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 Literature overview 1 Eckel and Neary (2010) 2 Eckel et al. (2015) 3 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 Products asymmetric on the demand side 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: � 1 U [ u ( z )] = u ( z ) dz (1) 0 with � � 2 � �� N � N � N q ( i ) di − 1 q ( i ) 2 di + e u ( z ) = a 2 b (1 − e ) q ( i ) di 0 0 0 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 U [ u ( z )] subject to q ( i ) � 1 � N p ( i ) q ( i ) didz ≤ I 0 0 p ( i ): price of variety i and I : individual income FOC: inverse individual demand function: � � N � λ p ( i ) = a − b (1 − e ) q ( i ) + e q ( i ) di (2) 0 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) � N a ′ ≡ a /λ , b ′ ≡ b /λ kL and Y ≡ 0 x ( i ) di : industry output Production and Supply “flexible manufacturing”technology (core competence): c j ( i ): marginal cost of firm j to produce variety i (independent of output, j > 0 and c j (0) = c 0 but different across products: c ′ j ; e.g. linear: c j ( i ) = c 0 j + γ i ) Niklas Herzig (Bielefeld University) Economies of Scope and Trade June 16, 2015 6 / 40
Eckel and Neary (2010) Figure 1 c j ( i ) a ′ − b ′ e ( X + Y ) 2 b ′ (1 − e ) X c j (0) i δ 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: � δ j max π j = [ p j ( i ) − c j ( i )] x j ( i ) − F x j ( i ) 0 δ j : mass of products produced (scope) and F : fixed cost FOC: (i) scale ∂π j ∂ x j ( i ) = p j ( i ) − c j ( i ) − b ′ [(1 − e ) x j ( i ) + eX j ] = 0 (4) proof � δ j X j ≡ 0 x j ( i ) di : firm’s aggregate output x j ( i ) = a ′ − c j ( i ) − b ′ e ( X j + Y ) (5) 2 b ′ (1 − e ) Niklas Herzig (Bielefeld University) Economies of Scope and Trade June 16, 2015 8 / 40
Eckel and Neary (2010) Figure 2 p ( 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 )] c ( i ) x ( i ) x ( i ) Niklas Herzig (Bielefeld University) Economies of Scope and Trade June 16, 2015 9 / 40
Eckel and Neary (2010) � � p j ( i ) = 1 a ′ + c j ( i ) − b ′ e ( Y − X j ) (6) 2 (ii) scope ∂π j = [ p j ( δ j ) − c j ( δ j )] x j ( δ j ) = 0 (7) ∂δ j product range: output of the marginal variety ( δ j ) zero: x j ( δ j ) = 0 c j ( δ j ) = a ′ − b ′ e ( X j + Y ) (8) p j ( δ j ) = 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 ) = w γ ( i ) Niklas Herzig (Bielefeld University) Economies of Scope and Trade June 16, 2015 10 / 40
Eckel and Neary (2010) total labour input: � δ l = γ ( i ) x ( i ) di 0 � δ 0 h ( i ) d x ( i ) d ln LP d ln θ di − d ln l d ln θ = (9) � δ d ln θ 0 h ( i ) x ( i ) di θ : any exogenous variable and h ( i ): weight of variety i x ( i ) = w [ γ ( δ ) − γ ( i )] 2 b ′ (1 − e ) � δ w β ( δ ) l = with β ( δ ) ≡ γ ( i ) [ γ ( δ ) − γ ( i )] di 2 b ′ (1 − e ) 0 d ln LP d ln θ = ∂ ln LP d ln δ proof ∂ ln δ d ln θ Niklas Herzig (Bielefeld University) Economies of Scope and Trade June 16, 2015 11 / 40
Eckel and Neary (2010) choice of weights h ( i ): � δ � 0 γ ( i ) ∂ x ( i ) � ∂ ln LP ∂ ln δ di − ∂ ln l � = ∂ ln δ = 0 � δ proof � ∂ ln δ 0 γ ( i ) x ( i ) di h ( i )= γ ( i ) Proposition 1: With given technology, any shock which raises the product range δ (a) leaves LP unchanged when output changes are marginal cost-weighted, proof and (b) reduces LP when output is a simple aggregate proof . (c) reduces LP but by less when output changes are price-weighted 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)): w γ ( δ ) = a ′ − e (1 + km ) b ′ X ⇒ scope: δ ( X ) FOC for scale (integrate over (5)): � � a ′ − w µ ′ δ γ proof ⇒ scale: X ( δ ) X = with △ 1 ≡ 2(1 − e )+ e δ (1+ km ) > 0 △ 1 b ′ � δ γ ≡ 1 with µ ′ 0 γ ( i ) di δ d ln δ = a ′ − w γ ( δ ) − e (1 + km ) b ′ X d ln X a ′ − w µ ′ γ Niklas Herzig (Bielefeld University) Economies of Scope and Trade June 16, 2015 13 / 40
Eckel and Neary (2010) Figure 3 s❝❛❧❡✿ X ( δ ) δ s❝♦♣❡✿ δ ( X ) X 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 output, 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 x ( i ) i Niklas Herzig (Bielefeld University) Economies of Scope and Trade June 16, 2015 16 / 40
Eckel and Neary (2010) full effect: on firm output: d ln X d ln k = 1 − e δ km (10) △ 1 where △ 1 − e δ km = △ 0 ( ≡ 2(1 − e ) + e δ ) > 0 on variety output: � � µ ′ γ − γ ( i ) d ln x ( i ) ekm α ( δ ) △ 1 [ γ ( δ ) − γ ( i )] = △ 0 1 − △ 0 = 1 − + γ ( δ ) − γ ( i ) (11) d ln k △ 1 △ 1 γ PE : labour requirement of the threshold variety whose output is � unchanged � � γ PE = △ 0 1 − △ 0 µ ′ � γ ( δ ) + γ △ 1 △ 1 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 or 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 = km δ : 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 − e δ km α ( δ ) δα δ △ 1 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
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