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Economies of Scope and Trade Niklas Herzig Bielefeld University May 2017 Niklas Herzig (Bielefeld University) Economies of Scope and Trade May 2017 1 / 31 Overview Literature overview 1 Eckel and Neary (2010) 2 Niklas Herzig (Bielefeld

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Economies of Scope and Trade

Niklas Herzig

Bielefeld University

May 2017

Niklas Herzig (Bielefeld University) Economies of Scope and Trade May 2017 1 / 31

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Overview

1

Literature overview

2

Eckel and Neary (2010)

Niklas Herzig (Bielefeld University) Economies of Scope and Trade May 2017 2 / 31

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Literature overview

Product symmetry Product asymmetry Symmetric products on both the demand and supply side Asymmetric products on the demand side Allanson and Montagna (IJIO 2005) Bernard, Redding and Schott (AER 2010, QJE 2011) Nocke and Yeaple (IER 2014) Asymmetric products on the supply (cost) side Arkolakis, Ganapati and Muendler (2015) Mayer, Melitz and Ottaviano (AER 2014) Cannibalization Ju (RIE 2003) Eckel and Neary (RES 2010) Eckel, Iacovone, Javorcik and Neary (RIE 2016) Feenstra and Ma (2008) Baldwin and Gu (2009) Eckel, Iacovone, Javorcik and Neary (JIE 2015) Dhingra (AER 2013) Qiu and Zhou (JIE 2013) Niklas Herzig (Bielefeld University) Economies of Scope and Trade May 2017 3 / 31

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Overview - Preview of results Scope adjustment to trade liberalization

types of scope reaction: economy-wide reduction

Baldwin and Gu (2009) Eckel and Neary (2010) Mayer, Melitz and Ottaviano (2014)

ambiguous reaction

Bernard, Redding and Schott (2011)

heterogeneous reaction throughout the firm distribution

Dhingra (2013) Qiu and Zhou (2013) Nocke and Yeaple (2014)

Niklas Herzig (Bielefeld University) Economies of Scope and Trade May 2017 4 / 31

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Eckel and Neary (2010)

Eckel, Carsten and Peter Neary (2010). Multi-Product Firms and Flexible Manufacturing in the Global Economy, Review of Economic Studies 77(1),

  • pp. 188-217.

Preferences and Demand two-tier utility function: U[u(z)] = 1 u(z)dz (1) with u(z) = a N q(i)di − 1 2b

  • (1 − e)

N q(i)2di + e N q(i)di 2 q(i): consumption of (horizontally diff.) product variety i, i ∈ [0, N] and N: measure of diff. varieties produced in each industry z, z ∈ [0, 1]

Niklas Herzig (Bielefeld University) Economies of Scope and Trade May 2017 5 / 31

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Eckel and Neary (2010)

utility maximization problem: max

q(i)

U[u(z)] subject to 1 N p(i)q(i)didz ≤ I p(i): price of variety i and I: individual income FOC: inverse individual demand function: λp(i) = a − b

  • (1 − e)q(i) + e

N q(i)di

  • (2)

λ: Lagrange multiplier (consumer’s marginal utility of income) L (homogeneous) consumers in each of k identical countries, integrated goods markets and free trade (single variety price worldwide)

Niklas Herzig (Bielefeld University) Economies of Scope and Trade May 2017 6 / 31

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Eckel and Neary (2010)

market demand for variety i: x(i) = kLq(i) inverse world market demand function: p(i) = a′ − b′[(1 − e)x(i) + eY ] (3) a′ ≡ a/λ, b′ ≡ b/λkL and Y ≡ N

0 x(i)di: industry output

Production and Supply “flexible manufacturing”technology (core competence): cj(i): marginal cost of firm j to produce variety i (independent of output, but different across products: c′

j > 0 and cj(0) = c0 j ; e.g. linear:

cj(i) = c0

j + γi)

Niklas Herzig (Bielefeld University) Economies of Scope and Trade May 2017 7 / 31

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Eckel and Neary (2010)

Figure 1

i a′ − b′e(X + Y ) cj(0) cj(i) δ 2b′(1 − e)X

Niklas Herzig (Bielefeld University) Economies of Scope and Trade May 2017 8 / 31

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Eckel and Neary (2010)

single-stage Cournot game profit maximization problem: max

xj(i)

πj = δj [pj(i) − cj(i)] xj(i)di − F δj: mass of products produced (scope) and F: fixed cost FOC: (i) scale ∂πj ∂xj(i) = pj(i) − cj(i) − b′ [(1 − e)xj(i) + eXj] = 0

proof

(4) Xj ≡ δj

0 xj(i)di: firm’s aggregate output

xj(i) = a′ − cj(i) − b′e (Xj + Y ) 2b′(1 − e) (5)

Niklas Herzig (Bielefeld University) Economies of Scope and Trade May 2017 9 / 31

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Eckel and Neary (2010)

Figure 2

x(i) p(i) c(i) a′ − b′eY p(i) = a′ − b′[(1 − e)x(i) + eY ] a′ − b′e(X + Y )

MR(i) = a′ − b′[2(1 − e)x(i) + e(X + Y )]

x(i)

Niklas Herzig (Bielefeld University) Economies of Scope and Trade May 2017 10 / 31

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Eckel and Neary (2010)

pj(i) = 1 2

  • a′ + cj(i) − b′e(Y − Xj)
  • (6)

(ii) scope ∂πj ∂δj = [pj(δj) − cj(δj)] xj(δj) = 0 (7) product range: output of the marginal variety (δj) zero: xj(δj) = 0 cj(δj) = a′ − b′e (Xj + Y ) (8) pj(δj) = a′ − b′eY labour productivity (LP) of multi-product firms: labour as the only factor of production and economy-wide and perfectly competitive labour market unit cost of producing each variety: c(i) = wγ(i)

Niklas Herzig (Bielefeld University) Economies of Scope and Trade May 2017 11 / 31

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Eckel and Neary (2010)

total labour input: l = δ γ(i)x(i)di d ln LP d ln θ = δ

0 h(i) d x(i) d ln θ di

δ

0 h(i)x(i)di

− d ln l d ln θ (9) θ: any exogenous variable and h(i): weight of variety i x(i) = w [γ(δ) − γ(i)] 2b′(1 − e) l = wβ(δ) 2b′(1 − e) with β(δ) ≡ δ γ(i) [γ(δ) − γ(i)] di d ln LP d ln θ = ∂ ln LP ∂ ln δ d ln δ d ln θ

proof Niklas Herzig (Bielefeld University) Economies of Scope and Trade May 2017 12 / 31

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Eckel and Neary (2010)

choice of weights h(i): ∂ ln LP ∂ ln δ

  • h(i)=γ(i)

= δ

0 γ(i) ∂x(i) ∂ ln δ di

δ

0 γ(i)x(i)di

− ∂ ln l ∂ ln δ = 0

proof

Proposition 1: With given technology, any shock which raises the product range δ (a) leaves LP unchanged when output changes are marginal cost-weighted, (b) reduces LP when output is a simple aggregate

proof and

(c) reduces LP but by less when output changes are price-weighted

proof . Niklas Herzig (Bielefeld University) Economies of Scope and Trade May 2017 13 / 31

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Eckel and Neary (2010)

Industry Equilibrium symmetric Cournot oligopoly with an exogenously given number of firms m in each of k countries industry output: Y = kmX FOC for scope (rewrite (8)): wγ(δ) = a′ − e(1 + km)b′X ⇒ scope: δ(X) FOC for scale (integrate over (5)): X =

  • a′ − wµ′

γ

  • δ

△1 b′ with △1≡ 2(1−e)+eδ(1+km) > 0

proof ⇒ scale: X(δ)

with µ′

γ ≡ 1 δ

δ

0 γ(i)di

d ln X d ln δ = a′ − wγ(δ) − e(1 + km)b′X a′ − wµ′

γ

proof Niklas Herzig (Bielefeld University) Economies of Scope and Trade May 2017 14 / 31

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Eckel and Neary (2010)

Figure 3

X δ

s❝♦♣❡✿ δ(X) s❝❛❧❡✿ X(δ) Niklas Herzig (Bielefeld University) Economies of Scope and Trade May 2017 15 / 31

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Eckel and Neary (2010)

Effects of Globalization globalization: increase in the number of countries k participating in the global economy two channels: market-size effect (L ↑) competition effect (m ↑) Proposition 2: The market-size effect of an increase in k is an equi-proportionate increase in the output of each variety and of total

  • utput, but no change in firm scope.

Proposition 3: The competition effect of an increase in k is a uniform absolute fall in the output of each variety, coupled with falls in both total firm output and firm scope, but a rise in industry output.

Niklas Herzig (Bielefeld University) Economies of Scope and Trade May 2017 16 / 31

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Eckel and Neary (2010)

Figure 4

i x(i)

Niklas Herzig (Bielefeld University) Economies of Scope and Trade May 2017 17 / 31

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Eckel and Neary (2010)

full effect:

  • n firm output:

d ln X d ln k = 1 − eδkm △1

proof

(10) where △1 −eδkm =△0 (≡ 2(1 − e) + eδ) > 0

  • n variety output:

d ln x(i) d ln k = 1− ekmα(δ) △1 [γ(δ) − γ(i)] = △0 △1 +

  • 1 − △0

△1 µ′

γ − γ(i)

γ(δ) − γ(i)

proof

(11)

  • γPE: labour requirement of the threshold variety whose output is

unchanged

  • γPE = △0

△1 γ(δ) +

  • 1 − △0

△1

  • µ′

γ

proof Niklas Herzig (Bielefeld University) Economies of Scope and Trade May 2017 18 / 31

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Eckel and Neary (2010)

Proposition 4: The total effect of an increase in k is a rise in total output coupled with a fall in scope. Relatively high-cost varieties are discontinued

  • r produced in lower volumes, whereas more is produced of all varieties

with average costs or lower. → “leaner and meaner“-response of multi-product firms to globalization Corollary 1: Firm productivity is unaffected by the market-size effect, but rises with the competition effect of an increase in k.

Niklas Herzig (Bielefeld University) Economies of Scope and Trade May 2017 19 / 31

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Eckel and Neary (2010)

Globalization and Product Variety number of varieties per firm δ ↓ + number of firms m ↑ → total variety effect? N = kmδ: total number of varieties produced in a symmetric equilibrium market-size effect: unaffected competition effect: conflicting effects (m ↑ and δ ↓) d ln N d ln k = 1 + d ln δ d ln k = 1 − eδkm △1 α(δ) δαδ Proposition 5: In partial equilibrium, an increase in the number of countries cannot lower the total number of varieties if the function relating costs to varieties has constant curvature, but it may do so if the technology is sufficiently flexible.

Niklas Herzig (Bielefeld University) Economies of Scope and Trade May 2017 20 / 31

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Appendix

frequently used notation: α(δ) = δ

  • γ(δ) − µ′

γ

  • β(δ) = δ
  • γ(δ)µ′

γ − µ′′ γ

  • = α(δ)µ′

δ − δσ2 γ

αδ = δγδ βδ = µ′

γαδ

Niklas Herzig (Bielefeld University) Economies of Scope and Trade May 2017 21 / 31

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Appendix

∂πj ∂xj(i) = pj(i) − cj(i) + δj ∂pj(i∗) ∂xj(i) xj(i∗)di∗ = 0 i = i∗ : ∂pj(i∗) ∂xj(i) = −b′ and i = i∗ : ∂pj(i∗) ∂xj(i) = −b′e ∂πj ∂xj(i) = pj(i) − cj(i) − b′ [(1 − e)xj(i) + eXj] = 0, Xj ≡ δj xj(i∗)di∗ (4)

back Niklas Herzig (Bielefeld University) Economies of Scope and Trade May 2017 22 / 31

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Appendix

d ln LP d ln θ = ∂ ln LP ∂ ln θ + ∂ ln LP ∂ ln δ d ln δ d ln θ l = ψ(θ)β(δ) and ∂ ln l ∂ ln θ = ∂ ln l ∂θ ∂θ ∂ ln θ = ψ′ ψ θ x = ψ(θ) [γ(δ) − γ(i)] and ∂x ∂ ln θ = ∂x ∂θ ∂θ ∂ ln θ = [γ(δ) − γ(i)] ψ′θ δ

0 h(i) ∂x ∂ ln θdi

δ

0 h(i)x(i)di

= δ

0 h(i)ψ′(θ)θ [γ(δ) − γ(i)] di

δ

0 h(i)ψ(θ) [γ(δ) − γ(i)] di

= ψ′ ψ θ d ln LP d ln θ = ∂ ln LP ∂ ln δ d ln δ d ln θ ∂ ln LP ∂ ln θ = 0

  • back

Niklas Herzig (Bielefeld University) Economies of Scope and Trade May 2017 23 / 31

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Appendix

∂ ln LP ∂ ln δ

  • h(i)=γ(i)

= δ

0 γ(i) ∂x(i) ∂ ln δ di

δ

0 γ(i)x(i)di

− ∂ ln l ∂ ln δ = 1 l δ γ(i)∂x(i) ∂ ln δ di − ∂ ln l ∂ ln δ = 1 l δ ∂γ(i)x(i) ∂ ln δ di − ∂ ln l ∂ ln δ = δ ∂ ln l ∂l ∂γ(i)x(i) ∂ ln δ di − ∂ ln l ∂ ln δ = ∂ ln l ∂ ln δ δ ∂γ(i)x(i) ∂l di − ∂ ln l ∂ ln δ = 0

back Niklas Herzig (Bielefeld University) Economies of Scope and Trade May 2017 24 / 31

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Appendix

∂ ln LP ∂ ln δ

  • h(i)=1

= ∂ ln X ∂ ln δ − ∂ ln l ∂ ln δ = ∂ ln α(δ) ∂ ln δ − ∂ ln β(δ) ∂ ln δ (since X = δ w [γ(δ) − γ(i)] 2b′(1 − e) di = w 2b′(1 − e)δ

  • γ(δ) − µ′

γ

  • =

wα(δ) 2b′(1 − e)) = δαδ α(δ) − δβδ β(δ) = − δ2αδσ2

γ

α(δ)β(δ) < 0

back Niklas Herzig (Bielefeld University) Economies of Scope and Trade May 2017 25 / 31

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Appendix

∂ ln LP ∂ ln δ

  • h(i)=p(i)

= δ

0 p(i) ∂x(i) ∂ ln δ di

δ

0 p(i)x(i)di

− ∂ ln l ∂ ln δ p(i)x(i) = 1 2

  • a′ + wγ(i) − b′e(Y − X)
  • w

2b′(1 − e) [γ(δ) − γ(i)] = 1 2

  • wγ(i) + wγ(δ) + 2b′eX
  • w

2b′(1 − e) [γ(δ) − γ(i)] = w 1 2 (γ(i) + γ(δ)) + e α(δ) 2(1 − e)

  • w

2b′(1 − e) [γ(δ) − γ(i)]

back Niklas Herzig (Bielefeld University) Economies of Scope and Trade May 2017 26 / 31

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Appendix

X = δ a′ − wγ(i) − b′e(X + Y ) 2b′(1 − e) di = 1 2b′(1 − e) δ (a′ − wγ(i) − b′e(1 + km)X)di X

  • 1 + b′eδ(1 + km)

2b′(1 − e)

  • =

1 2b′(1 − e) δ (a′ − wγ(i))di X 2b′(1 − e) + b′eδ(1 + km) 2b′(1 − e)

  • =

δ 2b′(1 − e)

  • a′ − wµ′

γ

  • X =

δ b′(2(1 − e) + eδ(1 + km))

  • a′ − wµ′

γ

  • back

Niklas Herzig (Bielefeld University) Economies of Scope and Trade May 2017 27 / 31

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Appendix

ln X = ln

  • a′ − wµ′

γ

  • δ
  • − ln
  • (2(1 − e) + eδ(1 + km)) b′

µ′

γ = 1

δ δ γ(i)di d dδµ′

γ = γ(δ)δ −

δ

0 γ(i)di

δ2 = γ(δ) − µ′

γ

δ d ln X d ln δ = δ

  • a′ − wµ′

γ

  • δ
  • a′ − wµ′

γ

  • + δ
  • −w γ(δ) − µ′

γ

δ

  • −

δ (2(1 − e) + eδ(1 + km))b′

  • eb′(1 + km)
  • d ln X

d ln δ = a′ − wγ(δ) a′ − wµ′

γ

− eb′(1 + km)X a′ − wµ′

γ

= a′ − wγ(δ) − eb′(1 + km)X a′ − wµ′

γ

back Niklas Herzig (Bielefeld University) Economies of Scope and Trade May 2017 28 / 31

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Appendix - Industry Equilibrium Comparative Statics

  • △1

e(1 + km)

2(1−e)δγδ α(δ)

d ln X d ln δ

  • =
  • △1

e(1 + km)

  • d ln L

−ekm δ 1

  • d ln m +

△0 e

  • d ln k −

δµ′

γ

γ(δ) 2(1 − e) α(δ) d ln w d ln X = d ln L − eδkm △1 d ln m + △0 △1 d ln k − 2(1 − e)δµ′

γ

△1 α(δ) d ln w d ln δ = −eδkmα(δ) △1 δαδ (d ln m + d ln k) − 2(1 − e)δµ′

δ+ △1 α(δ)

△1 δαδ d ln w

back Niklas Herzig (Bielefeld University) Economies of Scope and Trade May 2017 29 / 31

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Appendix - Industry Equilibrium Comparative Statics

d ln x(i) = d ln L − ekmα(δ) △1 [γ(δ) − γ(i)]d ln m + △0 △1 +

  • 1 − △0

△1

  • µ′

γ − γ(i)

γ(δ) − γ(i)

  • d ln k − 2(1 − e)γ(i) − eδ(1 + km)
  • µ′

γ − γ(i)

  • △1 [γ(δ) − γ(i)]

d ln w

back Niklas Herzig (Bielefeld University) Economies of Scope and Trade May 2017 30 / 31

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Appendix - Industry Equilibrium Comparative Statics

= △0 △1 +

  • 1 − △0

△1 µ′

γ − γ(i)

γ(δ) − γ(i) (γ(i) − γ(δ)) △0 △1 =

  • 1 − △0

△1 µ′

γ − γ(i)

  • γPE = γ(i)

= △0 △1 γ(δ) +

  • 1 − △0

△1

  • µ′

γ

back Niklas Herzig (Bielefeld University) Economies of Scope and Trade May 2017 31 / 31