International Trade. Lecture 3: the Krugman model of trade. Thomas Chaney. Sciences Po. Thomas Chaney (Sciences Po) International Trade 1 / 24

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1 International Trade Lecture 3: the Krugman model of trade Thomas Chaney Sciences Po Thomas Chaney (Sciences Po) International Trade 1 / 24

2 Ricardian model of trade (1817) Countries differ in their technology. Motive for trade: comparative advantages. Key assumption: it is easier to move goods than technologies. Thomas Chaney (Sciences Po) International Trade 2 / 24

3 Heckscher-Ohlin model of trade (1933) Countries differ in their factor endowments. Motive for trade: endogenous differences in technology. Key finding: trade alone may equalize factor prices. Key assumption: it is easier to trade goods than factors of production. Thomas Chaney (Sciences Po) International Trade 3 / 24

4 Empirical challenges Countries with seemingly similar technologies trade. Countries with seemingly similar factor endowments trade. Alargefractionoftradeistwo-waytradewithinindustry. Thomas Chaney (Sciences Po) International Trade 4 / 24

5 Krugman model of trade ( ) Countries have identical technologies, factor endowments, preferences... Differentiated goods (love for variety) ) consumers want to consume all possible goods. Increasing returns to scale ) countries specialize in producing a subset of goods. Thomas Chaney (Sciences Po) International Trade 5 / 24

6 Key assumptions Love for variety preferences. Increasing returns to scale. Imperfect competition. Thomas Chaney (Sciences Po) International Trade 6 / 24

7 Key simplifying assumptions Iso-elastic preferences. Fixed cost + constant marginal cost technology. Monopolistic competition with many firms. Multiplicative trade costs. Thomas Chaney (Sciences Po) International Trade 7 / 24

8 Preferences ˆ max U q (w) s s 1 dw q(w) W ˆ s.t. p (w) q (w) dw = wl W s s 1 Thomas Chaney (Sciences Po) International Trade 8 / 24

9 Demand p (w) q (w) = P ˆ with P = s wl P p (w) 1 W s dw 1 1 s Thomas Chaney (Sciences Po) International Trade 9 / 24

10 Technology and pricing Increasing returns to scale technology: l (q) = f + q j Iso-elastic demand ) constant mark-up over marginal cost: p (w) = s w s 1 j, 8w Thomas Chaney (Sciences Po) International Trade 10 / 24

11 Profits and free entry Gross profits proportional to size, p (p, P) + wf = pq (p, P) = w Free entry drives down profits to zero, q (p, P) (s 1) j wq (p, P) j p = 0 ) q = (s 1) jf (FE) Note 1: key assumption, fixed cost in units of labor (not of goods). Note 2: entry of new firms drives down P, ˆ P = p (w) 1 W 1 s 1 s 1 dw = n 1 s p Thomas Chaney (Sciences Po) International Trade 11 / 24

12 Number of firms and welfare Number of firms pinned down by aggregate ressource constraint (labor market clearing), n f + q = L ) n = L (LMC) j sf Welfare increases with size, P = sw 1 L 1 s (s 1) j sf W = w P = (s 1) j s 1 L s 1 sf Thomas Chaney (Sciences Po) International Trade 12 / 24

13 Trade 2countries,onlydifferinsize(L, L ). Icerberg transportation costs t > 1. Segmented markets: domestic price = p = s 1 w s j export price (c.i.f.) = tp Note: this is not "pricing-to-market." Thomas Chaney (Sciences Po) International Trade 13 / 24

14 Aggregate prices Both trade barriers and relative abundance of varieties affect trade, P 1 s = np 1 s + n (tp ) 1 s P 1 s = n (tp) 1 s + n p 1 s Novel intuition: trade enhances welfare through added varieties. Note: in Krugman, trade barriers (< + ) do not affect available varieties. Thomas Chaney (Sciences Po) International Trade 14 / 24

15 Production and profits Firms produce both for domestic and foreign consumers, q (p, P, P ) = q D (p, P) + tq X (tp, P ) Profits derived from global sales, p (p, P, P ) = w (s 1) j q (p, P, P ) wf Free entry drives down global profits to zero, p = 0, q = (s 1) jf Note: scale of production unaffected by trade (due to constant mark-ups, fixed costs in labor and free entry). Thomas Chaney (Sciences Po) International Trade 15 / 24

16 Number of firms Number of firms pinned down by aggregate ressource constraint (labor market clearing), 8 < n f + q j = L : n f + q j = L ) n = L sf n = L sf (LMC) Note: number of firms same as in autarky (due to constant mark-ups). Corrolary: number of products unaffected by changes in trade barriers. Thomas Chaney (Sciences Po) International Trade 16 / 24

17 Gains from trade do not come from increased variety Welfare depends on number of goods and prices, W = w P = w np 1 s + n (tp ) 1 s 1/(s 1) Number of varieties and local prices are constant, n = L sf n = L sf ( p = s 1 s p = s 1 s w j w j Gain from trade only comes from cheaper foreign goods, not from more foreign goods. Note: only true "on average", because relative wages adjust. Thomas Chaney (Sciences Po) International Trade 17 / 24

18 Aggregate trade Define the relative wage, w = w w,andnormalizew = 1. Aggregate trade flows, tw 1 X f.o.b. = l L L P s Foreign price index, P 1 s = l (tw) 1 s L + L Thomas Chaney (Sciences Po) International Trade 18 / 24

19 Wages and market size (Economic Geography) Trade balance, X f.o.b. = X f.o.b.,gives, In a large market: t 1 s L + L w ) w 2(1 s) = (wt) 1 s L + L if L = L, w = 1 if L > L, w > 1 More cheap (domestic) varieties ) lower price index. ) consumers are less willing to import (expensive) foreign varieties. ) to restore trade balance, "currency appreciates"., relative wage increases. Note: a larger market has higher nominal wages and a lower price index, sohigherreal wages. Thomas Chaney (Sciences Po) International Trade 19 / 24

20 Home market effect Definition Increasing returns to scale industries tend to locate in larger markets, and export their goods to other countries. Simple set-up in Helpman-Krugman. Cobb-Douglas preferences over 2 sectors. 1differentiatedgoodsector:CES(s), shareµ. 1 homogenous good sector: share(1 µ), CRS, freely tradable ) w w = 1 Note: only true if both countries produce homogenous good. Thomas Chaney (Sciences Po) International Trade 20 / 24

21 Labor market clearing As in Krugman, free entry pins down scale of production: q = q = (s 1) jf. Simplifying assumption: w = w ) p = p (all normalized to 1). Goods market clearing, ( n nq = µl + n+n n t 1 s µl t 1 s nt 1 s +n n q = nt1 s µl + n+n n µl t 1 s nt 1 s +n Thomas Chaney (Sciences Po) International Trade 21 / 24

22 Home market effect s n = n/ (n + n ), s L = L/ (L + L ),ands n = (1+t1 s )s L t 1 s. Home market effect 1 t 1 s Figure: Home market effect Thomas Chaney (Sciences Po) International Trade 22 / 24

23 Home market effect: intuition Intuition: from a symmetric equilibrium, increase size of home, more demand/profits for home firms. to restore free entry, entry of domestic firms. When t < +, marketsaresharedbydomesticandforeignfirms. Firm entry has a lower impact on profits than consumer entry. Firm entry must respond more than proportionally to size. Thomas Chaney (Sciences Po) International Trade 23 / 24

24 Home market effect: intuition Note: & t ) steeper line ) stronger home market effect. t high: most competitors to domestic firms are also domestic. domestic firms lose a lot from entry of domestic firms. to restore zero profits, entry must move a little. t low: many competitors to domestic firms are foreign. domestic firms lose little from entry of domestic firms. to restore zero profits, entry must move a lot. Thomas Chaney (Sciences Po) International Trade 24 / 24