4.58 International Trade Class notes on 5/6/03 Trade Policy Literature Key questions:. Why are countries protectionist? Can protectionism ever be optimal? Can e explain ho trade policies vary across countries, industries, and time?. Ho should trade agreements be designed? Can e explain the main institutional features of actual trade agreements (e.g. WTO, NAFTA, EU)? In order to shed light on these questions, one needs to take a stand on:. Economic environment: What is the market structure? Are there distortions, e.g. unemployment or pollution?. Political environment: What is the objective function that governments aim to maximize, e.g. social elfare, elfare of the median voter, political support? What are the trade policy instruments, e.g. import tari s, quotas, product standards? Are trade policy instruments the only instruments available? 3. Constraints on the set of feasible contracts: Do trade agreements need to be self-enforcing? Ho costly is it "to complete contracts? In this Lecture e ill restrict ourselves to environments such that:. All markets are perfectly competitive. There are no distortions 3. Governments only care about elfare Only motive for trade protection is price manipulation Consumers and rms are price-takers on orld markets Governments internalize that exports and imports a ect prices We ill be focusing on three questions:. Ho should trade taxes vary across countries and industries?. Quantitatively ho important are the gains from such manipulation? 3. What is the rationale for trade agreements in this environment? The notes are based on lecture slides ith inclusion of important insights emphasized during the class.
A First Look at Unilaterally Optimal Tari s. Economic Environment Consider a orld economy ith countries, c = ; There are to goods, i = ;, both produced under perfect competition good is used as the numeraire, p = Notations: p c p c =p c is relative price in country c p p =p is orld (i.e. untaxed) relative price d c i (pc ; p ) is demand of good i in country c yi c (pc ) is supply of good i in country c Country () is a natural importer of good (): m p ; p d (p ; p ) y p > 0 m p ; p d (p ; p ) y p > 0 x p ; p y(p ) d p ; p > 0 x p ; p y (p ) d p ; p > 0 Trade is balanced: p m p ; p = x p ; p m p ; p = p x p ; p Market clearing for good requires: x p ; p = m p ; p (). Political Environment.. Policy instruments Both governments can impose an ad-valorem tari t c on their imports p c c = ( + t c ) p c c = p c p c Tari s create a edge beteen the orld and local prices hich implies p = + t p () p = p = + t (3)
Comments: If the only taxes are import tari s, then local prices faced by consumers and producers are the same, as implicitly assumed in our previous slides Equations ()-(3) implicitly de ne p p t ; t and p c p c (t c ; p ).. Government s objective function Both governments are elfare-maximizer. They simultaneously set t c in order to maximize utility of representative agent here: c max V c (p c ; I c ) V [p c ; R c (p c ) + T c (p c ; p )] (4) t c R c (p c ) max y fp c y + p c y jy feasibleg p p m T c (p c ; p ) t c p c mc c (p c ; p ) = p =p p ; p if = ; p c m p ; p ; p p if c = satisfy Equations () (3)..3 Unilaterally Optimal Tari s Proposition For both countries, unilaterally optimal (Nash) tari s satisfy t c d ln x c =, here " c " c d ln p Proof:. For expositional purposes e focus on country. FOC )! p dp dr dp + dt dp dt V V I. Roy s identity ) V p V = I dp @p dm p ; p + dt m @t p ; p + t p dt d (p ; p ) 3. Perfect competition ) dr = y dp (p ; p ) d ln m (p ;p ) 4. ++3 ) t @ ln p = @t = dt 5. 4 + market clearing, m p ; p = x p ; p ) t = =" Ho Should Tari s Vary Across Countries (and Industries)? = 0 3
Proposition o ers a simple theory of tari formation: tari s inverse of the elasticity of foreign export supply this is true hether or not the other government is imposing its Nash tari though other government s tari does a ect elasticity of foreign export supply In the case of a small open economy, @p @t = 0 ) " = + a small open economy never has an incentive to impose a tari Import tari s are intimately related to countries market poer it is countries ability to improve their terms-of-trade that lead to strictly positive tari s Potential concerns about Proposition as a positive theory:. Do e really believe that governments maximize elfare?. Ho many countries are large enough to a ect their terms-of-trade? 3. Do trade negotiators really care about their terms-of-trade? 3 The Primal Approach So far e have focused on a speci c policy instrument: import tari s It is often easier to proceed in to steps:. Solve for the optimal allocation assuming that governments can directly choose output and consumption. Sho ho that allocation can be implemented using trade taxes Formally, the planning problem of country can be expressed as: max U m + y; m + y m ;m ;y ;y subject to: p m m + m = 0 F y; y 0 st constraint Trade balance; nd constraintppf p m inverse of country s export supply curve, i.e., orld price at hich country is illing to export m units of good to country 4
3. Optimal Wedges FOC associated ith m imply Intuition: U = U dp p + m dm = Country has monopsony poer MC of imports p + price increase infra-marginal units m dp dm At the optimum, there is a edge beteen MRS and orld price U = p d ln p U + d ln m The more elastic orld prices are, the bigger the edge is 3. Implementation In a competitive equilibrium, U c =U c domestic price in country d ln p d ln m so optimum can be implemented by creating a edge of size + beteen the domestic price and the orld price To natural candidates: Import tari t d ln p U Export tax equal to = +" () = p = ( Many other possible instruments: U = = () = p ( + t ) d ln m " ) U optimum U optimum )) Any combination of import tari s and export taxes s.t. ( + t ) = ( ) = d ln p + d ln m Identical consumption and production taxes Quantitative restrictions 5
3.3 Foreign Export Supply versus Foreign Import Demand Same result applies if e focus on country s import demand curve Let p~ m inverse of country s import demand curve p () and p~ satisfy p m (p ) = m (p ) ( ) The elasticities of foreign export supply, " d ln m d ln p (= d ln p ) and import demand, d ln(m ) d ln p (= ) thus satisfy + d ln p~ =d ln m " =. Using the same logic as before, one can sho that U p = U (d ln p~ =d ln m ) Thus optimal export tax should be equal to 3.4 Beyond To-ness d ln p~ ~ = = = = d ln m. + " =d ln m, To-good model is simple because only one relative price to keep track of Ho do the previous insights generalize to many goods? If p i only depends on m i, then results trivially extend (e.g. quasilinear preferences abroad + speci c factor model) But in general, one ould need to take into account that orld price of good i may also depend on imports of other goods (Dixit 985, Bond 990) In such situations, export subsidies may be optimal (Feenstra 986) A simple case that can be ork out analytically: Additive separability (natural in macro context)+ endoment economy; see Costinot, Lorenzoni, and Werning (03) 4 Quantitative Issues 4. Back to Armington Model The simplest place to start to get a sense of the quantitative importance of terms-of-trade motive is to go back to Armington model 6
In line ith previous analysis assume that: there are only to countries, and country is endoed ith e units of good (so that it is still a natural importer of good ) country is endoed ith e units of good (so that it is still a natural importer of good ) Representative agents have CES utility ith elasticity : c c U = (d ) + (d c ) Trade beteen and is subject to iceberg trade costs 4. Unilaterally Optimal Tari Armington model ith to countries is special case of models studied before. So e only need to compute elasticity of country s export supply Given endoment and CES assumptions e have p e (p ) e x (p ) = e = + (p ) + (p ) Country s export supply is thus given by d ( " ln x ( ) p ) = = d ln p + (p ) p d (p ) Let p = e ( ) +(p ) denote country s share of expenditure on its on good Using this notation, the optimal tari in country is given by t = ( ) 4.3 A First Look at Numbers Previous formula o ers simple ay to quantify optimal tari : From gravity equation e kno that ' 5 From most countries, ROW is almost under autarky, ' Thus previous formula suggests t ' 0% 7
Next e ill go through quantitative results from Costinot and Rodriguez- Clare (03) in more general gravity models Results suggest that this is not a bad approximation See also Ossa (0a, 0b) Analytically, one can sho that previous formula also applies to gravity models featuring monopolistic competition ith homogeneous rms à la Krugman (980); see Gros (987) and Helpman and Krugman (989) Compared to analysis in ACR, e only have to countries, no rm heterogeneity, no tari revenues in country. Not clear that equivalence ould still hold ithout these strong assumptions 4.3. What Do Unilaterally Optimal Tari s Look Like? Costinot and Rodriguez-Clare (03) Courtesy of Arnaud Costinot and Andrés Rodriguez-Clare. Used ith permission. 4.3. What Are the Welfare Consequences of 40% a Tari? Costinot and Rodriguez-Clare (03) 8
Courtesy of Arnaud Costinot and Andrés Rodriguez-Clare. Used ith permission. 4.3.3 Ho Important is Monopolistic Competition? Costinot and Rodriguez-Clare (03) Courtesy of Arnaud Costinot and Andrés Rodriguez-Clare. Used ith permission. 4.4 Summary of Welfare E ects in Gravity Models Welfare gains from unilateral import tari s over surprisingly large range In one-sector Armington model, unilaterally optimal tari ' =trade elasticity Trade elasticity of 5 implies optimal tari s of 0% around the orld It takes import tari s to be as high as 50% to get back to the elfare levels observed under free trade Welfare e ects of large unilateral tari s on other countries minimal 9
6 6 5 Rationale for Trade Agreements 5. Are Unilaterally Optimal Tari s Pareto-E cient? Folloing Bagell and Staiger (999), e introduce W c (p c ; p ) V c [p c ; R c (p c ) + T c (p c ; p )] Di erentiating the previous expression e obtain dp dw c = W c c + W c @ p p c c p @t c dt c + W c @p c p dt @t c dt The slope of the iso-elfare curves can thus be expressed as dt Wp @p @t = dt (5) =0 W dp dw p dt + W @p p @t dt W dp + W @p p dt p @t dt = (6) @p dw =0 Wp Proposition If countries are large, unilateral tari s are not Paretoe cient. Proof:. By de nition, unilateral (Nash) tari s satisfy dp Wp c c @p c dt c + W cp @t c = 0,. If @p @t and @p @t = 0, + (5) and (6) ) dt dt dt = + = 0 = dt dw =0 @t dw =0 3. Proposition directly derives from and the fact that Pareto-e ciency dt requires = dt dt dw dt =0 Graphical analysis (Johnson 953-54) dw =0 0
N corresponds to the unilateral (Nash) tari s E-E corresponds to the contract curve If countries are too asymmetric, free trade may not be on contract curve 5. What is the Source of the Ine ciency? The only source of the ine ciency is the terms-of-trade externality Formally, suppose that governments ere to set their tari s ignoring their ability to a ect orld prices: W p = W p = 0 Then Equations (5) and (6) immediately imply dt @p @p dt = = dt dw =0 @t @t dt Intuition: dw =0 In this case, both countries act like small open economies As a result, t = t = 0, hich is e cient from a orld standpoint Question for next lecture: Ho much does this rely on the fact that governments maximize elfare?
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