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Homework 1 - ARE 138 Winter 2011 M Whitney HOMEWORK 1 Due...

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Unformatted text preview: ARE 138 Winter 2011 M. Whitney HOMEWORK 1 Due at start of class Thursday, Jan 20th (16 ) 1. Two regions have the following supply and demand functions for a good: D"s=5000-50P"S S"5=-2000+100P“s DF=4000-80PF sF=-1,000+ 1500 PF a.(4) Assuming autarky (no trade possible), find the minimum, maximum and equilibrium price in each market, and the quantity produced /consumed. b. (6) If trade is opened, who will import and who will export? What range will the world price fall within? (verbal answer, before solving). Derive the import demand and export supply curves for this range of prices (write their formulas), checking to see whether either function is kinked in the relevant price range. Now, solve for the equilibrium world price. How much is produced, consumed, and exported or imported, in each country? c. (6) Sketch the import demand and export supply curves from part c, for the relevant price range. What is the net effect of flee trade on each region's total social welfare? On world social welfare? Who gains, and who loses from trade within each country (verbal answer)? 2. (l 8) A small country has the following demand and supply for a good: (h refers to home country) D”: 10,000 - 1,000 P“ 8s = -2,000 + 2,000 P” a. (2) Find the maximum price, minimum price, market price and quantity under autarky. b. (12) Now suppose free trade is allowed. (country can trade at world price PW). Under what price condition will the firm become an exporter? Derive the country's export supply firnction, showing the equation for each segment of the supply function, the price range it applies to, and the quantity of exports that corresponds to the ’kink“. Under what price condition will the firm become an importer? Derive the country's import demand function, showing the equation for each segment of the function, the price range it applies to, and the quantity of imports that correSponds to the kink c. (4)Using your answer from part b, find the quantity exported or imported by the home country, for the following world prices: $12, $7, $3 and $0.50. 3.(10) Imagine US demand for sugar is D“5 = 7,680 - 21,000 P, and domestic sugar supply is Sus = -320 + 4000P. Outside the US, the world sugar supply is perfectly elastic at PW = $0.12. a. What is the US sugar price, quantity, and producer and consumer surplus under autarky? b. How much would be produced and consumed in the US if fiee trade was allowed? (Assume the US is a “small country” relative to the world sugar market). Now what are PS and CS? What is the US net welfare gain from trade? Who is likely to oppose this trade liberalization policy? c. Now assume the US allows sugar imports as in part b, but charges a tariff of $.10/lb. on imports. Find the new US sugar price, production, consumption and PS and CS. Also, how much revenue does the US government make from the tariffs collected? d. What import quota could the US set to achieve the same domestic sugar price as in part c? In what way might social welfare differ as compared with the tariff result in part c? (6) 4. Imagine three countries have the following factor endowments: Country A Country B Country C Farmland 4000 200 100 Labor 1000 600 200 Capital 2000 300 600 These nations produce three products: grain (farmland-intensive), hand-knotted wool rugs (labor~ intensive) and heavy equipment (capital-intensive) 3. Calculate K/A, HA and K/L for each country. b. According to the Heckscher-Ohlin model, what general patterns of trade do you expect to see between these countries? ...
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