14.581 International Trade — Lecture 24: Trade Policy Theory (II)— 14.581 Week 13 Spring 2013 14.581 (Week 13) Trade Policy Theory (II) Spring 2013 1 / 27
Today’s Plan TOT Externality and Trade Agreements 1 Political-Economy Motives 2 Other Issues 3 14.581 (Week 13) Trade Policy Theory (II) Spring 2013 2 / 27
1. TOT Externality and Trade Agreements 14.581 (Week 13) Trade Policy Theory (II) Spring 2013 3 / 27
Basic Environment Like in previous lecture: All markets are perfectly competitive 1 There are no distortions 2 Governments only care about welfare 3 More speci…cally: 2 countries, c = 1 , 2 2 goods, i = 1 , 2 p c � p c 1 / p c 2 is relative price in country c p w � p w 1 / p w 2 is “world” (i.e. untaxed) relative price i ( p c , p w ) is demand of good i in country c d c y c i ( p c ) is supply of good i in country c 14.581 (Week 13) Trade Policy Theory (II) Spring 2013 4 / 27
Are Unilaterally Optimal Tari¤s Pareto-E¢cient? Following Bagwell and Staiger (1999), we introduce W c ( p c , p w ) � V c [ p c , R c ( p c ) + T c ( p c , p w )] Di¤erentiating the previous expression we obtain � � dp c � � ∂ p w �� � ∂ p w � dW c = dt c + W c W c + W c dt � c p c p w p w dt c ∂ t c ∂ t � c The slope of the iso-welfare curves can thus be expressed as � � � dt 1 � ∂ p w W 1 p w ∂ t 2 � � � � = (1) dt 2 dp 1 ∂ p w W 1 + W 1 dW 1 = 0 p w p 1 dt 1 ∂ t 1 � � � � � dt 1 � dp 2 ∂ p w W 2 + W 2 p w p 2 dt 2 ∂ t 2 � � = (2) dt 2 ∂ p w W 2 dW 2 = 0 p w ∂ t 1 14.581 (Week 13) Trade Policy Theory (II) Spring 2013 5 / 27
Are Unilaterally Optimal Tari¤s Pareto-E¢cient? Proposition 2 If countries are “large,” unilateral tari¤s are not Pareto-e¢cient. Proof: By de…nition, unilateral (Nash) tari¤s satisfy 1 � dp c � � ∂ p w � W c + W c = 0, p c p w dt c ∂ t c � � � � ∂ p w ∂ p w If and 6 = 0, 1+ ( 1 ) and ( 2 ) ) 2 ∂ t 1 ∂ t 2 � dt 1 � � dt 1 � = + ∞ 6 = 0 = dt 2 dt 2 dW 1 = 0 dW 2 = 0 Proposition 2 directly derives from 2 and the fact that Pareto-e¢ciency 3 � � � � dt 1 dt 1 requires dW 1 = 0 = dt 2 dt 2 dW 2 = 0 14.581 (Week 13) Trade Policy Theory (II) Spring 2013 6 / 27
Are Unilaterally Optimal Tari¤s Pareto-E¢cient? Graphical analysis (Johnson 1953-54) 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 14.581 (Week 13) Trade Policy Theory (II) Spring 2013 7 / 27
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 were to set their tari¤s ignoring their ability to a¤ect world prices: W 1 p 1 = W 2 p 2 = 0 Then Equations ( 1 ) and ( 2 ) immediately imply � dt 1 � � ∂ p w �� � ∂ p w � � dt 1 � = = dt 2 ∂ t 2 ∂ t 1 dt 2 dW 1 = 0 dW 1 = 0 Intuition: In this case, both countries act like small open economies As a result, t 1 = t 2 = 0, which is e¢cient from a world standpoint Question: How much does this rely on the fact that governments maximize welfare? 14.581 (Week 13) Trade Policy Theory (II) Spring 2013 8 / 27
2. Political-Economy Approach 14.581 (Week 13) Trade Policy Theory (II) Spring 2013 9 / 27
Economic Environment Endowment economy We consider a simpli…ed version of Grossman and Helpman (1994) Endowment rather than speci…c-factor model To abstract from TOT considerations, GH consider a small open economy If governments were welfare-maximizing, trade taxes would be zero There are n + 1 goods, i = 0 , 1 , ..., n , produced under perfect competition good 0 is the numeraire with domestic and world price equal to 1 p w and p i denote the world and domestic price of good i , respectively i Individuals are endowed with 1 unit of good 0 + 1 unit of another good i 6 = 0 we refer to an individual endowed with good i as an i -individual α i denote the share of i -individuals in the population total number of individuals is normalized to 1 14.581 (Week 13) Trade Policy Theory (II) Spring 2013 10 / 27
Economic Environment (Cont.) Quasi-linear preferences All individuals have the same quasi-linear preferences U = x 0 + ∑ n i = 1 u i ( x i ) Indirect utility function of i -individual is therefore given by V i ( p ) = 1 + p i + t ( p ) + s ( p ) where: t ( p ) � government’s transfer [to be speci…ed] ∑ n i = 1 u i ( d i ( p i )) � ∑ n s ( p ) � i = 1 p i d i ( p i ) Comment: Given quasi-linear preferences, this is de facto a partial equilibrium model 14.581 (Week 13) Trade Policy Theory (II) Spring 2013 11 / 27
Political Environment Policy instruments For all goods i = 1 , ..., n , the government can impose an ad-valorem import tari¤/export subsidy t i p i = ( 1 + t i ) p w i We treat p � ( p i ) i = 1 ,..., n as the policy variables of our government The associated government revenues are given by t ( p ) = ∑ n i = 1 ( p i � p w i ) m i ( p i ) = ∑ n i = 1 ( p i � p w i ) [ d i ( p i ) � α i ] Revenues are uniformly distributed to the population so that t ( p ) is also equal to the government’s transfer, as assumed before 14.581 (Week 13) Trade Policy Theory (II) Spring 2013 12 / 27
Political Environment Lobbies An exogenous set L of sectors/individuals is politically organized we refer to a group of agents that is politically organized as a lobby Each lobby i chooses a schedule of contribution C i ( � ) : ( R + ) n ! R + in order to maximize the total welfare of its members net of the contribution � p 0 � � p 0 � C i ( � ) α i V i � C i max p 0 = arg max subject to: G ( p ) p where G ( � ) is the objective function of the government [to be speci…ed] 14.581 (Week 13) Trade Policy Theory (II) Spring 2013 13 / 27
Political Environment Government Conditional on the contribution schedules announced by the lobbies, government chooses the vector of domestic prices in order to maximize a weighted sum of contributions and social welfare G ( p ) � ∑ i 2 L C i ( p ) + aW ( p ) max p where W ( p ) = ∑ n i = 1 α i V i ( p ) and a � 0 Comments: GH (1994) model has the structure of common agency problem Multiple principals � lobbies; one agent � government We can use Bernheim and Whinston’s (1986) results on menu auctions 14.581 (Week 13) Trade Policy Theory (II) Spring 2013 14 / 27
Equilibrium Contributions n� i 2 L , p 0 o � C 0 We denote by the SPNE of the previous game i we restrict ourselves to interior equilibria with di¤erentiable equilibrium contribution schedules whenever we say “in any SPNE”, we really mean “in any interior SPNE where C 0 is di¤erentiable” Lemma 1 In any SPNE, contribution schedules are locally truthful � p 0 � � p 0 � r C 0 = α i r V i i Proof: � p 0 � + a r W � p 0 � = 0 p 0 optimal for the government ) ∑ i 2 L r C 0 1 i C 0 i ( � ) optimal for lobby i ) 2 � p 0 � � r C i � p 0 � + ∑ i 0 2 L r C 0 � p 0 � + a r W � p 0 � = 0 α i r V i � p 0 � = α i r V i � p 0 � i 0 1+2 ) r C 0 3 i 14.581 (Week 13) Trade Policy Theory (II) Spring 2013 15 / 27
Equilibrium Trade Policies Lemma 2 In any SPNE, domestic prices satisfy � p 0 � ∑ n i = 1 α i ( I i + a ) r V i = 0 , where I i = 1 if i is politically organized and I i = 0 otherwise Proof: � p 0 � + a r W � p 0 � = 0 p 0 optimal for the government ) ∑ i 2 L r C 0 1 � p 0 � + a r W � p 0 � = 0 i 1 + Lemma 1 ) ∑ i 2 L α i r V i 2 � p 0 � Lemma 2 directly derives from this observation and the de…nition of W 3 Comment: In GH (1994), everything is as if governments were maximizing a social welfare function that weighs di¤erent members of society di¤erently 14.581 (Week 13) Trade Policy Theory (II) Spring 2013 16 / 27
Equilibrium Trade Policies (Cont.) Proposition 2 In any SPNE, trade policies satisfy ! t 0 z 0 = I i � α L i i for i = 1 , ..., n, (3) 1 + t 0 e 0 a + α L i i � � where α L � ∑ i 0 2 L α i 0 , z 0 i � α i / m i , and e 0 p 0 / d ln p 0 i � d ln m i i Proof: � p 0 � ) Roy’s identity + de…nition of V i 1 ∂ V i 0 � p 0 � � � m 0 � � p 0 i � p w p 0 = ( δ i 0 i � α i ) + i i ∂ p i where δ ii 0 = 1 if i = i 0 and δ ii 0 = 0 otherwise 1 + Lemma 2 ) for all i 0 = 1 , ..., n , 2 h � � m 0 � �i ∑ n p 0 i � p w p 0 i 0 = 1 α i 0 ( I i 0 + a ) δ i 0 i � α i + = 0 i i 2 + de…nition of α L � ∑ i 0 2 L α i 0 ) 3 � � m 0 � � p 0 i � p w p 0 ( I i � α L ) α i + ( α L + a ) = 0 i i 14.581 (Week 13) Trade Policy Theory (II) Spring 2013 17 / 27
Equilibrium Trade Policies (Cont.) Proof (Cont.): � � 4. 3 + t 0 p 0 i � p w / p w i = ) i i ! ! � � p 0 � z i m i = I i � α L α i = I i � α L i 0 t 0 i m 0 � � i m 0 � � � p w p 0 p w p 0 a + α L a + α L i i 0 5. Equation ( 3 ) directly derives from 4 and the de…nition of z 0 i and e 0 i 14.581 (Week 13) Trade Policy Theory (II) Spring 2013 18 / 27
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