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Problem set 3 - The Specific Factors Model Exercise 1 Consider the following table with outputs of x and y: x 4 3 2 1 |0 0 7 12 15 16 a) Plot the production possibilities frontier (PPF) of this economy. Characterize the following points: (7,2), (2,7) and (3,7). b) Departing from (0,16), compute the opportunity cost of each additional unity of x. Interpret the results. This PPF can be defined by the following expression: y =16-x2. c) Use this information to compute the opportunity cost of an infinitesimal increase of x at points x = 3 and x = 2. Consider that goods x and y are agricultural products. Both goods use labour and land in their production. Labour is homogeneous and can be employed in either sector but there are two types of land, each specific to the production of one good. Good x can only be produced in mountains and good y can only be produced in plains. The respective production functions are x = g(M, Lx )= VMLy , and y = f(P, Ly) = PLy. It is not possible to transform plains into mountain or vice versa. The quantities of the three factors are fixed and equal to: M=1, P=1 and L=16. d) Does the law of diminishing marginal returns hold in both sectors? e) Confirm the expression of the PPF. f) Show graphically if and how the PPF changes when: (i) The labour endowment increases; (ii) There is a technological improvement in the production of y; (iii) The consumers preference for good x increases; (iv) The economy opens up to free trade; (v) The productivity of mountain land decreases; (vi) Real wages increase. Suppose in autarky the economy produces at (3,7). By engaging in trade it is possible to exchange one unit of x for one unit of y in the international market place. g) Given the international relative price, will the production pattern remain unchanged? If not, what will be the optimal production? Quantify the 'gains from specialization', at free trade prices, in terms of units of y. afreitas@ua.pt Miguel Lebre de Freitas 11 International economics - Problem sets h) How did input prices change from autarky to free trade? What are your conclusions on the benefits of trade in the specific factors model? In particular who would lobby for protection? i) What would happen if land rents could not adjust downwards while the economy moved from autarky to free trade? Where would the new production point in that case? What can we conclude about the adjustment costs to free trade when factor prices are sticky?Exercise 4 Nebulous (N) produces two goods, oranges (X) and umbrellas (Y ), out of three productive factors: Labour (L), Land (7 ) and Capital (K )). The production functions are: X = TVL'p and Y =KLy Labour is perfectly mobile between industries. The social utility function is given by: U = XY . The factors endowments are: L= 48, 7-4 e K=4. g) Find the expression of the PPF in this economy. Plot it. h) Determine the autarky equilibrium in N (quantities consumed and produced, utility level and relative price). i) Sunny (S), is an economy identical to Nebulous in all aspects except for its capital endowment, which is K=2. Derive the PPF of Sunny. In which good does S hold comparative advantage? Find the expression for Sunny's relative supply and show that it is positively slopped. j) Discuss, the effects of free trade in S and N, using appropriate graphical representations. Plot also the world equilibrium. Exercise 5 'In a world of two economies with identical production possibilities there can not be gains from trade. ' Comment and use graphics to show your point. afreitas@ua.pt Miguel Lebre de Freitas 12 International economics - Problem sets Exercise 6 Home, a small open economy, produces two homogeneous goods: manufactures (x) and agriculture (v). The respective production functions are given by x = KL, and y = TL,. where capital (X) is specific to manufactures and land (7) is specific to agriculture. Labor (L) is homogeneous and perfectly mobile across industries. The endowments of Home are K = 400, T = 1 and Z = 300. Finally, assume that the world relative price of x is equal to 1. a) Determine Home's production possibility frontier (PPF). b) Find the expression for the marginal rate of transformation between the two goods. c) How much will the country produce of x and y under free trade? Now assume that preferences are given by U = xy. d) Assess the comparative advantages and the gains from trade in this case. Represent in a graph. Sticking with the assumption of free trade, examine the implications of an increase in the capital stock of the Home country to K = 600. e) Show graphically the change in Home's PPF. f) How will this change affect Home's comparative advantages and trade flows? Explain the intuition, quantify the change in production, the volumes of trade and represent in a graph. g) What would change in your answer to the previous question if Home was a large country? Finally assume that, departing from question (f), Home's government was considering the possibility of banishing international trade. Answer the following questions (no computations required): h) Would the country as a whole be better off or worse off? Explain, with the help of a graph. i) Which groups would be in favor of the government's decision and which groups would oppose? Explain.Exercise 7 Assume that two homogeneous goods are produced in the World economy: agriculture (x) and manufactures (v). The respective production functions are equal across all countries and given by x = TL, and y = K052,5, where 7 stands for land (specific afreitas@ua.pt Miguel Lebre de Freitas 13 International economics - Problem sets to agriculture) and K stands for capital (specific to manufactures). Labour (L) is homogeneous and mobile across industries. Finally, assume that preferences are given by U = xy. a) Show that the World PPF can be written as = L, where L represents the total endowment of labour. Find also the general expression of the marginal rate of transformation. b) Now assume that T = K =100 and Z = 200. Given the preferences, describe the equilibrium in the world economy (prices and production). Represent in a graph. The world economy is populated by many small economies, which trade freely among each other. In one of these countries (Alfa), factor endowments are T = K = 1 and L = 2. a) Will Alfa benefit with trade openness? Explain, taking into account the differences vis-a-vis the World economy. b) Now assume that Alfa managed to expand its arable land to T=7. Describe the implications of such change in comparative advantages, and in the patterns of production, consumption and trade. Represent in a graph and explain