Labor productivity and comparative advantages: The Ricardian model Robert Stehrer Version: March 6, 2013
Historical background Assumptions 1 input factor: homogenous labor L fixed supply mobile across industries immobile across countries 2 industries differ in labor productivity 1/a Li a Li... input of labor for one unit of output
Autarkic economy Production possibility frontier (under full employment (FE) assumption): L = a L1 y 1 + a L2 y 2 y 2 = 1 L a L1 y 1 a L2 a L2 Price = costs: p i = a Li w [Ricardian Labor Theory of Value] Budget constraint wl = p 1 y 1 + p 2 y 2 y 2 = 1 p 2 wl p 1 p 2 y 1 = = 1 a L2 w wl a L1w a L2 w y 1 1 L a L1 y 1 a L2 a L2
Equilibrium in autarky y 2 L/a 2 L/a 1 y 1 PPF: absolute value of slope equals opportunity cost of y 1 in terms of y 2 Slope = q 2 / q 1 = p 1 /p 2 = a L1 /a L2 PPF = Budget constraint
Opening up under small country assumption World prices given at p1 /p 2 ; i.e. small country cannot influence world prices Assume that p 1 p 2 > p 1 p 2
Free trade under small country assumption y 2 L/a 2 Consumption point Imports Production point Exports L/a 1 y 1 As p 1 /p 2 > p 1/p 2 country specializes (completely) in production of good 1 Gains from trade Utility curve shifts out Consumption point is above PPF The larger the difference between autarky and world price, the higher are the gains from trade
Two trading economies Second country with endowment L Assume that a L1 a L2 > a L1 a L2 p 1 p 2 > p 1 p 2 i.e. home country has comparative advantage in production of good 1 or the home autarky price of good 1 is lower than that abroad; denote by p a < p a Assume (for now) that free trade price is between autarky prices: p a < p < p a
Free trade situation y 2 Home country y 2 * Foreign country L*/a 2 * L/a 2 L/a 1 y 1 L*/a 1 * y 1 * Home country specializes in good 1, foreign country in good 2 Both countries gain from trade (are better off)
Free trade situation: World transformation curve
Trade patterns are determined by comparative advantage: Countries specialise and export in comparative advantage sectors al1 a L2 > a L1 a L2 Even if a country has an absolute advantage in both sectors, i.e. a L1 > a L1 and a L2 > a L2 patterns of trade determined by comparative advantages. Both countries gain from trade. al1 Maybe wage (or exchange rate) dynamics necessary: > w a L1 w > a L2 a L2 Countries specialise and export in comparative advantage sectors Real wage level determined by absolute advantages Real wages in terms of import goods are rising When using price index including imported goods, real wages are rising Volume of trade is larger the more different are countries If countries would be equal, there would be no trade Intra-industry trade discussed later Gains from trade for a country are larger the larger difference between autarky and world (free trade) price
Special cases: World relative supply and demand curves p Panel A Panel B p a * Relative supply p a * Relative supply p p a Relative demand p a =p Relative demand (L/a L1 )/(L*/a* L2 ) (y 1 +y 1 *)/(y 2 +y 2 *) (L/a L1 )/(L*/a* L2 ) (y 1 +y 1 *)/(y 2 +y 2 *) Assumes utility functions to be homothetic and identical across countries Panel A: Complete specialization of both countries Panel B: Home country not fully specialized and exhibits no gains from trade; Reasons: size and biased preferences
Numerical example Autarky Industry 1 Industry 2 Wage rate Labor Home a L1 = 1 a L2 = 2 w = 2 L = 100 Foreign a L1 = 6 a L2 = 3 w = 1 L = 200 Relative prices in autarky: p a = 1/2 and p a = 2. Income: Lw = 200 and L w = 200. Demand: U = y1 0.5 y2 0.5 Home country: Foreign country: y 1 = 0.5 200/2 = 50 y 2 = 0.5 200/4 = 25 y 1 = 0.5 200/6 = 16.7 y 2 = 0.5 200/3 = 33.3
Free trade Home country has comparative advantage in good 1, as World price: p = 2/3 Demand: U = y 0.5 1 y 0.5 2 Home country: Foreign country: p a = 0.5 < p < p a = 2 y 1 = 0.5 200/2 = 50 y 2 = 0.5 200/3 = 33.3 y 1 = 0.5 200/2 = 50 y 2 = 0.5 200/3 = 33.3
Production: Home country: Foreign country: Trade balance: TB = X M Home country: Foreign country: y 1 = 100/1 = 100 y 2 = 0 y1 = 0 y 2 = 200/3 = 66.6 TB = 50 2 33.3 3 = 0 TB = 33.3 3 50 2 = 0
Gains from trade (expressed in real wages) Home country: w p 1 = 2 2 = 1 Foreign country: w p 2 = 2 3 > 2 4 w p 1 = 1 2 = 0.5 > 1 6 w p 2 = 1 3
Discussion A number of empirical studies (first study was MacDougall (1951) 140 years after Ricardo...) generally supports Ricardian model. Though Ricardian model is not fully adequate (e.g. complete specialization not observed, other factors of production,...) and discussions about empirical strategies: Productivity differences play an important role in international trade Comparative rather than absolute advantage matters Countries gain from trade
Supplementary material
Extensions Many countries Many goods A continuum of goods (Dornbusch, Fischer and Samuelson, AER 1977) Transport costs and non-traded goods Dynamics of productivity, specialization and wage structures Krugman, P. (1986): A Technology Gap Model of International Trade, in: Jungenfeldt, K. and D. Hague (1986): Structural Adjustments in Advanced Economies, Macmillan. Redding, S (2002): Specialization Dynamics, Journal of International Economics, vol. 58, pp. 299-334.
Many countries 2 goods 3 countries Country A: Most productive in good 1 Country C: Most productive in good 2 Country B: More productive in good 1 compared to C More productive in good 2 compared to A Chain of labor productivity ratios: a A L1 a A L2 < ab L1 al2 B < ac L1 al2 C
Patterns of specialization (Example) Country A Country B Country C y A 2 y B 2 y C 2 L B /a B 2 L C /a C 2 L A /a A 2 L A /a A 1 y A 1 L B /a B 1 y B 1 L C /a C 1 y C 1 If relative world price equals (or is close to) relative autarkic price of B Countries A and C completely specialize Trade patterns of country B determined only in conjunction with demand conditions Country B gains least from free trade (because relative world price is closest to Country B autarky price Bilateral trade not determined (would require stronger assumptions on demand)
Many goods N industries; Wage rates w and w Arrange productivity ratios according to a L1 al1 < a L2 al2 < < a LN aln Goods will will be produced where it is cheapest to make them: Good i will be produced at home if wa Li < w a Li a Li a Li Good j will be produced abroad if > w w wa Lj > w a Lj a Lj a Lj < w w If a Lk a Lk = w w good k will be produced by both countries; export structure only determined by demand.
Numerical example (Krugman and Obstfeld, 2003, p. 26ff) Relative Home Unit Labor Foreign Unit Labor Home Productivity Requirement Requirement Advantage ali /a Li Apples 1 10 10 Bananas 5 40 8 Caviar 3 12 4 Dates 6 12 2 Enchiladas 12 9 0.75 With w/w = 3 the domestic country will produce apples, bananas and caviar; the foreign economy will produce dates and enchiladas
Determination of relative wages Relative (derived) demand for domestic labor is falling when w/w rises. Goods produced in domestic country become more expensive, and demand for these goods and the labor to produce them falls Example: Suppose w/w increases from 3 to 3.99: Domestic country still produces A, B, and C; but demand for these goods is falling Suppose w/w increases from 3.99 to 4.01: Caviar becomes too expensive to be produced in domestic country and moves to foreign country causing a discrete drop in demand for labor Relative supply of labor L/L is assumed to be fix.
Many goods case: Graphics Basic structure w/w* Apples Relative supply Bananas Caviar Dates Enchiladas Relative demand L/L*
A continuum of goods (Dornbusch, Fischer and Samuelson, AER 1977) Homogenous labor; not mobile internationally; Continuum of goods defined on interval z [0, 1] 2 countries with endowments L and L Input coefficients a L (z) = l(z)/q(z) and a L (z) = l (z)/q (z) Prices p(z) = a L (z)w and p (z) = a L (z)w Goods ranked according to z 1 < z 2 a L(z 1 ) a L (z 1) < a L(z 2 ) a L (z 2) i.e. diminishing home country comparative advantage.
Denote A(z) = a L (z)/a L(z); i.e. A(z) decreasing in z [or A (z) < 0] Particular good z will be produced at home if wa L (z) w a L (z) w w A(z) Home country will produce range [0, z] and foreign country [ z, 1]; z is determined by w/w.
Supply condition in a continuum of goods w/w* A(z) z
Demand side Cobb-Douglas demand: 1 0 α(z)dz = 1 where α(z) is constant expenditure share Identical across countries, i.e α(z) = α (z) Fraction of income spent on goods produced in home country: v( z) = z 0 b(z)dz in foreign country: 1 v( z) = 1 z b(z)dz
Equilibrium Domestic labor income equals world spending on goods produced at home: wl = v( z)(wl + w L ) w w = v( z) L 1 v( z) L Upward sloping in z Alternative interpretation as balance-of-trade form [1 v( z)]wl = v( z)w L
Equilibrium with a continuum of goods w/w* B(z;L*/L) A(z) z
Comparative statics Increase in size of foreign country Effects of uniform technical progress w/w* B(z;L*/L) w/w* B(z;L*/L) A(z) A(z) z z
Comparative statics Size of foreign economy increasing Relative wage of home is increasing Range of goods produced at home declines Per capita income is rising (Uniform) Technical progress in foreign country Relative wage of home is decreasing Range of goods produced at home declines Domestic and foreign real income increases However, welfare effects depend on exact form of technical progress
Empirics
Overview of related empirical studies Empirical evidence supports that productivity differences are an important determinant of trade structures though not unambiguously... MacDougall (1951, 1962 [140 years after Ricardo]), Stern (1962), Balassa (1963) comparing productivity ratios and export ratios for UK and US Kreinin (1969) does not support this view (studying Canada, Australia, US and UK) Sailors and Bronson (1970) and McGilvray and Simpson (1973) reject Ricardo hypothesis for a number of countries Bhagwati (1964, 1972): Empirical tests should focus on relationship between relative productivity and export prices Objection of third-country method Different productivity measures (e.g. TFP; see also Agarwal et al. 1975) Caves and Jones (1973), Deardorff (1984) and Balassa (1972) are critical to Bhagwati critique
..., with some caveats... Simple empirical specifications not including other potential determinants of trade (transport costs, imperfect competition, trade barriers, product differentiation, etc.) Cross-country differences in industry wage structures Results might be consistent with other trade theories and some misleading predictions: Extreme degree of specialization not observed in real world Changes of distribution of income within country not considered (though country as a whole has gains from trade) Does not take differences in resources across economies into account Model cannot explain trade flows between similar countries