⇒ “love of variety”

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Productivity

Peter Eppinger

Outline

Introduction

Motivation

Contribution

Closed Economy

Demand Side

Supply Side


Open Economy

Demand & Supply

Free Entry

Equilibrium

Impact of Trade

TradeLiberalization

References

Closed Economy IVProduction

Markets for labor & the homogenous good:

I Each consumer inelastically supplies 1 unit of labor L,which is the only input factor of production.

I q0 produced with constant returns to scale at unit cost

I assuming perfect competition for L & q0 =⇒ w = 1

Monopolistic competition in the differentiated sector:

I After having incurred sunk entry cost fE (R & D), firmsdraw their marginal cost c (unit labor requirement)from the distribution G (c) with support on [0, cM ].

I Then, they find out whether they can produce or not.

I Production technology is also CRS (no fixed prod. cost)

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Productivity

Peter Eppinger

Outline

Introduction

Motivation

Contribution

Closed Economy

Demand Side

Supply Side


Open Economy

Demand & Supply

Free Entry

Equilibrium

Impact of Trade

TradeLiberalization

References

Closed Economy VFirm Performance

I Firms which can cover their marginal cost c producethe profit-maximizing quantity q(c) = L

γ [p(c)− c],otherwise they exit.

I The firm with cost cD is just indifferent whether toproduce: p(cD) = pmax = cD (< cM by ass.)

Then, each firm’s performance depends only on its cost drawc and the cutoff cD :

p(c) = 12 (cD + c)

µ(c) = 12 (cD − c)

q(c) = L2γ (cD − c)

r(c) = p(c)q(c) = L4γ (c2

D − c2)

π(c) = r(c)− q(c)c = L4γ (cD − c)2

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Productivity

Peter Eppinger

Outline

Introduction

Motivation

Contribution

Closed Economy

Demand Side

Supply Side


Open Economy

Demand & Supply

Free Entry

Equilibrium

Impact of Trade

TradeLiberalization

References

Closed Economy VIFree Entry & Equilibrium

Zero expected profits in equilibrium =⇒ Free entry (FE):∫ cD

0π(c) dG (c) =

L

4γ

∫ cD

0(cD − c)2 dG (c) = fE .

Using these results, we can determine the cutoff:

cD =1

ηN + γ(γα + ηNp)

and the zero cutoff profit (ZCP) condition:

N =2γ

η

α− cDcD − c

,

where c = [∫ cD

0 c dG (c)]/G (cD) is the average cost ofsurviving firms. This yields the equilibrium number of firmsN and entrants NE = N/G (cD).

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Productivity

Peter Eppinger

Outline

Introduction

Motivation

Contribution

Closed Economy

Demand Side

Supply Side


Open Economy

Demand & Supply

Free Entry

Equilibrium

Impact of Trade

TradeLiberalization

References

Closed Economy VIIParametrization of Technology

Assuming productivity 1/c is Pareto distributed implies thepower cost distribution of surviving firms:

G (c) =

(c

cD

)k

, c ∈ [0, cD ]

Given this assumption, the cost cutoff is:

cD =

[2(k + 1)(k + 2)γ(cM)k fE

L

] 1k+2

The zero cutoff profit (ZCP) condition then implies:

N =2(k + 1)γ

η

α− cDcD

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Productivity

Peter Eppinger

Outline

Introduction

Motivation

Contribution

Closed Economy

Demand Side

Supply Side


Open Economy

Demand & Supply

Free Entry

Equilibrium

Impact of Trade

TradeLiberalization

References

Closed Economy VIIIEquilibrium Outcome

The cutoff cD uniquely determines the averages of allfirm-level performance measures:

c = kk+1cD

p = 2k+12k+2cD

µ = 12

1k+1cD

q = L2γ

1k+1cD = (k+2)(cM)k

(cD)k+1 fE

r = L2γ

1k+2 (cD)2 = (k+1)(cM)k

(cD)kfE

π = fE(cM)k

(cD)k

...as well as welfare, which increases with a lower cutoff cD :

U = 1 +1

2η(α− cD)

(α− k + 1

k + 2cD

)

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Productivity

Peter Eppinger

Outline

Introduction

Motivation

Contribution

Closed Economy

Demand Side

Supply Side


Open Economy

Demand & Supply

Free Entry

Equilibrium

Impact of Trade

TradeLiberalization

References

Open Economy IDemand & Supply

I 2 countries indexed l , h = H,F (for simplicity, can beextended) that only differ in size Ll and trade barriers(same preferences and technology)

I per-unit trade costs τ l > 1 (no fixed export costs)

I Due to CRS and segmented markets, firms maximizedomestic and export profits independently s. t. thesame demand condition as in the closed economy.

I This leads to the following cutoff rules:I c lD = plmaxI c lX = phmax/τ

h = chD/τh for firms exporting from l to h

I As before, cutoffs summarize all performance measures,in particular:

plD(c) = 12 (c lD + c) plX (c) = 1

2 (c lX + c)

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Productivity

Peter Eppinger

Outline

Introduction

Motivation

Contribution

Closed Economy

Demand Side

Supply Side


Open Economy

Demand & Supply

Free Entry

Equilibrium

Impact of Trade

TradeLiberalization

References

Open Economy IIFree Entry

Assuming Pareto productivity distribution, free entry implies:

Ll(c lD)k+2 + Lhρh(chD)k+2 = γφ,

I where φ ≡ 2(k + 1)(k + 2)(cM)k fE (technology index)

I and ρl ≡ (τ l)−k ∈ (0, 1) measures ’freeness of trade’.

This system of equations can be solved for the cutoffs:

c lD =

[γφ

Ll1− ρh

1− ρlρh

] 1k+2

, l = H,F .

The mass of firms N l in the open economy is then given by

N l =2(k + 1)γ

η

α− c lDc lD

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Productivity

Peter Eppinger

Outline

Introduction

Motivation

Contribution

Closed Economy

Demand Side

Supply Side


Open Economy

Demand & Supply

Free Entry

Equilibrium

Impact of Trade

TradeLiberalization

References

Open Economy IIIEquilibrium

I The expressions for all average firm performancemeasures are analogous to the closed economy and so isthe term for welfare:

U l = 1 +1

2η(α− c lD)

(α− k + 1

k + 2c lD

)I Melitz and Ottaviano (2008) show that c lX < c lD , so

only relatively more productive firms export.

I Furthermore, it can be shown that in the tradeequilibrium reciprocal dumping occurs:plX (c)/τh < plD(c),∀c ≥ c lX . This arises due to thehomogenous good and equals a no-arbitrage condition.

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Productivity

Peter Eppinger

Outline

Introduction

Motivation

Contribution

Closed Economy

Demand Side

Supply Side


Open Economy

Demand & Supply

Free Entry

Equilibrium

Impact of Trade

TradeLiberalization

References

Open Economy IVImpact of Trade

I The cost cutoff is lower in the open economy: c lD < cDI Similar outcome as in Melitz (2003), but through a

different channel:

[...] import competition increases competition in thedomestic product market, shifting up residual demand priceelasticities for all firms at any given demand level. Thisforces the least productive firms to exit. [...] the increasedcompetition induces a downward shift in the distribution ofmarkups across firms. Although only relatively moreproductive firms survive (with higher markups than the lessproductive firms who exit), the average markup is reduced.The distribution of prices shifts down due to the combinedeffect of selection and lower markups. [...] average firm sizeand profits increase - as does product variety.

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Productivity

Peter Eppinger

Outline

Introduction

Motivation

Contribution

Closed Economy

Demand Side

Supply Side


Open Economy

Demand & Supply

Free Entry

Equilibrium

Impact of Trade

TradeLiberalization

References

Open Economy IVImpact of Trade

[...] In this model, welfare gains from trade thus come froma combination of productivity gains (via selection), lowermarkups (pro-competitive effect), and increased productvariety.

Hence, the model captures altogether:

I pro-competitive effect

I selection (& reallocation) effect

I variety effect

=⇒ combined modelling of all these welfare channels inone framework!

I Market size still matters, as trade barriers preclude fullintegration of markets:If LH > LF , then ceteris paribus cHD < cFD .

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Productivity

Peter Eppinger

Outline

Introduction

Motivation

Contribution

Closed Economy

Demand Side

Supply Side


Open Economy

Demand & Supply

Free Entry

Equilibrium

Impact of Trade

TradeLiberalization

References

Trade Liberalization

Bilateral (symmetric) liberalization

I decrease in symmetric trade costs τH = τF = τ ↓I increases competition in both markets:

cHD , cFD ↓ =⇒ . . . =⇒ U ↑

Unilateral liberalization (of country H)

I τH ↓ or ρH ↑ while ρF = const. =⇒ cHD ↑ & cFD ↓I The liberalizing country suffers a welfare loss while its

trading partner gains!

I In the short run, the pro-competitive effect drives downcHD , but in the long run the relocation of firms from Hto F causes cHD ↑ & cFD ↓

18 / 20


Productivity

Peter Eppinger

Outline

Introduction

Motivation

Contribution

Closed Economy

Demand Side

Supply Side


Open Economy

Demand & Supply

Free Entry

Equilibrium

Impact of Trade

TradeLiberalization

References

References

Melitz, M. J. (2003). The impact of trade on intra-industryreallocations and aggregate industry productivity.Econometrica, 71(6):1695–1725.

Melitz, M. J. and Ottaviano, G. I. P. (2008). Market size,trade, and productivity. Review of Economic Studies,75(1):295–316.

Ottaviano, G. I. P., Taglioni, D., and Mauro, F. D. (2009).The euro and the competitiveness of european firms.Economic Policy, 24(57):553.

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Productivity

Peter Eppinger

Outline

Introduction

Motivation

Contribution

Closed Economy

Demand Side

Supply Side


Open Economy

Demand & Supply

Free Entry

Equilibrium

Impact of Trade

TradeLiberalization

References

Thank you for your attention!

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Documents

Outline Market Size, Trade, and Productivity Introduction … · 2012-08-19 · Market Size, Trade, and Productivity Peter Eppinger Outline Introduction Motivation Contribution Closed