Simple Ricardian Model (20 marks) Consider a small country that produces two goods: cloth (Qc) measured in bolts and wine (Qw) measured in barrels. The unit labour requirement for a bolt of cloth is 4 days of labour (aLC) and the unit labour requirement for a barrel of wine is 2 days of labour (aLW). If the total available labour is 400 days and the social welfare function for this country is W = Qc Qw, (a) Calculate the equilibrium quantities produced and consumed in autarky, the level of welfare achieved (W), and the amount of labour provided in each good (i.e., Lc and Lw). Graphically illustrate this equilibrium [cloth on the X-axis and wine on the Y-axis] and be certain to identify and properly label your diagram. (10 marks) (b) Suppose this nation now faces an international trade pricedefined as (Pc/Pw)Tof 4. Calculate the new equilibrium consumption of cloth and wine and the new level of welfare. Identify the pattern of tradethat is how much (and what good) is exported and how much (and what good) is imported. Using the same graph from part (a), graphically illustrate this new equilibrium. (10 marks) B2. Relationship Between K/L Ratios and their Factor Prices (10 marks) Consider a nation that has constant returns to scale (CRS) in the production of cloth in the generic form of:where, Qc = bolts of cloth; Kc = units of capital in the production of cloth: Lc = units of labour in the production of cloth; and . Show, at equilibrium levels of production, the precise relationship between the capital-labour ratio and the wage (w)-rental (r) ratio. That is, derive the generic relationship: (Hint: Use Lagrangian for firms decision-making process) (10 marks) B3. Two-factor, Two-good, Two-nation Model (30 marks) Consider a small country that produces two goods: cloth (Qc) measured in bolts and wine (Qw) measured in barrels. The total amount of labour is 2 million (L = 2) workers and the total amount of capital is 4 million (K = 4) units. The production functions for cloth and wine are:and the social welfare function is given as: (a) Derive the production possibilities frontier and calculate the first and second derivatives in order to determine its shape. (5 marks) (b) Determine the autarky equilibrium; calculate the equilibrium levels of cloth and wine produced/consumed, the autarky price ratio , and the level of social welfare. (10 marks) (c) Suppose the country can trade at the given world prices of cloth and wine:With free trade, i. calculate the new production of cloth and wine. (5 marks) ii. calculate the new consumption of cloth and wine. (5 marks) iii. what is the pattern of trade (i.e., quantities exported and imported) and show that free trade is beneficial for this nation. (5 marks)
Use the order calculator below and get started! Contact our live support team for any assistance or inquiry.
[order_calculator]