Factor endowments and trade I (Part A) Robert Stehrer The Vienna Institute for International Economic Studies - wiiw May 7, 2014
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
Autarkic equilibrium Introduction 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 1 x 1
Factor and goods prices 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
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 = 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 ( ) w r 2 A change in price of labour has stronger effect on price of labour intensive good, etc.
Schematic presentation Factor and goods prices Endowments and output structures w r w r Good 1 Good 2 p 1 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)
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) 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 27.92 27.92 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
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 = 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
Endowments and output structures 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.
Change in endowment structures Factor and goods prices Endowments and output structures x 2 p 1 p 1 x 1
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) 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 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 1 x 1
Schematic presentation Assumptions and conjectures w r w r Good 1 Good 2 p 1 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 implies that workers gain from trade in nominal terms (wage-rental ratio increases) 3 Marginal product of labour increases, marginal product of labour decreases in both sectors 4 Implies that workers also gain in real terms, whereas capital income looses in real terms
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, ) 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.
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 27.92 28.05 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
Comparisons Introduction and factor prices Assumptions imply 1 Capital (labour) abundant country produces relatively more of capital (labour) intensive good 2 Relative price of capital (labour) intensive product lower in capital (labour) abundant country 3 Capital (labour) abundant country has comparative advantage in capital-intensive (labour-intensive) good [see also numerical example]
Conjectures Introduction and factor prices 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 factor endowments are not too different 3 Capital abundant country specializes in capital intensive good 4... exports this good, imports the other 5 Specialisation not complete 6 Gains from trade
Schematic presentation and factor prices w r w r Good 1 Good 2 p 1 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 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