Question

Problem 1

A country (”Home”) is populated with 300 workers who produce either food (F) and/or clothing (C). Each food worker produces 6 units of food and each clothing worker produces 3 units of clothing. The preferences of the consumers over food and clothing are represented by the utility function: u(D_F , D_C) = (D_F ) ^2/3 (D_C) ^1/3

1) Assuming that at the optimum, consumers set their marginal rate of substitution, MRS_{DF ,DC} , to the relative price, i.e., MRS_{DF ,DC} ≡ (∂U/∂D_F)/ (∂U/∂D_C )= PF/PC find the relationship between relative demand, D_F /D_C , and the relative price, P_F/P_C.

2) What is the autarky price (the relative price of food and clothing) in this economy?

3) Assuming that relative demand is equal to relative supply in equilibrium in autarky (tangency condition), what is the equilibrium relative produced quantity (Q_F /Q_C) in Home? Represent graphically the autarky equilibrium in Home.

4) After finding the expression of the production possibility frontier, find the quantities of food (Q_F ) and clothing (Q_C) produ There also exists another country (”Foreign”), which is populated with 900 workers. These workers have different (lower) productivity levels: a food worker can produce only 1 unit of food while a clothing worker can only produce 2 units of clothing. The consumers in Foreign share the same preferences as those in Home.

5) Answer questions (2) and (3) for the Foreign economy in autarky.

6) Now assume that these two countries open to trade with one-another. (a) Draw the world relative supply curve by choosing on the x-axis the relative quantity Q_F /Q_C . (5 points) (b) What will be the world equilibrium relative price (P_F /P_C) (8 points) (c) Will both countries specialize? What will be the pattern of potential trade between the two countries, and who will benefit?

Problem 2

Problem 2 (30 points) Assume that only two countries, A and B, exist; they have identical tastes and preferences and they produce two goods 1 and 2 with capital and labour using the same constant-returns-to-scale technology Countries Factor Endowments AB Labour Force 45 20 Capital Stock 15 10 1. If good 1 is capital intensive and trade is allowed between the two countries, using the Heckscher-Ohlin Theory, mention the good that will be exported by each country. Explain! (10 points) 2. Using the same theory, what will be the pattern of trade between the two countries ii you have the additional information stating that coun- try A is very much richer than country B? Explain! (10 points)

Answer 1

Let Df = f and DC = C for convenience MRS (of any individual) = partial differential u/ partial differential f/ partial differential u/ partial differential c u(f, c) = f^2/3 c^1/3 partial differential u/ partial differential f/ partial differential u/ partial differential c = 2/3 f^-1/3 a^1/3/1/3 f^2/3 - 2/3 = 2 e/f M R S = p E/P c 2 c/p = p p/p c \r\n budget constraint of each pF(DF) + Pc(DC) = 6 pE + 3 PC or, PE + cpc = 6 pE + 3 pc or, f/a PF/PC + c = 6 pe/pc + 3 c = 2 pf/pc + 1 PF/PC c - 1/2 2) at arbitrary the equilibrium will satisfy the tangent condition so, 2 DC/DF = PF/PC or, DC/DP = 1/2 PF/PC

So, DF/DC= 2PC/PF= QF/QC