Factor endowments and trade I

Transcription

1 Part A: Part B: Part C: Two trading economies The Vienna Institute for International Economic Studies - wiiw April 29, 2015

2 Basic assumptions 1 2 factors which are used in both sectors 1 Fully mobile across sectors 2 Immobile across countries 3 Full employment assumption 2 2 sectors (industries) 1 Differ in relative factor intensities (at any relative factor prices) k 1 l 1 > k2 l 2 a 1,k a 1,l > a 2,k a 2,l Industry 1 is capital intensive in production 2 Standard production functions x i = f(k i, l i) (e.g. Cobb-Douglas, CES, etc.) 3 Identical and homothetic preferences across countries 4 2 countries differ with respect to relative endowments 1 Use same technology (though production techniques can differ) 2 Differ in relative factor endowments k 1 l 1 > k2 l 2 Country 1 is relatively capital abundant

3 Autarkic equilibrium Introduction General equilibrium Factor and goods prices Endowments and output structures Equilibrium relative price determined by technology, endowment and demand conditions x 2 MRT = MRS = p 1 p 2 p 1 p 2 x 1

4 Factor and goods prices General equilibrium Factor and goods prices Endowments and output structures 1 Substitution between labour and capital inputs in both sectors 1 Input coefficients depend on (relative) factor prices (and technology): a i,f = a i,f (w, r) 2 the higher w/r the higher is capital-labour ratio (the lower is labour intensity) w r ki l i 3 Results from cost minimisation (unit cost functions) at given factor prices 2 Assumption of no factor intensity reversal

5 General equilibrium Factor and goods prices Endowments and output structures 1 Mobility of factors across sectors 1 w 1 = w 2 = w and r 1 = r 2 = r 2 Perfect competition (prices equals marginal and average costs) 3 Relationship between goods and factor prices p 1 = a 1,l w + a 1,k r p 2 = a 2,l w + a 2,k r 1 Bijective relationship between (relative) goods and factor prices ( p1 ) ( ) ( ) ( ) 1 ( ) a1,l a = 1,k w a1,l a 1,k p1 = a 2,l a 2,k r a 2,l a 2,k p 2 p 2 ( ) w r 2 A change in price of labour has stronger effect on price of labour intensive good, etc.

6 Schematic presentation General equilibrium Factor and goods prices Endowments and output structures w r w r Good 1 Good 2 p 1 p 2 k 1 k 2 l1 l2 k i l i 1 Larger wage-rental ratio (w/r) implies higher relative price of relatively labour-intensive good (good 1) 2 Capital intensity is increasing with wage-rental ratio (substitution effect) 3 At any wage-rental ratio, good 2 is relatively capital intensive (no factor intensity reversal)

7 General equilibrium Factor and goods prices Endowments and output structures Numerical example Consider two economies with 2 sectors, Cloth (C) and Wine (W ). The two factors of production are labour l and capital k. Endowments in both countries are given by l A = 60 and k A = 40 and l B = 40 and k B = 60. The production functions in each sector are given by x C = l 0.25 C k0.75 C and x W = l 0.75 W k0.25 W. Assume that the utility function is U c = x 0.50 C x0.50 W. Set p C = 1 (numeraire). 1 Autarkic equilibria: Sector Factor Country A Country B Goods prices 1 (Wine) (Cloth) Output 1 (Wine) (Cloth) Demand 1 (Wine) (Cloth) Factor prices 1 (Labour) (Capital) Factor demand 1 (Wine) 1 (Labour) (Capital) (Cloth) 1 (Labour) (Capital) Utility GDP Price index GDP real Factor prices (real) 1 (Labour) (Capital)

8 General equilibrium Factor and goods prices Endowments and output structures Numerical example: Interpretation 1 Country A is relatively better endowed with labour k A l = 40 A 60 < kb l = 60 B 40 2 Wine production is relatively more labour intensive 1 See share parameters (for CD production functions) 2 See relative factor demands 3 Relative price of wine in country A is lower (as compared to B) p A W p A C = < pb W p B C = Relative demand (output) of wine in A is larger (as compared to B) x A W x A C = > xb W x B C = Relative price of labour (wage-rental ratio) in A is lower (as compared to B) w A r = 0.42 A 0.63 < wb r = 0.77 B 0.51

9 Endowments and output structures General equilibrium Factor and goods prices Endowments and output structures 1 Assume fixed factors and goods prices 2 Implies fixed input coefficients a i,f 3 Full-employment assumption implies l = a 1,l x 1 + a 2,l x 2 k = a 1,k x 1 + a 2,k x 2 or ( ) l = k ( ) ( ) ( a1,l a 2,l x1 a1,l a 2,l a 1,k a 2,k x 2 a 1,k a 2,k ) 1 ( ) l = k ( x1 x 2 ) Rybczynski theorem An increase in the endowment of one factor will increase the output of the industry using it intensively, and decrease the output of the other industry.

10 Change in endowment structures General equilibrium Factor and goods prices Endowments and output structures x 2 p 1 p 2 p 1 p 2 x 1

11 General equilibrium Factor and goods prices Endowments and output structures Numerical example Assume that endowments in country A changes to l A = 70 and k A = 40. Prices remain at their autarkic levels. 1 Autarkic equilibria: Sector Factor Country A l A = 70 Output 1 (Wine) (Cloth) Factor demand 1 (Wine) 1 (Labour) (Capital) (Cloth) 1 (Labour) (Capital)

12 Introduction Assumptions and conjectures 1 Relative world price differs from autarky prices, e.g. p w 1 p w 2 > p 1 p 2 2 Specialisation towards product with comparative advantages (good 1) 3 Consumption shifts towards product which becomes relatively cheaper (good 2) 4 Exports of comparative advantage good (good 1), imports of other good 5 Country A: 1 Specialisation towards labour intensive product implies higher demand for labour 2 Relative price of labour (wage-rental ratio) increases 3 As labour becomes relatively more expensive, capital-labour ratio in both sectors increase

13 Introduction Assumptions and conjectures x 2 p 1 p 2 p 1 p 2 x 1

14 Schematic presentation Assumptions and conjectures w r w r Good 1 Good 2 p 1 p 2 1 Wage-rental ratio (w/r) increases k 1 k 1 k 2 k 2 l1 l1 l2 l2 k i l i 2 Capital intensity is increasing in both sectors

15 Income distribution effects Assumptions and conjectures 1 Comparative advantage in labour intensive product 2 Specialisation towards labour intensive product 1 (Relative) Demand for workers increase 2 (Relative) Price of workers increase (wage-rental ratio increases) 3 Workers gain from trade in (nominal) relative terms 3 Capital-intensity (capital-labour ratio) in both sectors increase 1 Marginal product of labour increases in both sectors 2 Marginal product of capital decreases in both sectors 4 Implies that... 1 workers also gain in real terms 2 capital owners loose in real terms

16 Assumptions and conjectures Numerical example (contd.) Assume in above example that Country A opens to free trade. World price of Wine is given by p w W = 0.90 (with price of cloth being the numeraire). 1 equilibrium (small open economy): Sector Factor Country A Goods prices 1 (Wine) (Cloth) Output 1 (Wine) (Cloth) Demand 1 (Wine) (Cloth) Factor prices 1 (Labour) (Capital) Factor demand 1 (Wine) 1 (Labour) (Capital) (Cloth) 1 (Labour) (Capital) Utility GDP Price index GDP real Factor prices (real) 1 (Labour) (Capital) Net trade 1 (Wine) (Cloth) -5.17

17 Assumptions and conjectures Factor price insensitivity As long as both goods are produced, and factor intensity reversals do not occur, then each price vector (p 1, p 2) corresponds to unique factor prices (w, r). This implies that 1 Factor endowments do not matter for determination of (w, r) (if commodity prices are fixed) 2 Growth of capital stock or labour would not affect factor prices. Stolper-Samuelson theorem: A rise in the price of a commodity will increase the real reward of the factor used intensively in the sector and decrease the real reward of the other factor. Compensation criteria Gains from trade strong enough to compensate loosers

18 Conjectures Introduction and factor prices Application: Trade and wages Empirics 1 price in between autarky prices p A 1 p A 2 < pw 1 p w 2 < pb 1 p B 2 2 Holds if relative factor endowments are not too different 3 Specialisation according to comparative advantages 4 Export patterns according to comparative advantages 5 Specialisation not complete 6 Gains from trade for both countries

19 : Comparisons and factor prices Application: Trade and wages Empirics Assumptions imply 1 Structure of comparative advantages 1 Capital abundant country has comparative advantage in capital-intensive industry 2 Labour abundant country has comparative advantage in labour-intensive industry 2 Specialisation patterns: 1 Capital abundant country produces relatively more of capital intensive good 2 Labour abundant country produces relatively more of labour intensive good 3 Both countries gain from trade 4 Factor prices 1 Wage-rental ratio decreases in capital abundant country 2 Wage-rental ratio increases in labour abundant country [see also numerical example]

20 Schematic presentation and factor prices Application: Trade and wages Empirics w r w r Good 1 Good 2 p 1 p 2 k w 1 l w 1 k w 2 l w 2 k i l i 1 Wage-rental ratio (w/r) converges (factor price equalisation) 2 Capital intensity is increasing in both sectors in labour-abundant country (w/r is increasing) 3 Capital intensity is decreasing in both sectors in capital-abundant country (w/r is decreasing)

21 and factor prices Application: Trade and wages Empirics Numerical example The two economies A and B engage in free trade. 1 equilibria: Autarky Sector Factor A B A B Goods prices 1 (Wine) (Cloth) Output 1 (Wine) (Cloth) Demand 1 (Wine) (Cloth) Factor prices 1 (Labour) (Capital) Factor demand 1 (Wine) 1 (Labour) (Capital) (Cloth) 1 (Labour) (Capital) Utility GDP Price index GDP real Factor prices (real) 1 (Labour) (Capital) Net exports 1 (Wine) (Cloth)

22 and factor prices Application: Trade and wages Empirics Heckscher-Ohlin theory would predict: 1 2 factors of production: skilled and unskilled workers 2 Advanced countries are relatively better endowed with skilled labour 3 would imply that advanced countries specialise in skill-intensive industries 2... face an increase in the price of skill-intensive product 3... face an increase in the relative wage of skilled workers 4... face overall gains from trade allowing to compensate unskilled workers 4 would imply that emerging countries specialise in unskill-intensive industries 2... face an increase in the price of the unskill-intensive product 3... face an increase in the relative wage of unskilled workers 4... face overall gains from trade allowing to compensate skilled workers

23 Empirics Introduction and factor prices Application: Trade and wages Empirics 1 Leontief paradoxon : 1 Leontief (1953) showed that capital-labour ratio in US imports was higher than in its exports 2 Surprising, as US was deemed to be the capital abundant country (and therefore should export capital intensive goods) 2 Theoretical background: Factor content of trade studies and Heckscher-Ohlin-Vanek theory 1 Circumvents problems with dimensionalities of model 2 Calculates e.g. employment content of exports 3 Many follow up studies could not confirm HO-theory (... results are like coin toss... ) 4 However, when allowing for technology differences HO-theory is confirmed (Trefler, 1993:... Leontief was right!) 1 If labour productivity in US is higher, than US is labour abundant country in efficiency terms