Economies of Scope and Trade

Transcription

1 Economies of Scope and Trade Niklas Herzig Bielefeld University June 16, 215 Niklas Herzig (Bielefeld University) Economies of Scope and Trade June 16, / 4

2 Overview 1 Literature overview 2 Eckel and Neary (21) 3 Eckel et al. (215) Niklas Herzig (Bielefeld University) Economies of Scope and Trade June 16, / 4

3 Literature overview Product symmetry Products symmetric on both the demand and supply side Product asymmetry Products asymmetric on the demand side Allanson and Montagna (IJIO 25) Bernard, Redding and Schott (AER 21, QJE 211) Nocke and Yeaple (IER 214) Products asymmetric on the supply (cost) side Arkolakis, Ganapati and Muendler (215) Mayer, Melitz and Ottaviano (AER 214) Cannibalization Ju (RIE 23) Eckel and Neary (RES 21) Feenstra and Ma (28) Baldwin and Gu (29) Eckel, Iacovone, Javorcik and Neary (JIE 215) Dhingra (AER 213) Qiu and Zhou (JIE 213) Niklas Herzig (Bielefeld University) Economies of Scope and Trade June 16, / 4

4 Eckel and Neary (21) Eckel, Carsten and Peter Neary (21). Multi-Product Firms and Flexible Manufacturing in the Global Economy, Review of Economic Studies 77(1), pp Preferences and Demand two-tier utility function: with U[u(z)] = 1 u(z)dz (1) N u(z) = a q(i)di 1 N { N } 2 ] [(1 2 b e) q(i) 2 di + e q(i)di q(i): consumption of (horizontally diff.) product variety i, i [, N] and N: measure of diff. varieties produced in each industry z, z [, 1] Niklas Herzig (Bielefeld University) Economies of Scope and Trade June 16, / 4

5 Eckel and Neary (21) 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, / 4

6 Eckel and Neary (21) 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 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, but different across products: c j > and c j() = cj ; e.g. linear: c j (i) = cj + γi) Niklas Herzig (Bielefeld University) Economies of Scope and Trade June 16, / 4

7 Eckel and Neary (21) Figure 1 c j (i) 2b (1 e)x a b e(x + Y ) c j () δ i Niklas Herzig (Bielefeld University) Economies of Scope and Trade June 16, / 4

8 Eckel and Neary (21) single-stage Cournot game profit maximization problem: max x j (i) π j = j [p j (i) c j (i)] x j (i) F 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 ] = proof (4) X j j x j(i)di: firm s aggregate output x j (i) = a c j (i) b e (X j + Y ) 2b (1 e) (5) Niklas Herzig (Bielefeld University) Economies of Scope and Trade June 16, / 4

9 Eckel and Neary (21) Figure 2 p(i) a b ey a b e(x + Y ) p(i) = a b [(1 e)x(i) + ey ] 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, / 4

10 Eckel and Neary (21) (ii) scope p j (i) = 1 2 [ a + c j (i) b e(y X j ) ] (6) π j δ j = [p j (δ j ) c j (δ j )] x j (δ j ) = (7) product range: output of the marginal variety (δ j ) zero: x j (δ j ) = 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) = wγ(i) Niklas Herzig (Bielefeld University) Economies of Scope and Trade June 16, / 4

11 Eckel and Neary (21) total labour input: l = γ(i)x(i)di d x(i) d ln LP d ln θ = h(i) d ln θ di δ h(i)x(i)di d ln l d ln θ θ: any exogenous variable and h(i): weight of variety i (9) x(i) = w [γ(δ) γ(i)] 2b (1 e) l = wβ(δ) 2b (1 e) d ln LP d ln θ with β(δ) ln LP d ln δ = ln δ d ln θ γ(i) [γ(δ) γ(i)] di proof Niklas Herzig (Bielefeld University) Economies of Scope and Trade June 16, / 4

12 Eckel and Neary (21) choice of weights h(i): ln LP ln δ = h(i)=γ(i) x(i) γ(i) ln δ di γ(i)x(i)di ln l ln δ = 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. proof Niklas Herzig (Bielefeld University) Economies of Scope and Trade June 16, / 4

13 Eckel and Neary (21) 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)): ( a wµ ) γ δ X = 1 b with 1 2(1 e)+eδ(1+km) > proof scale: X (δ) with µ γ 1 δ 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, / 4

14 Eckel and Neary (21) Figure 3 δ scale: X(δ) scope: δ(x) X Niklas Herzig (Bielefeld University) Economies of Scope and Trade June 16, / 4

15 Eckel and Neary (21) 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, / 4

16 Eckel and Neary (21) Figure 4 x(i) i Niklas Herzig (Bielefeld University) Economies of Scope and Trade June 16, / 4

17 Eckel and Neary (21) full effect: proof on firm output: where 1 eδkm = ( 2(1 e) + eδ) > on variety output: d ln x(i) d ln k ekmα(δ) = 1 1 [γ(δ) γ(i)] = d ln X d ln k = 1 eδkm (1) 1 ( ) µ γ γ(i) γ(δ) γ(i) (11) γ PE : labour requirement of the threshold variety whose output is unchanged γ PE = ( γ(δ) + 1 ) µ γ 1 1 Niklas Herzig (Bielefeld University) Economies of Scope and Trade June 16, / 4

18 Eckel and Neary (21) 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, / 4

19 Eckel and Neary (21) 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 α(δ) 1 δα δ 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, / 4

20 Eckel et al. (215) Eckel, Carsten, Leonardo Iacovone, Beata Javorcik and Peter Neary (215). Multi-Product Firms at Home and Away: Cost- versus Qualitybased Competence, Journal of International Economics 95(2), pp determinants of economic success of firms (exporters): 1 firm productivity (among others, Melitz (Econ 23)) 2 product quality (among others, Manova and Zhang (QJE 212)) two views opposed? No, focus on: ïntra-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 21) 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, / 4

21 Eckel et al. (215) Preferences for quantity and quality single market (L consumers) representative consumer: quadratic sub-utility function u = u 1 + βu 2 u 1 = a Q 1 2 b [ (1 e) i Ω q(i)2 di + eq 2] (12) u 2 = 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 ( e 1) z(i): perceived quality (premium) of variety i Niklas Herzig (Bielefeld University) Economies of Scope and Trade June 16, / 4

22 Eckel et al. (215) Product Demand optimization problem: max u subject to budget constraint p(i)q(i)di = I (I : individual expenditure on Ω) i 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) = a + 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, / 4

23 Eckel et al. (215) Cost-based Competence ignoring quality (β = ) optimization problem: max π π = [p(i) c(i) t] x(i)di (14) i Ω 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) > (c() = c ) Niklas Herzig (Bielefeld University) Economies of Scope and Trade June 16, / 4

24 Eckel et al. (215) Scale and Scope 1 scale x(i): x(i) = 2 scope δ: a(i) c(i) t 2 bex 2 b(1 e) i Ω (15) 3 price p(i): x(δ) = p(i) = 1 [a(i) + c(i) + t] (16) 2 Niklas Herzig (Bielefeld University) Economies of Scope and Trade June 16, / 4

25 Eckel et al. (215) Figure 5: Profiles of outputs, prices and costs with cost-based competence x() a() x(i) p() p(i) c(i) + t c() + t δ i Niklas Herzig (Bielefeld University) Economies of Scope and Trade June 16, / 4

26 Eckel et al. (215) Quality-based Competence considering quality (β > ) 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).5 2 investment in quality of the brand, K: costs: ΓK and benefits: Z = 2ΘK.5 Niklas Herzig (Bielefeld University) Economies of Scope and Trade June 16, / 4

27 Eckel et al. (215) optimization problem: max Π Π = [(p(i) c(i) t) x(i) γk(i)] di ΓK (18) i Ω FOCs for scale and scope unchanged FOCs for investment: (i) γk(i).5 = β(1 e)θx(i) i [, δ] ; (ii) ΓK.5 = βeθx (19) comparison: total investment in quality of individual varieties (K k(i)di) and investment in brand quality (K): ( K 1 e K = e ) θ Γ 2 Φ where Φ Θ γ x(i)2 di X 2 (2) Niklas Herzig (Bielefeld University) Economies of Scope and Trade June 16, / 4

28 Eckel et al. (215) scale x(i): ) a c(i) t 2 ( b ηe ex x(i) = ] 2 [ b η(1 e) (1 e) η, η: marginal effectiveness of investment scale x(i): i [, δ] η β2 θ 2 γ η β2 Θ 2 Γ (21) x(i) = c(δ) c(i) ] 2 [ b η(1 e) (1 e) i [, δ] (22) Niklas Herzig (Bielefeld University) Economies of Scope and Trade June 16, / 4

29 Eckel et al. (215) price p(i): p(i) = b 2η(1 e) ]c(i) + 2 [ b η(1 e) Proposition: b ]c(δ) + t + 2 [ b bex (23) η(1 e) i [, δ] 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, / 4

30 Eckel et al. (215) Figure 6: Profiles of outputs, prices and costs with quality-based competence x() p() x(i) a(i) p(i) a() c(i) + t c() + t δ i Niklas Herzig (Bielefeld University) Economies of Scope and Trade June 16, / 4

31 Eckel et al. (215) Comparative Statics Evaluate (1) at i = δ: c(δ) = a t 2( b ηe)ex (24) [c(δ) c(i)] di Integrate (11) over i: X = ] 2 [ b η(1 e) (1 e) (25) Increase in: η η t L X x() δ /- Niklas Herzig (Bielefeld University) Economies of Scope and Trade June 16, / 4

32 Appendix often used terms: α(δ) = δ [ γ(δ) µ ] γ β(δ) = δ [ γ(δ)µ γ µ γ] = α(δ)µ δ δσ 2 γ α δ = δγ δ β δ = µ γα δ Niklas Herzig (Bielefeld University) Economies of Scope and Trade June 16, / 4

33 Appendix π δj j x j (i) = p j(i) c j (i) + p j (i ) x j (i) x j(i )di = i = i : p j(i ) x j (i) = b and i i : p j(i ) x j (i) = b e π j x j (i) = p j(i) c j (i) b [(1 e)x j (i) + ex j ] =, X j j x j (i )di (4) back Niklas Herzig (Bielefeld University) Economies of Scope and Trade June 16, / 4

34 Appendix d ln LP d ln θ ln LP = ln θ ln LP d ln δ + ln δ d ln θ l = ψ(θ)β(δ) x = ψ(θ) [γ(δ) γ(i)] and and ln l ln θ = ln l θ θ ln θ = ψ ψ θ x ln θ = x θ θ ln θ = [γ(δ) γ(i)] ψ θ h(i) x ln θ di h(i)x(i)di = d ln LP d ln θ h(i)ψ (θ)θ [γ(δ) γ(i)] di h(i)ψ(θ) [γ(δ) γ(i)] di = ψ ψ θ ln LP d ln δ = ln δ d ln θ ( ln LP ) ln θ = back Niklas Herzig (Bielefeld University) Economies of Scope and Trade June 16, / 4

35 Appendix ln LP ln δ = h(i)=γ(i) = 1 l = 1 l = x(i) γ(i) ln δ di γ(i)x(i)di ln l ln δ = ln l ln δ γ(i) x(i) ln l di ln δ ln δ γ(i)x(i) di ln l ln δ ln δ ln l γ(i)x(i) l ln δ di ln l ln δ γ(i)x(i) di ln l l ln δ = back Niklas Herzig (Bielefeld University) Economies of Scope and Trade June 16, / 4

36 Appendix ln LP ln δ (since X = = ln X h(i)=1 ln δ ln l ln δ = w [γ(δ) γ(i)] 2b di = (1 e) = ln α(δ) ln δ ln β(δ) ln δ w 2b (1 e) δ ( γ(δ) µ ) γ wα(δ) 2b (1 e) ) = δα δ α(δ) δβ δ β(δ) = δ2 α δ σ 2 γ α(δ)β(δ) < back Niklas Herzig (Bielefeld University) Economies of Scope and Trade June 16, / 4

37 Appendix ln LP ln δ = h(i)=p(i) x(i) p(i) ln δ di p(i)x(i)di ln l ln δ p(i)x(i) = 1 ( a + wγ(i) b e(y X ) ) w 2 2b [γ(δ) γ(i)] (1 e) = 1 ( wγ(i) + wγ(δ) + 2b ex ) w 2 2b [γ(δ) γ(i)] (1 e) ( ) 1 = w 2 (γ(i) + γ(δ)) + e α(δ) w 2(1 e) 2b [γ(δ) γ(i)] (1 e) back Niklas Herzig (Bielefeld University) Economies of Scope and Trade June 16, / 4

38 Appendix X = = a wγ(i) b e(x + Y ) 2b di (1 e) 1 2b (1 e) (a wγ(i) b e(1 + km)x )di X ( ) X 1 + b eδ(1 + km) 2b (1 e) ( 2b (1 e) + b ) eδ(1 + km) 2b (1 e) = = 1 2b (a wγ(i))di (1 e) δ ( a 2b wµ (1 e) γ) X = δ ( a b wµ (2(1 e) + eδ(1 + km)) γ) back Niklas Herzig (Bielefeld University) Economies of Scope and Trade June 16, / 4

39 Appendix - Industry Equilibrium Comparative Statics [ 1 e(1 + km) [ ] δ ekm d ln m + 1 2(1 e)δγ δ α(δ) [ e ] [d ] [ ] ln X = 1 d ln L d ln δ e(1 + km) ] [ ] δµ d ln k γ 2(1 e) d ln w γ(δ) α(δ) d ln X = d ln L eδkm d ln m + d ln k 2(1 e)δµ γ α(δ) d ln w d ln δ = eδkmα(δ) (d ln m + d ln k) 2(1 e)δµ δ + 1 α(δ) d ln w 1 δα δ 1 δα δ [ ( ekmα(δ) d ln x(i) = d ln L 1 [γ(δ) γ(i)] d ln m ) 1 1 µ ] γ γ(i) d ln k 2(1 e)γ(i) eδ(1 + km) [ µ γ γ(i) ] d ln w γ(δ) γ(i) 1 [γ(δ) γ(i)] Niklas Herzig (Bielefeld University) Economies of Scope and Trade June 16, / 4 back

40 Appendix - Industry Equilibrium Comparative Statics = (γ(i) γ(δ)) 1 = ( + 1 ( 1 1 γ PE = γ(i) = 1 γ(δ) + 1 ) µ γ γ(i) 1 γ(δ) γ(i) ) (µ γ γ(i) ) ( 1 1 ) µ γ back Niklas Herzig (Bielefeld University) Economies of Scope and Trade June 16, / 4