Part A: Part B: Part C: Two trading economies The Vienna Institute for International Economic Studies - wiiw May 5, 2017
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 2 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 (e.g. Cobb-Douglas, CES, etc.) 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
Important properties of (standard) production function: x i = f i (l i, k i ) 1 Constant returns to scale: If both input factors are changed by a factor λ, then also output changes by λ f i (λl i, λk i ) = λf i (l i, k i ) = λx i 2 Positive but decreasing marginal product Increasing one factor of production increases output, but at a decreasing rate; formally for input factor f i = l i, k i f i f i > 0 and 2 f i f 2 i < 0
Autarkic equilibrium Introduction Equilibrium relative price determined by technology, endowment and demand conditions x 2 MRT = MRS = p 1 p 2 p 1 p 2 x 1 1 Shape of production possibility frontier is caused by properties of production function (decreasing marginal products); no analytical derivation from underlying production functions 2 Proof of existence of equilibrium by fix-point theorems
Factor prices and factor intensities 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
Cost minimising factor input bundle k i (capital input) k i l i Factor input ratio ki l i depends on relative factor prices w r w r k i l i k i l i x i = 1 l i (labour input)
Cost minimising factor input bundle k i (capital input) k 2 l2 At given factor price ratio, industry 2 is the capital-intensive industry k 1 l1 x 2 = 1 x 1 = 1 l i (labour input)
Schematic presentation w r Industry 1 Industry 2 k 1 k 2 l1 l2 k i l i 1 At given factor price ratio w r, industry 2 is the capital-intensive industry 2 Assumption of no factor-intensity reversal : This holds true for all factor price ratios (lines do not cross)
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. 3 because cost-share of labour is larger
Schematic presentation w r p 1 p 2 1 An increase in the wage/rental price, increases the relative price of the labour-intensive product 2 An increase in the price of the labour intensive product, must be aligned with an increase in the wage/rental ratio (to satisfy no-profit condition)
Schematic presentation of GE w r w r Industry 1 Industry 2 p 1 p 2 k 1 k 2 l1 l2 k i l i 1 The relative price determines the factor price ratio... 2... which determines the factor intensity of production in both industries
Autarkic equilibrium: Comparing two economies Cloth Cloth p W pc p W pc Wine Wine 1 Wine: relative labour intensive; Cloth: relative capital intensive 2 Left country: labour abundant; right country: capital abundant 3 Wine is relatively cheaper in labour abundant country
Schematic presentation: Comparing two economies w r w r Wine industry Cloth industry p W pc Labour-abundant economy (black)... 1... faces lower w/r ratio... k i l i 2... lower relative price of labour-intensive product 3... lower capital intensities in production
Numerical example: Assumptions 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 (scaled) utility function is ( ) U c xc 0.50 ( ) xw 0.50. = 0.5 0.5 Set pc = 1 (numeraire).
Numerical example: Results 1 Autarkic equilibria: Sector Factor Country A Country B Goods prices 1 (Wine) 0.82 1.22 2 (Cloth) 1.00 1.00 Output 1 (Wine) 30.90 25.23 2 (Cloth) 25.23 30.90 Demand 1 (Wine) 30.90 25.23 2 (Cloth) 25.23 30.90 Factor prices 1 (Labour) 0.42 0.77 2 (Capital) 0.63 0.51 Factor demand 1 (Wine) 1 (Labour) 45.00 30.00 2 (Capital) 10.00 15.00 2 (Cloth) 1 (Labour) 15.00 10.00 2 (Capital) 30.00 45.00 Utility 55.84 55.84 GDP 50.45 61.79 Price index 0.90 1.11 GDP real 55.84 55.84 Factor prices (real) 1 (Labour) 0.47 0.70 2 (Capital) 0.70 0.47
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 = 0.82 1.00 < pb W p B C = 1.22 1.00 4 Relative demand (output) of wine in A is larger (as compared to B) x A W x A C = 30.90 25.12 > xb W x B C = 25.12 30.90 5 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
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.
Change in endowment structures x 2 p 1 p 2 p 1 p 2 x 1
Numerical example Assume that endowments in country A changes to l A = 70 (from l A = 60) with k A = 40 remaining. Prices remain at their autarkic levels. 1 Autarkic equilibria: Sector Factor Country A l A = 70 Output 1 (Wine) 30.90 38.62 2 (Cloth) 25.23 23.12 Factor demand 1 (Wine) 1 (Labour) 45.00 56.25 2 (Capital) 10.00 12.50 2 (Cloth) 1 (Labour) 15.00 13.75 2 (Capital) 30.00 27.50
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
Introduction Assumptions and conjectures x 2 p 1 p 2 p 1 p 2 x 1
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
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
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) 0.82 0.90 2 (Cloth) 1.00 1.00 Output 1 (Wine) 30.90 35.31 2 (Cloth) 25.23 21.45 Demand 1 (Wine) 30.90 29.57 2 (Cloth) 25.23 26.61 Factor prices 1 (Labour) 0.42 0.49 2 (Capital) 0.63 0.60 Factor demand 1 (Wine) 1 (Labour) 45.00 48.98 2 (Capital) 10.00 13.23 2 (Cloth) 1 (Labour) 15.00 11.02 2 (Capital) 30.00 26.77 Utility 55.84 56.10 GDP 50.45 53.22 Price index 0.90 0.95 GDP real 55.84 56.10 Factor prices (real) 1 (Labour) 0.47 0.51 2 (Capital) 0.70 0.63 Net trade 1 (Wine) 5.17 2 (Cloth) -5.17
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 supply 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
and factor prices Application: Trade and wages (2 economies): Conjectures 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
: Comparisons and factor prices Application: Trade and wages 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]
Schematic presentation and factor prices Application: Trade and wages 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)
and factor prices Application: Trade and wages 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) 0.82 1.22 1.00 1.00 2 (Cloth) 1.00 1.00 1.00 1.00 Output 1 (Wine) 30.90 25.23 39.90 17.10 2 (Cloth) 25.23 30.90 17.10 39.90 Demand 1 (Wine) 30.90 25.23 28.50 28.50 2 (Cloth) 25.23 30.90 28.50 28.50 Factor prices 1 (Labour) 0.42 0.77 0.57 0.57 2 (Capital) 0.63 0.51 0.57 0.57 Factor demand 1 (Wine) 1 (Labour) 45.00 30.00 52.50 22.50 2 (Capital) 10.00 15.00 17.50 7.50 2 (Cloth) 1 (Labour) 15.00 10.00 7.50 15.50 2 (Capital) 30.00 45.00 22.50 52.50 Utility 27.92 27.92 28.50 28.50 GDP 50.45 61.79 57.00 57.00 Price index 0.90 1.11 1.00 1.00 GDP real 55.84 55.84 57.00 57.00 Factor prices (real) 1 (Labour) 0.47 0.70 0.57 0.57 2 (Capital) 0.70 0.47 0.57 0.57 Net exports 1 (Wine) 11.40-11.40 2 (Cloth) -11.40 11.40
Application: Trade and wages and factor prices Application: Trade and wages 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... 1... 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... 1... 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 5 BUT:...