International Macroeconomics #4 Pricing to market

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1 Internatonal Macroeconomcs #4 rcng to market. rologue: Marshall-Lerner-Robnson 2. Incomplete pass-through n a smple olgopolstc model 3. TM n monopolstc competton Bénassy-Quéré - Internatonal Macroeconomcs

2 Trade balance n domestc currency: Total dfferentaton: Exports: Imports:. rologue: Marshall-Lerner-, M /S, τ ε S ε M M M Robnson db wth d τ db + M B d M τ d M M M M + dm M d ε + ε + d M A real exchange-rate deprecaton rases the trade balance f and only f ε + ε M > Marshall-Lerner condton ds S Volume effects Value effect Bénassy-Quéré - Internatonal Macroeconomcs

3 J-curve Bénassy-Quéré - Internatonal Macroeconomcs

4 Export prces: Import prces: The MLR condton M γ γ / S γ M M γ / S Incomplete pass-through rcng to market Impact of real exchange-rate varatons on the trade balance: db d d ε γ + ε γ + M M ds S A real exchange-rate deprecaton rases the trade balance f and only f: ε - γ - ε M - γ M + > 0 Marshall-Lerner Robnson condton Same as before f γ γ M 0 Bénassy-Quéré - Internatonal Macroeconomcs Joan Robnson,

5 Implcatons Non-trval relatonshp between real exchange rate and trade balance Nomnal exchange-rate volatlty Real exchange rate dffers from terms of trade Bénassy-Quéré - Internatonal Macroeconomcs

6 Mcro-foundatons of ncomplete pass-through Standard supply-demand effect: If euro deprecates, the global demand for European goods ncreases, hence the prce of these goods ncreases n ; However no dscrmnaton between Europe and foregn countres. Olgopolstc competton Monopolstc competton Bénassy-Quéré - Internatonal Macroeconomcs

7 2. Olgopolstc competton Dornbusch 987, «Exchange rates and prces», AER, 77, Two types of producers home and foregn One homogenous prce, prce p on home market Lnear demand functon: Q d a bp Supply: Q s nq + nq Cournot competton: each frm takes sales of the others as gven roft: Home frm: π p w a bp n q n q Foregn frm: π p / e w a bp nq n q e: nomnal exchange rate No. of domestc currency unts n one foregn currency unt Bénassy-Quéré - Internatonal Macroeconomcs

8 Home frm: Foregn frm These two FOCs rewrte: Equlbrum prce π p π p e a bp n q n q b p w 0 a bp nq n q b p / e w 0 a bp nq n a bp nq n q q b q q + q b + q ew w We can then wrte q as a functon of p, w, ew: a bp nq n q + bw bew + q b p w n + n q a 2bp n bw bew + bw p w eb p / e w Smlarly, we can wrte q as a functon of p, w, ew: a bp n q + bew bw n q + q eb p / e w n + n q a 2bp n bew bw + bew Bénassy-Quéré - Internatonal Macroeconomcs

9 Equlbrum prce ctd Aggregate supply then wrtes: Q s nq+nq a 2bp + n bew bw + bw + n a 2bp + n bw bew + bew n Q s n + n n + n a 2bp + nbw + n bew n + n Q s Market equlbrum Q s Q d : n + n a 2bp + nbw + n bew n + n a bp n + n a 2bp + nbw + n bew n + n a bp 0 a n + n + bp + nbw + n bew 0 p a bn + nw + n N ew wth N n + n + rceavg cost+markup Bénassy-Quéré - Internatonal Macroeconomcs

10 Elastcty: Incomplete pass-through The extent of exchange-rate pass-through depends on: The relatve number of foregn frms who are ht by the shock Ther ntal markup p/ew: a hgher markup reduces the pass-through because frms can compress ther margns b: ths result s hghly dependent on the functonal form of the demand functon. dp n w N de Here, the utlty functon dsplay a prce elastcty that s an ncreasng functon of the prce level: Q d a bp dp de bp When the apprecates, Europeans see ther prces n $ ncrease, hence also the prce elastcty of the US demand ncreases, whch nctes them to reduce the prce hke. Why should ths be the case? Study a CES utlty functon. / / p e dqdqd dp / p n N ew p a < Bénassy-Quéré - Internatonal Macroeconomcs

11 3. Monopolstc competton Krugman 987, «rcng to market when the exchange rate changes», n S. Arndt & J. Rchardson eds., Real-fnancal lnkages among open economes, Cambrdge, Mass.: MIT ress. Mcro-foundatons of long-lved devatons from the law of one prce Can these devatons be optmal? rcng to market: dfferent prces on dfferent markets Varable prce-demand elastctes; Strategc nteractons; Composton effects: productvty, qualty; Dstrbuton costs; Intra-frm trade. Bénassy-Quéré - Internatonal Macroeconomcs

12 rcng to market under monopolstc competton Utlty Budget constrant: 0 d c Log LogC U > R d c p C 0 Consumers A contnuum of varetes 0 to 2 Lagrangan FOC: 0 R d c p d c Log R C LogC L 0 0 λ λ 0 p C c c L λ 0 C C L λ C p c Demand functon 2 Bénassy-Quéré - Internatonal Macroeconomcs

13 rcng to market under monopolstc competton 2 roducers: y l ; where y denotes output and l labor nput. Domestc demand: c ; foregn: x ; domestc prce: p ; export prce n foregn currency: q ; nomnal exchange rate: S nb of foregn currency unts n one domestc currency unt. roft : π p c + x W c + x wth: and FOCs: q S p q c C x C rce settng π 0 + Wp 0 p π 0 + Wq 0 q S p W q SW Markup on margnal cost, expressed n foregn currency Bénassy-Quéré - Internatonal Macroeconomcs

14 TM and pass-through p W q W S Denote by µ, µ the markup: If, then p q/s: law of one prce If <, then p > q/s: prcng-to-market µ, µ > If, constant, then complete pass-through: dp/pdw/w, dq/q dw/w+ds/s If, varable, then: dp/pdµ/µ +dw/w, dq/qdµ/µ+dw/w+ds/s Impact of a currency apprecaton ds/s+%: dp/p<% f dµ/µ<0 dµ d 2 dµ d µ Interpretaton: f a hgher prce nvolves sales beng more senstve to an addtonal prce ncrease, then the markup must dmnsh followng a cost-push shock: ncomplete pass-through. Bénassy-Quéré - Internatonal Macroeconomcs

15 Ex. lnear demand functon x α βq x l Elastcty of substtuton: roft: FOC π wth α, β > 0 and α > βq. q S α q + 2 β W SW 2 q x W S dx dq / / x q α βq α βq > s an ncreasng functon of q ass-through: dq q + α βws ds S 0 dq / q < ds / S < Bénassy-Quéré - Internatonal Macroeconomcs

16 Mcroeconomc foundatons of varable elastctes Competton effect Krugman, 987: Some exporters are unable to reduce ther markup when the exchange rate apprecates They ext the market, whch reduces competton Survvng exporters reap more market power, whch rases the extent of pass-through Composton effects: Extng exporters may be those wth lower productvty; survvng exporters thus have a hgher productvty, hence lower costs and prces: lower aggregate pass-through Extng exporters may be those wth lower qualty; survvng frms thus have hgher qualty and hgher prces: hgher aggregate pass-through Auer & Méltz, 2009 Dstrbuton costs Corsett and Dedola, 2005: Exportng a good may nvolve local dstrbuton costs nvoced n the local currency. In ths case, the unt cost for the exporter rses less than proportonally to hs exchange rate: ncomplete pass through. Dstrbuton costs + frm heterogenety Berman et al. 2009: lower pass-through for hghproductvty frms. Bénassy-Quéré - Internatonal Macroeconomcs

17 A model of ncomplete pass-through under monopolstc competton Atkeson, A. and A. Bursten, rcng-to-market, trade costs, and nternatonal relatve prces, AER 2008, 98:5, Two symmetrc countres,2 Each frm of a country produces a dstnct good n a specfc sector A lmted number of frms k n each sector j Consumer prce ndex n country : /η η j dj 0 Inverse demand functons: For each sector j of country : K j For each good jk of country : j j /η yj c q yj / ρ k ρ / ρ Bénassy-Quéré - Internatonal Macroeconomcs ρ >η > More substtutablty wthn each sector than between sectors Andrew Atkeson UCLA Arel Bursten UCLA 7

18 A model of ncomplete pass-through under monopolstc competton ctd Margnal cost: W frm-specfc productvty Optmal prce: ε W ε wth elastcty ε s + ρ s η functon of market share q 2K K q s 2 k k ρ ρ harmonc weghted average of ntra-sector and nter-sector elastctes Bénassy-Quéré - Internatonal Macroeconomcs

19 A model of ncomplete pass-through under monopolstc competton ctd Impact of a shock on W Optmal prce varaton wth and dε ds ds s + ρ η s s ρ + d η 2 ds ε dε ε + ε η ρ 2 dw W ds 2K ρ ρ ρ ρ ρ k ρ s d 2K k ρ 2 dε ε ρ d ε η ρ ρ s s ds s s 2 d Bénassy-Quéré - Internatonal Macroeconomcs

20 A model of ncomplete pass-through under monopolstc competton ctd We then have: d ε s ε η ρ ρ s d + dw W d dw Hence: wth Φ W Φ ε ε η ρ ρ s s < 0 Incomplete pass-through related to the fact that the frm s market share falls whenever ts prce rses; and the elastcty rses when the frm s market share declnes: ds s ρ s d and Implcaton: the extent of pass-through depends not only on the sector through ntra-sectoral elastcty ρ but also on the frm wthn each sector through ts market share s. dε ε η ε ρ s ds s Bénassy-Quéré - Internatonal Macroeconomcs

21 rcng to market: emprcal evdence Berman, N., Martn, h. And Th. Mayer, «How do dfferent exporters react to exchange rate changes?», QJE 202, 27, pp UV jt : unt value of exports of frm j to country at tme t; ~ ϕ jt : relatve productvty of frm j at tme t- Stablté des taux de change RER t : real exchange rate relatve to country at tme t Ψ t, µ j, ε jt ; tme fxed effects, frm destnaton fxed effect, resdual. French, annual data, Result: Followng a 0% exchange rate deprecaton, the average exporter ncreases ts export prce n euro by 0.8% so that the average pass-through s 92%»: 0-0.8/ Sgnfcant mpact of the nteracton term: less pass-through for more productve frms whch can compress ther margns than for less productve ones. 2