Economies of Scope and Trade Niklas Herzig Bielefeld University - - PowerPoint PPT Presentation

Economies of Scope and Trade

Niklas Herzig

Bielefeld University

June 16, 2015

Niklas Herzig (Bielefeld University) Economies of Scope and Trade June 16, 2015 1 / 40

Overview

1

Literature overview

2

Eckel and Neary (2010)

3

Eckel et al. (2015)

Niklas Herzig (Bielefeld University) Economies of Scope and Trade June 16, 2015 2 / 40

Literature overview

Product symmetry Product asymmetry Products symmetric on both the demand and supply side Products asymmetric on the demand side Allanson and Montagna (IJIO 2005) Bernard, Redding and Schott (AER 2010, QJE 2011) Nocke and Yeaple (IER 2014) Products asymmetric 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) 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 June 16, 2015 3 / 40

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 June 16, 2015 4 / 40

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 June 16, 2015 5 / 40

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 June 16, 2015 6 / 40

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 June 16, 2015 7 / 40

Eckel and Neary (2010)

single-stage Cournot game profit maximization problem: max

xj(i)

πj = δj [pj(i) − cj(i)] xj(i) − 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 June 16, 2015 8 / 40

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 June 16, 2015 9 / 40

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 June 16, 2015 10 / 40

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 June 16, 2015 11 / 40

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 June 16, 2015 12 / 40

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

Niklas Herzig (Bielefeld University) Economies of Scope and Trade June 16, 2015 13 / 40

Eckel and Neary (2010)

Figure 3

X δ

s❝♦♣❡✿ δ(X) s❝❛❧❡✿ X(δ) Niklas Herzig (Bielefeld University) Economies of Scope and Trade June 16, 2015 14 / 40

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 June 16, 2015 15 / 40

Eckel and Neary (2010)

Figure 4

i x(i)

Niklas Herzig (Bielefeld University) Economies of Scope and Trade June 16, 2015 16 / 40

Eckel and Neary (2010)

full effect:

• n firm output:

d ln X d ln k = 1 − eδkm △1 (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) (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 June 16, 2015 17 / 40

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 June 16, 2015 18 / 40

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 June 16, 2015 19 / 40

Eckel et al. (2015)

Eckel, Carsten, Leonardo Iacovone, Beata Javorcik and Peter Neary (2015). Multi-Product Firms at Home and Away: Cost- versus Quality- based Competence, Journal of International Economics 95(2), pp. 216-232. determinants of economic success of firms (exporters):

1

firm productivity (among others, Melitz (Econ 2003))

2

product quality (among others, Manova and Zhang (QJE 2012))

two views opposed? No, focus on: ¨ ıntra-firm extensive margin” model of multi-product firms with an endogenous choice of product quality extension of the ”flexible-manufacturing”model by Eckel and Neary (RES 2010) to investment in quality simplification: single monopoly firm (possible: Cournot competition in a heterogeneous-firm industry)

Niklas Herzig (Bielefeld University) Economies of Scope and Trade June 16, 2015 20 / 40

Eckel et al. (2015)

Preferences for quantity and quality single market (L consumers) representative consumer: quadratic sub-utility function u = u1 + βu2 u1 = a0Q − 1

2b

• (1 − e)
• i∈

Ω q(i)2di + eQ2

(12) u2 =

• i∈

Ω q(i)

z(i)di

• Ω: set of differentiated products, q(i): consumption of variety i,

Q ≡

• i∈

Ω q(i)di and e: substitution index between goods (0 ≤ e ≤ 1)

• z(i): perceived quality (premium) of variety i

Niklas Herzig (Bielefeld University) Economies of Scope and Trade June 16, 2015 21 / 40

Eckel et al. (2015)

Product Demand

• ptimization problem: max u subject to budget constraint
• i∈

Ω p(i)q(i)di = I (I: individual expenditure on

Ω) market inverse demand functions (market-clearing: x(i) = Lq(i)): p(i) = a(i) − b [(1 − e)x(i) + eX] i ∈ Ω ⊂ Ω a(i) = a0 + β z(i) (13)

• b ≡ b

L

X ≡

• i∈Ω x(i)di (Ω: set of goods actually consumed)

Niklas Herzig (Bielefeld University) Economies of Scope and Trade June 16, 2015 22 / 40

Eckel et al. (2015)

Cost-based Competence ignoring quality (β = 0)

• ptimization problem: max π

π =

• i∈Ω

[p(i) − c(i) − t] x(i)di (14) t: (uniform) trade cost ”flexible manufacturing”technology

1

marginal production costs are independent of output but differ across products: c(i)

2

marginal production cost rise as the firm moves away from its ”core competence”variety: c′(i) > 0 (c(0) = c0)

Niklas Herzig (Bielefeld University) Economies of Scope and Trade June 16, 2015 23 / 40

Eckel et al. (2015)

Scale and Scope

1 scale x(i):

x(i) = a(i) − c(i) − t − 2 beX 2 b(1 − e) i ∈ Ω (15)

2 scope δ:

x(δ) = 0

3 price p(i):

p(i) = 1 2 [a(i) + c(i) + t] (16)

Niklas Herzig (Bielefeld University) Economies of Scope and Trade June 16, 2015 24 / 40

Eckel et al. (2015)

Figure 5: Profiles of outputs, prices and costs with cost-based competence

i c(0) + t p(0) p(i) a(0) x(0) x(i) δ c(i) + t

Niklas Herzig (Bielefeld University) Economies of Scope and Trade June 16, 2015 25 / 40

Eckel et al. (2015)

Quality-based Competence considering quality (β > 0) perceived quality (premium) of variety i:

• z(i) = (1 − e)z(i) + eZ

(17) z(i): variety-specific perceived quality and Z: perceived quality of the firm‘s brand (Z =

• i∈Ω z(i)di)

(linear-quadratic) specification for the costs of and returns to investment in quality:

1

investment in quality of variety i, k(i): costs: γk(i) and benefits: z(i) = 2θk(i)0.5

2

investment in quality of the brand, K: costs: ΓK and benefits: Z = 2ΘK

0.5

Niklas Herzig (Bielefeld University) Economies of Scope and Trade June 16, 2015 26 / 40

Eckel et al. (2015)

• ptimization problem: max Π

Π =

• i∈Ω

[(p(i) − c(i) − t) x(i) − γk(i)] di − ΓK (18) FOCs for scale and scope unchanged FOCs for investment: (i) γk(i)0.5 = β(1 − e)θx(i) i ∈ [0, δ] ; (ii) ΓK

0.5 = βeΘX (19)

comparison: total investment in quality of individual varieties (K ≡ δ

0 k(i)di) and investment in brand quality (K):

K K = 1 − e e θ Θ Γ γ 2 Φ where Φ ≡ δ

0 x(i)2di

X 2 (20)

Niklas Herzig (Bielefeld University) Economies of Scope and Trade June 16, 2015 27 / 40

Eckel et al. (2015)

scale x(i): x(i) = a0 − c(i) − t − 2

• b − ηe
• eX

2

• b − η(1 − e)
• (1 − e)

i ∈ [0, δ] η ≡ β2θ2 γ (21) η ≡ β2Θ2 Γ η, η: ”marginal effectiveness of investment” scale x(i): x(i) = c(δ) − c(i) 2

• b − η(1 − e)
• (1 − e)

i ∈ [0, δ] (22)

Niklas Herzig (Bielefeld University) Economies of Scope and Trade June 16, 2015 28 / 40

Eckel et al. (2015)

price p(i): p(i) =

• b − 2η(1 − e)

2

• b − η(1 − e)

c(i) +

• b

2

• b − η(1 − e)

c(δ) + t + beX (23) i ∈ [0, δ] Proposition:

1

• b > 2η(1 − e): cost-based competence dominates (price rises with i)

2

• b < 2η(1 − e): quality-based competence dominates (price falls with i)

quality-based competence more likely to dominate:

1

when investment in quality is more effective (η larger)

2

when market size L is larger

3

when products are more differentiated (e smaller)

Niklas Herzig (Bielefeld University) Economies of Scope and Trade June 16, 2015 29 / 40

Eckel et al. (2015)

Figure 6: Profiles of outputs, prices and costs with quality-based competence

i c(0) + t p(0) p(i) a(i) a(0) x(0) x(i) δ c(i) + t

Niklas Herzig (Bielefeld University) Economies of Scope and Trade June 16, 2015 30 / 40

Eckel et al. (2015)

Comparative Statics Evaluate (10) at i = δ: c(δ) = a0 − t − 2( b − ηe)eX (24) Integrate (11) over i: X = δ

0 [c(δ) − c(i)] di

2

• b − η(1 − e)
• (1 − e)

(25) Increase in: η η t L X + +

• +

x(0) + +

• +

δ +

• +/-

Niklas Herzig (Bielefeld University) Economies of Scope and Trade June 16, 2015 31 / 40

Appendix

• ften used terms:

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 June 16, 2015 32 / 40

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 June 16, 2015 33 / 40

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 June 16, 2015 34 / 40

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 June 16, 2015 35 / 40

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 June 16, 2015 36 / 40

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 June 16, 2015 37 / 40

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 June 16, 2015 38 / 40

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 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 June 16, 2015 39 / 40

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 June 16, 2015 40 / 40