Monopolistic Competition in Trade III Trade Costs and Gains from Trade

Transcription

1 Monopolistic Competition in Trade III Trade Costs and Gains from Trade Notes for Graduate International Trade Lectures J. Peter Neary University of Oxford January 21, 2015 J.P. Neary (University of Oxford) Monopolistic Competition III January 21, / 31

2 Plan of Lectures 1 Preliminaries 2 Integrated versus Segmented Markets 3 Globalization versus Colder Icebergs 4 Gains from Trade 5 Calibrating Gains from Trade 6 Conclusion 7 Supplementary Material J.P. Neary (University of Oxford) Monopolistic Competition III January 21, / 31

3 Introduction The Bottom Line Trade Costs and General Demands: Together at Last! J.P. Neary (University of Oxford) Monopolistic Competition III January 21, / 31

4 Introduction Motivation Traditional trade theory assumes that countries are different and explains why some countries export agricultural products whereas others export industrial goods. The new theory clarifies why worldwide trade is in fact dominated by countries which not only have similar conditions, but also trade in similar products... This kind of trade enables specialization and large-scale production, which result in lower prices and a greater diversity of commodities. Press Release for Paul Krugman s Nobel Prize (Emphasis added) Note: 3 of the 4 highlighted effects do not hold with CES preferences! This is an unsatisfactory result. In another paper [1979] I have developed a slightly different model in which trade leads to an increase in scale of production as well as an increase in diversity. That model is, however, more difficult to work with, so that it seems worth sacrificing some realism to gain tractability here. Krugman (1980) J.P. Neary (University of Oxford) Monopolistic Competition III January 21, / 31

5 Introduction In this file Search for tractability without sacrificing realism Combine trade costs and additive separability in a simple model Highlight the importance of demand properties, esp. subconvexity Focus on information needed to calibrate gains from trade J.P. Neary (University of Oxford) Monopolistic Competition III January 21, / 31

6 Introduction Literature: Monopolistic Competition in GE Closed economy; additively separable preferences; CES as a special case: Dixit-Stiglitz (1977) Trade costs with CES preferences: Krugman (1980) etc. Trade costs and gains from trade with CES preferences: Arkolakis-Costinot-Rodríguez-Clare (AER 2012), Simonovska-Waugh (2012), Melitz-Redding (2013), Ossa (2013) Free trade with additively separable preferences: Krugman (1979) Neary (2009), Zhelobodko-Kokovin-Parenti-Thisse (2012), Dhingra-Morrow (2012), Mrázová-Neary (2013) Trade costs with non-ces preferences: Bertoletti-Epifani (2012) Arkolakis-Costinot-Donaldson-Rodríguez-Clare (mimeo. 2012) Bykadorov-Kokovin (2012) J.P. Neary (University of Oxford) Monopolistic Competition III January 21, / 31

7 Introduction Outline 1 Preliminaries 2 Integrated versus Segmented Markets 3 Globalization versus Colder Icebergs 4 Gains from Trade 5 Calibrating Gains from Trade 6 Conclusion 7 Supplementary Material J.P. Neary (University of Oxford) Monopolistic Competition III January 21, / 31

8 Preliminaries Plan of Lectures 1 Preliminaries Monopolistic Competition in the Global Economy 2 Integrated versus Segmented Markets 3 Globalization versus Colder Icebergs 4 Gains from Trade 5 Calibrating Gains from Trade 6 Conclusion 7 Supplementary Material J.P. Neary (University of Oxford) Monopolistic Competition III January 21, / 31

9 Preliminaries Monopolistic Competition in the Global Economy Equilibrium in the Global Economy κ + 1 identical countries; n homogeneous firms in each Symmetric iceberg trade costs τ; no fixed costs of trade L identical worker-consumers per country, additively separable preferences: [ ] U = F u{x(i)}di, F > 0, u > 0, u < 0 i N With symmetry: x(i) = x, x (i) = x U = F [ n{u(x) + κu(x )} ] Market clearing: Goods-Market Equilibrium: y = L(x + κτx ) Labor-Market Equilibrium: L = n (f + cy) J.P. Neary (University of Oxford) Monopolistic Competition III January 21, / 31

10 Integrated versus Segmented Markets Plan of Lectures 1 Preliminaries 2 Integrated versus Segmented Markets 3 Globalization versus Colder Icebergs 4 Gains from Trade 5 Calibrating Gains from Trade 6 Conclusion 7 Supplementary Material J.P. Neary (University of Oxford) Monopolistic Competition III January 21, / 31

11 Integrated versus Segmented Markets Integrated versus Segmented Markets Integrated: Prices equalized allowing for transport costs: p = τp Segmented: Marginal revenues equalized allowing for transport costs: r x = c, rx = τc rx = τr x These are the same if and only if preferences are CES: r x = ε 1 ε p, rx = ε 1 ε p Proof Segmented markets and subconvex demands imply Reciprocal Dumping: Lower price-cost margins abroad: p τc < p c Lower τ-inclusive prices abroad: p < τp Proof J.P. Neary (University of Oxford) Monopolistic Competition III January 21, / 31

12 Globalization versus Colder Icebergs Plan of Lectures 1 Preliminaries 2 Integrated versus Segmented Markets 3 Globalization versus Colder Icebergs 4 Gains from Trade 5 Calibrating Gains from Trade 6 Conclusion 7 Supplementary Material J.P. Neary (University of Oxford) Monopolistic Competition III January 21, / 31

13 Globalization versus Colder Icebergs Profit Maximization Assume segmented markets Profit maximization: r x = τr x x * = 1 MR=MC ηˆx = η ˆx + ˆτ Elasticity of marginal revenue: η xr xx = 2 ρ r x ε 1 > 0 x positively related to x: Decreasing in τ; Independent of κ > 1 O x CES: η = η = 1 σ ; x = τ σ x J.P. Neary (University of Oxford) Monopolistic Competition III January 21, / 31

14 Globalization versus Colder Icebergs Free Entry Zero profits: π + κπ = f π = (p c)lx = clx ε 1 π = (p τc)lx = τclx ε 1 x ε 1 + κτ ε 1 = f cl x x * f ( * 1) Lc = 1 = 0 > 1 ω π εηˆx + (1 ω π ) ε η ˆx = (1 ω π ) (ˆκ + ˆτ) ω π : Home market profit share x negatively related to x: Decreasing in τ and κ O f ( 1) Lc CES: x + κτx = (σ 1) f cl = y L x J.P. Neary (University of Oxford) Monopolistic Competition III January 21, / 31

15 Globalization versus Colder Icebergs Equilibrium Sales Home and export sales: ε π ηˆx = (1 ω π ) [ ˆκ + (ε 1) ˆτ] x * MR=MC ε π η ˆx = (1 ω π ) ˆκ = 0 [1 + ω π (ε 1)] ˆτ π-weighted aggregate elasticity: B A ε π ω π ε + (1 ω π ) ε Globalization (κ ): x x O x J.P. Neary (University of Oxford) Monopolistic Competition III January 21, / 31

16 Globalization versus Colder Icebergs Equilibrium Sales Home and export sales: ε π ηˆx = (1 ω π ) [ ˆκ + (ε 1) ˆτ] x * MR=MC ε π η ˆx = (1 ω π ) ˆκ = 0 [1 + ω π (ε 1)] ˆτ A π-weighted aggregate elasticity: C ε π ω π ε + (1 ω π ) ε O x Globalization (κ ): x x Lower τ: x x CES: ε = σ, εη = εη = 1 J.P. Neary (University of Oxford) Monopolistic Competition III January 21, / 31

17 Globalization versus Colder Icebergs Implications for Prices, Output, and Firm Numbers Prices: p = ε ε 1 c, p = ε ε+1 ερ ε 1τc ˆp = ε(ε 1) ˆx, ˆp = ε +1 ε ρ ε (ε 1) ˆx + ˆτ Both increasing with sales if and only if demands are subconvex Intensive margin: y = x + κτx ŷ = ω xˆx + (1 ω x ) (ˆκ + ˆτ + ˆx ) ω x : Share of home sales in total output In free trade: ( ŷ = (1 ω) 1 1 ) (ˆκ + ˆτ) τ=1 εη Positive if and only if η > 1 ε i.e., if and only if demand is subconvex: η 1 ε = ε+1 ερ ε(ε 1) So: Trade liberalization ambiguous Lower τ reduces firm output if and only if demand is subconvex. Extensive margin: L = n (f + cy) ˆn = ψŷ Application ψ cy f+cy : Share of variable costs in total costs Inverse measure of returns to scale; ψ = ε h 1 ε h ε h : A sales-weighted harmonic mean of ε and ε Details J.P. Neary (University of Oxford) Monopolistic Competition III January 21, / 31

18 Gains from Trade Plan of Lectures 1 Preliminaries 2 Integrated versus Segmented Markets 3 Globalization versus Colder Icebergs 4 Gains from Trade 5 Calibrating Gains from Trade 6 Conclusion 7 Supplementary Material J.P. Neary (University of Oxford) Monopolistic Competition III January 21, / 31

19 Gains from Trade Welfare Change and the Elasticity of Utility Measure welfare change by the change in equivalent income, Y : ( ) εz 1 Ŷ = 1 ˆN Y ω Y ˆp (1 ω Y )ˆp ε u ξ u ξ xu u : Elasticity of utility Recall Near free trade: ( Ŷ 1 ξ = (1 ω) τ=1 ξ Direct effect: Always welfare-improving ) ˆκ ˆτ + ψ ξ ψξ ˆn Indirect effect: Sufficient conditions for a net gain: ψ = ξ: CES preferences guarantee efficiency: ψ = σ 1 = ξ; or σ Activist anti-trust policy adjusts n to ensure efficiency. ψ ξ and ˆn have the same sign; e.g.: Utility is subconcave: ψ > ξ, varieties are under-supplied; and Demand is subconvex: τ y n. Details properties J.P. Neary (University of Oxford) Monopolistic Competition III January 21, / 31 Recall

20 Calibrating Gains from Trade Plan of Lectures 1 Preliminaries 2 Integrated versus Segmented Markets 3 Globalization versus Colder Icebergs 4 Gains from Trade 5 Calibrating Gains from Trade 6 Conclusion 7 Supplementary Material J.P. Neary (University of Oxford) Monopolistic Competition III January 21, / 31

21 Calibrating Gains from Trade Calibrating Gains from Trade { home market share ACRC: 2 sufficient statistics: elasticity of import demand Calibrating home market shares: ω x = ω π = ω u either in free trade or with CES preferences But not in general Calibrating demand elasticities: Calibrated elasticities frequently taken from import demand studies Broda-Weinstein (2006): Median elasticity of 2.9 Recall: ε i ω i ε + (1 ω i ) ε i = x, z, π, Y, u With subconvexity and x < x: ε > ε ε an upward-biased estimate of ε i which underestimates the gains from trade Details J.P. Neary (University of Oxford) Monopolistic Competition III January 21, / 31

22 Conclusion Plan of Lectures 1 Preliminaries 2 Integrated versus Segmented Markets 3 Globalization versus Colder Icebergs 4 Gains from Trade 5 Calibrating Gains from Trade 6 Conclusion 7 Supplementary Material J.P. Neary (University of Oxford) Monopolistic Competition III January 21, / 31

23 Conclusion Summary Integrated versus segmented markets: Different except in CES case Segmented markets and subconvexity imply reciprocal dumping Globalization versus colder icebergs: Globalization reduces spending on all existing varieties Lower trade costs switch spending from home to imported varieties Isomorphic only in CES case Calibrating gains from trade: Many more parameters need to be calibrated than in CES case Home market shares in output, profits, and welfare differ in general Import demand elasticities likely to be upward-biased estimates J.P. Neary (University of Oxford) Monopolistic Competition III January 21, / 31

24 Conclusion Thanks and Acknowledgements Thank you for listening. Comments welcome! The research leading to these results has received funding from the European Research Council under the European Union s Seventh Framework Programme (FP7/ ), ERC grant agreement no The contents reflect only the authors views and not the views of the ERC or the European Commission, and the European Union is not liable for any use that may be made of the information contained therein. J.P. Neary (University of Oxford) Monopolistic Competition III January 21, / 31

25 Supplementary Material 7 Supplementary Material Review: Superconvex Demands, Superconcave Utility Proofs Share Parameters J.P. Neary (University of Oxford) Monopolistic Competition III January 21, / 31 Plan of Lectures 1 Preliminaries 2 Integrated versus Segmented Markets 3 Globalization versus Colder Icebergs 4 Gains from Trade 5 Calibrating Gains from Trade 6 Conclusion

26 Supplementary Material Review: Superconvex Demands, Superconcave Utility Review: Superconvexity and Superconcavity Perceived demand function: p = p(x) p < 0 Elasticity: ε(x) p(x) xp (x) FOC: ε 1 Sub-utility function: u = u(x) u > 0, u < 0 Elasticity: ξ(x) xu (x) u(x) Taste for variety: 0 < ξ < 1 Convexity: ρ(x) xp (x) p (x) SOC: ρ < 2 CES: p(x) = βx 1 σ ε = σ, ρ = σ+1 σ > 1 Superconvexity: p(x) more convex than CES ρ > ε+1 ε ε increasing in sales: ε x 0. CES: u(x) = σ σ 1 σ 1βx σ ξ = σ 1 σ Superconcavity: u(x) more concave than CES ξ > ε 1 ε ξ decreasing in sales: ξ x 0. Application J.P. Neary (University of Oxford) Monopolistic Competition III January 21, / 31

27 Supplementary Material Proofs Proofs Marginal revenue and price: r(x) xp(x) r x = p + xp = ) (1 + xp p = ε 1 p p ε Back to Text Proof that mark-ups rise with sales if and only if demands are subconvex: p c = p = ε(x) r x ε(x) 1 Back to Text d log p [ ] c = 1 ε(ε 1) ε 1 ε + 1 xdx = ρ ε(ε 1) ε So: x < x ε(x ) > ε(x) ε(x ) ε(x ) 1 < ε(x) ε(x) 1 p τc < p c ˆx J.P. Neary (University of Oxford) Monopolistic Competition III January 21, / 31

28 Supplementary Material Proofs Proofs (cont.) Linking variable cost share ψ cy f+cy to elasticities of demand: Back In free trade: ψ = cy py = c p = p+xp p = ε 1 ε With trade costs: ψ = ε h 1 ε h Proof: ε h : A sales-weighted harmonic mean of ε and ε ψ = c(x+κτx ) px+κp x = ω x c p = ω x ε 1 ε = 1 1 ε h, + (1 ωx) τc p + (1 ω x) ε 1 ε Alternatively: ψ = c(x+κτx ) px+κp x ε h [ ω xε 1 + (1 ω x)(ε ) 1] 1 = c p to Text p ω xp + (1 ω x) p : A sales-weighted average of the net prices τ received by the firm in the home and foreign markets (p and p ). τ J.P. Neary (University of Oxford) Monopolistic Competition III January 21, / 31

29 Supplementary Material Share Parameters Shares: Summary Recap: x ω x x+κτx : Share of home sales in total output ω π π π+κπ : Share of home market profits in total profits ω u u u+κu : Share of utility from home goods in total utility ω z Share of home goods in total spending (z = npx) Special Cases: z z+κz : 1 Free trade: ω x = ω π = ω u = ω z = 1 1+κ 2 CES: ω x = ω π = ω u = ω z = 1 1+κτ 1 σ In general: Demand Subconcave Utility Superconcave Subconvex ω π > ω z > {ω x, ω u } {ω π, ω u } > ω z > ω x Superconvex ω x > ω z > {ω π, ω u } {ω x, ω u } > ω z > ω π Back to Text J.P. Neary (University of Oxford) Monopolistic Competition III January 21, / 31

30 Supplementary Material Share Parameters Shares: Proofs 1 Rewrite: ω x =, ω 1+κ τx π = 1, ω x 1+κ π u = 1, ω π 1+κ u z = 1 u 1+κ z z Assume τ > 1 and x > x throughout ω π > ω z > ω x if and only if demands are subconvex (i.e., ε < ε ): p = εc ε 1 z z = p x px = ε ε 1 ε 1 τx ε x < τx x ω z > ω x π = clx ε 1 = Lpx ε = Lz ε π π = ε z ε z < z z ω π > ω z ω u > ω z if and only if utility is superconcave (i.e., ξ < ξ ): ξ xu u u u = ξ x (u ) ξ xu = ξ p x ξ px = ξ z ξ z < z z ω u > ω z CES: ε = ε = σ, ξ = ξ, x = τ σ x ω x = ω π = ω u = ω z = 1 1+κτ 1 σ J.P. Neary (University of Oxford) Monopolistic Competition III January 21, / 31

31 Supplementary Material Change in Real Income: Details Change in Real Income: Details Back to Text Additive separability: U = F [N u(x)] Budget constraint: I = i N Taste for variety requires ξ < 1 p(i)x(i)di = Npx x = I Np Proof: Npx = I, ˆp = Î = 0 ˆx = ˆN Û = (1 ξ) ˆN [ ( )] Indirect utility function: V (N, p, I) = F Nu I Np Define equivalent income Y (N, p) : V ( N, p, I ) Y = U0 ( ) So: Nu is fixed by U 0 I NpY With I = wl fixed: ˆN = ξ( ˆN + ˆp + Ŷ ) Change in Real Income: Ŷ = 1 ξ ξ ˆN ˆp J.P. Neary (University of Oxford) Monopolistic Competition III January 21, / 31