Part C: Two open economies The Vienna Institute for International Economic Studies - wiiw April 13, 2017
Assumptions and autarkic equilibria Absolute and comparative advantages 1 Two economies endowed with labour l c 2 Productivity levels given by ϕ c i 3 Countries differ in relative productivity levels, i.e. for example ϕ 1 1 ϕ 1 < ϕ2 1 2 ϕ 2 a1 1 2 a 1 > a2 1 2 a 2 2 1 Country 1 is relatively more productive in sector 2 2 Relative price of good 1 in country 1 is relatively larger a 1 1 > a2 1 p1 1 > p1 2 a 1 2 a 2 2 p 1 2 p 2 2 4 A country can have absolute productivity advantage in both sectors, i.e. ϕ r i > ϕ s i for i = 1, 2
Absolute and comparative advantages Numerical example: Absolute and comparative advantages 1 Example 1: Assume that ϕ 1 1 = 2, ϕ1 2 = 4, ϕ2 1 = 5 and ϕ2 2 = 6. 1 Country 2 has absolute advantage in both sectors as ϕ 1 i < ϕ2 i a1 i > a2 i for all i. 2 Country 1 has comparative advantage in sector 2 as 2 Example 2: ϕ 1 1 ϕ 1 2 = 2 4 < ϕ2 1 ϕ 2 = 5 2 6 a1 1 a 1 = 0.50 2 0.25 > a2 1 a 2 = 0.20 2 0.17 Assume that ϕ 1 1 = 1, ϕ1 2 = 3, ϕ2 1 = 4 and ϕ2 2 = 2. 1 Country 2 has absolute advantage in sector 1 as: ϕ 1 1 < ϕ2 1 a1 1 > a2 1 Country 1 as absolute advantage in sector 2 as: ϕ 1 2 > ϕ2 2 a1 2 < a2 2 2 Country 1 has comparative advantage in sector 2 as ϕ 1 1 ϕ 1 2 = 1 3 < ϕ2 1 ϕ 2 = 4 2 2 a1 1 a 1 = 1.00 2 0.33 > a2 1 a 2 = 0.25 2 0.50
Equilibria in both economies under autarky x 1 2 x 2 2 ϕ 1 2 l1 ϕ 2 2 l2 ϕ 1 1 l1 x 1 1 ϕ 2 1 l2 x 2 1
Characteristics of autarkic equilibrium 1 Relative productivity determines relative prices ϕ 1 1 ϕ 1 < ϕ2 1 2 ϕ 2 a1 l1 2 a 1 > a2 l1 l2 a 2 l2 1 p1($ ) 1 p 1($1 ) 2 2 > p2($ ) 1 p 2($2 ) 2 2 Relative prices determine relative consumption patterns p 1($1 ) 1 p 1($1 ) 2 2 > p2($ ) 1 f 1 1 p 2($2 ) f 1 2 2 < f 2 1 f 2 2 3 Relative consumption patterns determine relative production f1 1 f2 1 < f 2 1 f 2 2 x1 1 x 1 < x2 1 2 x 2 2
Numerical example Consider the Ricardian model of international trade with 2 countries - Home (H) and Foreign (F ) - and 2 sectors - Cloth (C) and Wine (W ). The only factor of production is labour l c and endowment is l 1 = 40 and l 2 = 100. Productivity levels are given by: ϕ H C = 1; ϕh W = 0.5; ϕ F C = 0.25; ϕf W = 1 3. Wage rates in each country are given by wh = 4 and w F = 1, respectively. Assume that the utility function is U c = x 0.45 C x0.55 W. Let a c l,i with i = C, W and c = H, F represent the unit labour requirements. The input coefficients are as follows: a H l,c a H l,w = 1 2 and a F l,c a F l,w = 4 3 1 Structure of absolute and comparative advantages: 1 Country H has absolute advantages in both sectors 2 Country H has comparative advantage in cloth, country F in wine 2 Autarkic equilibria: Home Foreign Nominal income y c 160 100 Prices p c C 4 4 p c W 8 3 Consumption/Production x c C 18 11.3 x c W 11 18.3 Utility level U c 13.7 14.7
Comparative advantages and mutual gains from trade Dynamics: 1 Country 1 has comparative advantage in production of good 2 1 Country 1 consumers would start buying goods 1 in country 2 2 Country 1 producers would start selling goods 2 in country 2 2 Country 2 has comparative advantage in production of good 1 1 Country 2 consumers would start buying goods 2 in country 1 2 Country 2 producers would start selling goods 1 in country 1 3 Assuming that there is appropriate exchange rate or wage adjustments 1 Technically model has to be solved under BoP constraint (BoP = 0)
Equilibrium under free trade x 1 2 x 2 2 ϕ 1 2 l1 (0, x 1 2 ) (f 1 1, f 1 2 ) ϕ 2 2 l2 ϕ 1 1 l1 x 1 1 ϕ 2 1 l2 x 2 1
Numerical example (contd.) 3 Specialisation patterns Home Foreign Production q c C 40 0 q c W 0 33.3 Wages (w F = 1) 2.045 1 Prices p C 2.05 2.05 p W 3.00 3.00 Consumption f c C 18 22 f c W 15 18.3 Trade (quantities) e c C 22-22 e c W -15 15 4 Gains from trade Home Foreign Utility U c 16.3 19.9
Characteristics of Ricardian free trade equilibrium: 1 Both countries specialise in good for which they have comparative advantage 2 Countries export good for which they have comparative advantage and import the other good 3 Relative free trade price is in between autarky prices: p 1 1 p 1 2 > p trade pfree 1 Free trade 2 > p2 1 p 2 2 (Note: Absolute price levels might require bilateral exchange rate or nominal wage rate adjustments) 4 Balance of payment is balanced; imports of one country match exports of the other country (both in quantitative and value terms) 5 Consumption patterns converge (under assumption of same preferences) 6 Both countries gain from trade 1 Achieve higher utility levels 2 Real income level increases 7 Also holds when a country has absolute advantages in both sectors!
1 Country size 1 If a country is very large, the other country though fully specialising cannot cover all demand in that product 2 Large country not completely specialised; determines world price 3 Small country has all gains from trade 4 Large country has no gains from trade 2 Biased demand 1 If a country s consumption is heavily biased towards the industry for which it has comparative advantage (in which it specialises) 2 Other country cannot completely specialise (as has still to produce both products to satisfy demand) 3 This other country determines relative world prices (equal to its autarky relative prices) 4 Country with biased preferences has all gains from trade 5 Other country do not gain from trade
World production frontier x 2 Country 2 Country 1 x 1
Graphics: 1 Difference in country sizes 2 Biased preferences
Deriving relative demand and supply curves Calculating the equilibrium (Cobb-Douglas) (assuming that relative world prices are in between autarky prices, i.e. no special cases) Relative demand x 1 = α ( ) 1 1 p1 = α ( ) 1 p2 x 2 α 2 p 2 α 2 p 1 Country 1 (2) specialises in good 2 (1) and using FE condition Reformulating using ϕ c i = 1/ac i ϕ 2 1l 2 ϕ 1 2 l1 = α 1 α 2 w 1 a 1 2 w 2 a 2 1 ϕ 2 1l 2 ϕ 1 = (1/a2 1)l 2 2 l1 (1/a 1 = a1 2l 2 2 )l1 a 2 = α 1 w 1 a 1 2 1 }{{ l1 α 2 w } 2 a 2 α 2l 2 1 α 1 l }{{} 1 = w1 w 2 Relative supply Relative demand
Adjustments... 1 If w 1 is fixed (numeraire) and E given (e.g. E = 1), this defines level of w 2 α 1 l 1 α 2 l 2 w1 = w 2 2 Alternatively, if w c are fixed in NCU, this defines exchange rate E α 1 l 1 α 2 l 2 w1 = Ew 2
Assume that w 2 is such fixed allows for interpretation as BoP equilibrium α 1 w 1 l 1 = α 2 w 2 l 2 or (noting that country 1 [2] specialises in industry 2 [1]) Value of imports 1 = Value of imports 2 Under the FE-assumption it holds that w c l c = y c (i.e. GDP) α 1 y 1 = (1 α 1 )y 2 = y 2 α 1 y 2 α 1 (y 1 + y 2 ) = y 2 α 1 y = y 2 World demand for goods produced in country 2 equals income (GDP) of country 2.
Numerical example (contd.) 1 Calculate relative wages: According to formula (and noting that country F specializes in Wine w H = α C l F α W l H wf = 0.45 100 0.55 40 1 = 2.045 Using these equilibrium wage rates, the world prices follow: p C = a H lc wh = 1 2.045 = 2.045 and p W = a F lw wf = 3 1 = 3.000
World production frontier x 2 Country 2 Country 1 World indifference curve Free trade relative price p 1 p 2 x 1
Relative supply and demand curves (in Ricardo model with 2 countries) p 1 p 2 a 1 l1 a 2 l1 RS p 1 p 2 a 2 l1 a 2 l2 RD x 1 x = l2 a 2 l1 2 l 1 a 1 l1 x 1 1 +x2 1 x 1 2 +x2 2
Calculating the equilibrium (CES) Relative demand x 1 x 2 = ασ 1 α σ 2 p σ 1 p σ = ασ 1 p σ 2 α σ 2 2 p σ 1 Country 1 (2) specialises in good 2 (1) and reformulating ϕ 2 1 l2 ϕ 1 2 l1 = a1 2 l2 a 2 1 l1 = ασ 1 (w 1 a 1 2 )σ α σ 2 (w 2 a 2 1 )σ α σ 2 a 1 2 l2 α σ 1 a 2 = (w1 ) σ (a 1 2 )σ 1 l1 (w 2 ) σ (a 2 1 )σ α σ 2 a 1 2 l2 (a 2 1 )σ α σ 1 a 2 1 l1 (a 1 = ασ 2 (a 1 2 )1 σ l 2 2 )σ α σ 1 (a 2 = (w1 ) σ 1 )1 σ l 1 (w 2 ) σ α σ 2 (a 1 2 )1 σ l 2 α σ 1 (a 2 1 )1 σ l 1 (w2 ) σ = (w 1 ) σ α 2 (a 1 2 ) 1 σ σ (l 2 ) σ 1 α 1 (a 2 1 ) 1 σ (w 2 ) σ (l 1 ) σ 1 = (w 1 ) 1 Depends on productivity, country size and demand shares 2 For σ = 1 this collapses to CD case