Problem set 4 -Heckscher-Ohlin model.

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1 Problem set -Heckscher-Ohlin model. Eercise Home can produce two goods: which is capital-intensive and y which is laborintensive. As a result of opening up for trade with the rest of the world we see that P /P y at Home increases. a) What good does Home eport and what good does it import? Is Home capital or labor abundant? b) What should happen to: i) the wage-rental ratio; ii) capital intensity in each sector; iii) capital employed in each sector. c) Plot the changes resulting from opening up for trade in the Harrod-Johnson diagram. As a result of trade, what happens to the real price of labor and capital? Which group benefits from trade: capital-owners or workers? Eercise B is a small economy where two goods are produced, scarfs ( ) and flags ( ), according to the following production functions: 0.5 K L = and = K L. The labor and capital endowments in this economy are respectively, L = 0 and K =50. It is known that in B the preferences are homothetic and the autarky relative wage is ω = w r = 9. a) Draw the diagram that relates capital intensity with the relative wage. Identify the capital intensive good and the points of full specialization. b) Eamine the effects of opening to international trade, assuming that in the rest of the world ω = 8 and k = K L = : (i) (ii) (iii) Which of the countries is relatively abundant in capital? Eplain your answer, specifying the concept of abundance; Describe the passage from autarky to free trade and show graphically the gains from trade in B. Quantify when possible; Eplain the evolution of the factors returns after opening to trade. c) Assume that, in the short run, capital cannot move between sectors. Describe the short-run effects from opening to trade on production, consumption and factors returns, compare it with the long run solution from b). afreitas@ua.pt Miguel Lebre de Freitas 6

2 Eercise Consider a world with two countries (N and R), two goods and two factors. The technologies are CRS and identical in both countries and the substitution elasticity between factors in both industries is constant and equal. Allow y to be the capitalintensive good. Determine the specialization pattern when both countries are identical in everything ecept in the fact that: a) The consumers of N have a larger relative preference for good. b) Country N has more capital and labor than country R, but with the same proportion of both factors. c) County N has more capital than country R, being the labor endowments equal. d) Country N has a larger relative labor endowment and the consumers of N have a larger relative preference for good. Eercise Consider a small open economy where goods, and, are produced using labor and capital according to the following epressions: a) Complete the following figure: = K L and = K L. ω? y? k Suppose that this economy is open to international trade and that the relative wage in the rest of the world is equal to. b) Determine the relative return of factors in this country. Justify it. c) Check which of the following conditions are compatible with this eercise: (i) This country has comparative advantage in the production of ; (ii) This country has the same preferences as the rest of the world but a smaller endowment of labor; (iii) This country has the same endowments and technology as the rest of the world but its consumers have a larger relative preference for good. afreitas@ua.pt Miguel Lebre de Freitas 7

3 Eercise 5 Comment the accuracy of the following statements: If, after opening to international trade, the capital intensive sector has contracted and the labor intensive sector has epanded, then a) "... it is because the country had a larger labor endowment than the rest of the world ; b) "... workers are worse with trade and capital owners are better with trade"; c) "... the national product, measured at autarky prices, has decreased, so the gains from specialization are negative. Eercise 6 Consider a small open economy, described by the following equations: U = K L = K L = L = 00 e K = 0 a) Show that in both industries the average and marginal productivity of labor and capital depends only on the factors proportion and not on the absolute production levels. Why does this occur? b) Use the Pareto efficiency conditions in the factors market to determine the relation between: ω = w r and k j = K j L j. c) Find out the relationship between ω and p = P P as well as the maimum range of ω. Draw the Harrod-Johnson diagram. d) Determine the epression for the production contract curve. Represent it graphically. e) Compute the epression for the relative supply curve of y. Hint: (i) Based on the Harrod-Johnson diagram, compute the relation between p and k ; (ii) Use the contract curve epression in (i) to obtain a relationship between L and p; (iii) Use the productivity of labor in both sectors obtained in (a) and the epressions obtained in (a) to compute the relative supply of in terms of L and p; (iv) Use (ii) and (iii) to eliminate L ; 0 p (v) If you reached = p 0 p S you are correct! afreitas@ua.pt Miguel Lebre de Freitas 8

4 f) Determine the relative demand curve of. g) Define the autarky equilibrium, finding the: (i) (ii) (iii) (iv) (v) Relative price and relative wage; Capital intensity in both sectors; Absolute levels of labor and capital usage; Absolute production levels of and. Check that the results are compatible with the relative demand epression; Autarky utility level. h) Suppose now that the country opens to international trade. Assuming that, in the world economy, p = 0., find: (i) The relative wage under free trade. Were you epecting a change in this direction? (ii) The capital intensity in both sectors; (iii) Absolute levels of labor and capital usage; (iv) Absolute production levels of and. Check that the results are compatible with the relative supply. (v) The national income in units of ; (vi) The optimal consumption quantities; (vii) Echanged quantities of both goods. Show it graphically; (viii) The utility level with trade. i) Suppose that the country eperiences a strong immigration wave increasing the labor endowment to 50. (i) (ii) (iii) (iv) Compute the new contract curve; Using the information about capital intensity, compute the employment level in both industries; Compute the new production optimum. Which important theorem have you just confirmed? Show it graphically; Using the fact that the Engel Curve in this eercise is a straight line, discuss whether the trade triangle has increased or decreased. If the labor endowment were larger, would it be possible to invert the specialization pattern? Why? Eercise 7 Consider a small open economy where goods, and, are produced using labor and capital according to the following epressions: afreitas@ua.pt Miguel Lebre de Freitas 9

5 = K L = K L U = L =00 K = 00 a) Find out the epression of the PPF assuming that both factors are perfectly mobile across industries. Compute the MRT. b) Eplain why in this economy endowments of labour and capital are not relevant to eplain the specialization pattern. c) Find out the equilibrium allocation under autarky. Suppose that in the rest of the world, the production functions are: 0. 75K L = = K L d) Compute the equilibrium price under free trade. e) Under free trade, will there be convergence of real incomes? f) Find out the specialization pattern of the home country under free trade. g) Suppose that in the short term, capital was immobile. Departing from the autarky equilibrium, find out the epression for the short term PPF. Confirm the optimality of the allocation found in (c). h) Eamine again the move from autarky to free trade, but disentangling the short term and the long term effects on production, welfare and real incomes. afreitas@ua.pt Miguel Lebre de Freitas 0

6 Solutions PS Eercise Solved in class. Eercise a) y is capital intensive. b)!!! As eplained in class, due to a mistake, I solved the eercise with ω = (and not with ω = 8 k = K L = ). These solutions are for ω =. b.i) Country B is capital abundant. b.ii) Production points will be (.0, 5) in autarky and (.0, 7.5) under free trade. b.iii) Real returns of capital increase in country B; real wages decrease. c) We are back in the Specific factors model;( ) p ( w p ) increase. r and ( w ) decrease; ( ) r and Eercise a) Country R: eports, imports y. b) No trade. c) Country R: eports, imports y. d) Ambiguous. Eercise a) k = ; ω = w r =. b) Relative return in B: = w r = ( ) = 0. 5 r, ( ). 6 p r. ω ; Real returns: ( ) = w, ( ) 6. 5 p w, c) (i) es; (ii) No (if smaller labor endowment is meant in relative terms); (iii) No. Eercise 5 a) True (large labor endowment in relative terms). b) Wrong. c) Wrong. Eercise 6 afreitas@ua.pt Miguel Lebre de Freitas

7 a) Due to CRS. b) k = ω, = ω. c) p = ω d) K 90L = L e) Additional hint: manipulate the epression used in c) to write it as a function of and. k y f) = p g) (i) p = 0., ω = 0. ; (ii) k = 0., k =/ 0 ; (iii) L = 5, K = 7. 5; (iv) 0.56, ; (v) U h) (i) ω = 0. 0 ; (ii) k = 0., k =/ 75 ; (iii) L = 8. 5, K = 9. 75; (iv) y 66.67, ; (v) National income = 7.598; (vi) , i) (i) K 90L = ; (ii) = L y L, K = 9; (iii) , Rybczynski theorem. (iv) Trade triangle decreases; es, pattern may change if labor endowment increases further. Eercise 7 a) y = b) Both sectors use the same factor intensities. This is does not correspond to the HO model. c) (, y) = ( 7,6). d) p P P =. = e) There will be no convergence of real incomes. f) The small open economy eports and imports y. g) The short-run PPF is: = 00 + y 6. h) New production point will be (, y) = ( 0.9, 0). afreitas@ua.pt Miguel Lebre de Freitas