14.581 International Trade — Lecture 23: Trade Policy Theory (I)— 14.581 Week 13 Spring 2013 14.581 (Week 13) Trade Policy Theory (I) Spring 2013 1 / 29
Trade Policy Literature A Brief Overview Key questions : Why are countries protectionist? Can protectionism ever be “optimal”? Can 1 we explain how trade policies vary across countries, industries, and time? How should trade agreements be designed? Can we explain the main 2 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, 1 e.g. unemployment or pollution? Political environment: What is the objective function that governments aim 2 to maximize, e.g. social welfare, welfare 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? Constraints on the set of feasible contracts: Do trade agreements need to 3 be self-enforcing? How costly is it "to complete” contracts? 14.581 (Week 13) Trade Policy Theory (I) Spring 2013 2 / 29
This Lecture We will restrict ourselves to environments such that: All markets are perfectly competitive 1 There are no distortions 2 Governments only care about welfare 3 Only motive for trade protection is price manipulation Consumers and …rms are price-takers on world markets Governments internalize that exports and imports a¤ect prices We will be focusing on three questions: How should trade taxes vary across countries and industries? 1 Quantitatively how important are the gains from such manipulation? 2 What is the rationale for trade agreements in this environment? 3 14.581 (Week 13) Trade Policy Theory (I) Spring 2013 3 / 29
1. A First Look at Unilaterally Optimal Tari¤s 14.581 (Week 13) Trade Policy Theory (I) Spring 2013 4 / 29
Economic Environment Consider a world economy with 2 countries, c = 1 , 2 There are two goods, i = 1 , 2, both produced under perfect competition good 2 is used as the numeraire, p w 2 = 1 Notations: 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 (I) Spring 2013 5 / 29
Economic Environment (Cont.) Country 1 (2) is a natural importer of good 1 (2): � p 1 , p w � � p 1 � 1 ( p 1 , p w ) � y 1 m 1 d 1 � > 0 1 1 � p 2 , p w � � p 2 � 2 ( p 2 , p w ) � y 2 m 2 d 2 � > 0 2 2 � p 1 , p w � � p 1 , p w � x 1 y 1 2 ( p 1 ) � d 1 � > 0 2 2 � p 2 , p w � � p 2 , p w � x 2 y 2 1 ( p 2 ) � d 2 � > 0 1 1 Trade is balanced: � p 1 , p w � � p 1 , p w � p w m 1 x 1 = 1 2 � p 2 , p w � � p 2 , p w � p w x 2 m 2 = 2 1 Market clearing for good 2 requires: � p 1 , p w � � p 2 , p w � x 1 = m 2 (1) 2 2 14.581 (Week 13) Trade Policy Theory (I) Spring 2013 6 / 29
Political Environment Policy instruments Both governments can impose an ad-valorem tari¤ t c on their imports p c ( 1 + t c ) p w = c c p c p w = � c � c Tari¤s create a wedge between the world and local prices which implies � 1 + t 1 � p 1 p w = (2) � 1 + t 2 � p w / p 2 = (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 ( 1 ) - ( 3 ) implicitly de…ne p w � p w � t 1 , t 2 � and p c � p c ( t c , p w ) 14.581 (Week 13) Trade Policy Theory (I) Spring 2013 7 / 29
Political Environment Government’s objective function Both governments are welfare-maximizer. They simultaneously set t c in order to maximize utility of representative agent t c V c ( p c , I c ) � V c [ p c , R c ( p c ) + T c ( p c , p w )] max (4) where: R c ( p c ) � max y f p c 1 y 1 + p c 2 y 2 j y feasible g � � p 1 � p w � � p 1 , p w � m 1 if c = 1 T c ( p c , p w ) � t c p w c ( p c , p w ) = c m c � � � p 2 , p w � 1 p w / p 2 � 1 m 2 if c = 2 2 p 1 , p 2 , p w satisfy Equations ( 1 ) � ( 3 ) 14.581 (Week 13) Trade Policy Theory (I) Spring 2013 8 / 29
Unilaterally Optimal Tari¤s Proposition 1 For both countries, unilaterally optimal (Nash) tari¤s satisfy ε � c , where ε � c � d ln x � c 1 t c = d ln p w Proof: For expositional purposes we focus on country 1. FOC ) 1 ! � dp 1 � � dR 1 � � dp 1 � V 1 p + V 1 dt 1 dp 1 dt 1 I � p 1 , p w � � dp 1 � � p 1 , p w � + t 1 p w dm 1 dt 1 � ∂ p w m 1 1 + = 0 1 ∂ t 1 dt 1 Roy’s identity ) V 1 1 ( p 1 , p w ) I = � d 1 p 2 V 1 Perfect competition ) dR 1 1 ( p 1 , p w ) dp 1 = y 1 3 � � � � d ln m 1 1 ( p 1 , p w ) ∂ ln p w 1+2+3 ) t 1 = / 4 ∂ t 1 dt 1 � p 1 , p w � = x 2 � p 2 , p w � ) t 1 = 1 / ε 2 4 + market clearing, m 1 5 1 1 14.581 (Week 13) Trade Policy Theory (I) Spring 2013 9 / 29
How Should Tari¤s Vary Across Countries (and Industries)? Proposition 1 o¤ers a simple theory of tari¤ formation: tari¤s � inverse of the elasticity of foreign export supply this is true whether 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 w ∂ t 1 = 0 ) ε 2 = + ∞ a small open economy never has an incentive to impose a tari¤ Import tari¤s are intimately related to countries’ market power it is countries’ ability to improve their terms-of-trade that lead to strictly positive tari¤s Potential concerns about Proposition 1 as a positive theory: Do we really believe that governments maximize welfare? 1 How many countries are “large” enough to a¤ect their terms-of-trade? 2 Do trade negotiators really care about their terms-of-trade? 3 14.581 (Week 13) Trade Policy Theory (I) Spring 2013 10 / 29
2. The Primal Approach 14.581 (Week 13) Trade Policy Theory (I) Spring 2013 11 / 29
The Primal Approach So far we have focused on a speci…c policy instrument: import tari¤s It is often easier to proceed in two steps: Solve for the optimal allocation assuming that governments can directly 1 choose output and consumption Show how that allocation can be implemented using trade taxes 2 Formally, the planning problem of country 1 can be expressed as: U 1 � � m 1 1 + y 1 1 , m 1 2 + y 1 max 2 m 1 1 , m 1 2 , y 1 1 , y 1 2 subject to: p w � � m 1 m 1 1 + m 1 = 0 1 2 � � y 1 1 , y 1 F � 0 2 1st constraint � Trade balance; 2nd constraint � PPF p w � � � inverse of country’s 2 export supply curve, i.e., world price at m 1 1 which country 2 is willing to export m 1 1 units of good 1 to country 1 14.581 (Week 13) Trade Policy Theory (I) Spring 2013 12 / 29
The Primal Approach Optimal Wedges FOC associated with m 1 imply ! dp w p w + m 1 U 1 = λ 1 1 dm 1 1 U 1 = λ 2 Intuition: Country 1 has monopsony power dp w MC of imports � p w + price increase infra-marginal units m 1 1 dm 1 1 At the optimum, there is a “wedge” between MRS and world price ! U 1 1 + d ln p w 1 = p w 1 U 1 d ln m 1 2 1 The more elastic world prices are, the bigger the wedge is 14.581 (Week 13) Trade Policy Theory (I) Spring 2013 13 / 29
The Primal Approach Implementation In a competitive equilibrium, U c 1 / U c 2 � domestic price in country 1 so optimum can be implemented by creating a wedge of size 1 + d ln p w 1 d ln m 1 1 between the domestic price and the world price Two natural candidates: � U 1 � Import tari¤ t 1 = d ln p w optimum = p w ( 1 + t 1 ) ) 1 = 1 ε 2 ( ) 1 1 d ln m 1 U 1 � U 1 2 � optimum = p w / ( 1 � τ 1 ) ) 1 Export tax equal to τ 1 = 1 + ε 2 ( ) 1 U 1 2 Many other possible instruments: Any combination of import tari¤s and export taxes s.t. ( 1 + t 1 ) / ( 1 � τ 1 ) = 1 + d ln p w 1 d ln m 1 1 Identical consumption and production taxes Quantitative restrictions 14.581 (Week 13) Trade Policy Theory (I) Spring 2013 14 / 29
The Primal Approach Foreign Export Supply versus Foreign Import Demand Same result applies if we focus on country 2’s import demand curve p w � � � inverse of country 2’s import demand curve m 1 Let ˜ 2 p w satisfy p w � � m 2 � = m 2 p w ( � ) and ˜ 1 ( p w ) 2 ( p w ) d ln ( � m 2 1 ) The elasticities of foreign export supply, ε 2 � 1 (= 1 ) , and d ln p w d ln p w / d ln m 1 d ln ( m 2 2 ) import demand, η 2 � 2 ) thus satisfy 1 + ε 2 = η 2 . 1 d ln p w (= p w / d ln m 1 d ln ˜ Using the same logic as before, one can show that U 1 p w 1 � � = p w / d ln m 1 U 1 1 � d ln ˜ 2 2 Thus optimal export tax should be equal to p w τ 1 = d ln ˜ = 1 1 ˜ η 2 = 1 + ε 2 = τ 1 . d ln m 1 2 14.581 (Week 13) Trade Policy Theory (I) Spring 2013 15 / 29
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