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EC 391 – International Trade Spring 2025 Problem Set 1 Please, submit your problem set on Blackboard by Thursday, February 6th, at 9.30am. 1. Gravity. The World Development Indicators is a large dataset assembled by the World Bank, containing aggregate data for a large set of countries and a long time horizon. Visit: https://databank.worldbank.org/source/world-development-indicators and follow these instructions. Click on the “Country” tab, and select the following countries: Austria, Canada, France, Republic of Korea, Mexico, Norway. Click on the “Series” tab, and select GDP (constant 2015 US$). Click on the “Time” tab, and select the year 2016. Export and save the data. Keeping in mind the economic mechanisms at the hearth of the gravity equation in international trade, answer the following questions: (a) Do you think that Norway will export more to Austria or to France Why (b) Do you think that Canada will export more to Austria or to France Why (c) Do you think that Canada will export more to Mexico or to Korea Why Now we can check your answers examining bilateral trade flows data from Comtrade, a high- quality, worldwide trade flows dataset assembled by UNCTAD. Visit: 1 https://comtradeplus.un.org/TradeFlow Frequency=A&Flows=X&CommodityCodes=TOTAL&Partners=0&Reporters=all.=2022&AggregateBy=none&BreakdownMode=plus and follow these instructions. Under “Type of Product”, select “Goods” Under “Frequency”, select “Annual” Under “Classification”, select “HS -As reported” Under “Refine your search” choose “Periods (years): 2016”; “Reporters: Canada, Norway”; “Partners: Austria, France, Mexico, Rep. of Korea”; ”Trade flows: Exports”; “HS (as reported) commodity codes: TOTAL – Total of all commodities”. Under “Set your query options”, select ”Breakdown model classic” Select “Preview”. (d) Are actual bilateral trade flows consistent with your answers to the previous questions Why or why not 2. Consumer problem, homothetic preferences, demand. Assume preferences for food (f) and cloth (c) are described by the following Cobb-Douglas utility function: U(xc, xf ) = x α c x 1 α f (1) where α ∈ (0, 1). Denote by pc, pf the prices of the two goods, and by I a consumer’s income. (a) Write down the problem of utility maximization subject to the consumer’s budget con- straint. (b) Solve the maximization problem, i.e., compute the optimal consumption values x c , x f as functions of prices and income.1 (c) Compute the expenditure share in each of the good, defined by sj ≡ pjx j I , for j = c, f . Interpret your findings. (d) Compute relative demand: x c/x f expressed as a function of pc/pf . Cobb-Douglas prefer- ences are homothetic: does relative demand depend on income 1Hint: write down the first order conditions, combine them as I did in class, and use the resulting equilibrium condition together with the budget constraint to solve for x c , x f as functions of pc, pf and I. 2 (e) Consider two consumers, whose preferences are described by (1), and whose income levels are I1 = 10, and I2 = 20, respectively. Set α = 1/2, and prices pf = 1, pc = 5. Using your results from part (2b), compute the optimal quantities consumed of each good by each agent, x c1, x f1, x c2, x f2. Compute the total quantity demanded of each good, X j = x j1 + x j2, for j = f, c. Compute the relative total quantity demanded X c /X f . (f) Compute the optimal quantities Xˉc, Xˉf consumed by an “aggregate consumer” with income Iˉ = I1 + I2, and his relative quantity demanded, Xˉc/Xˉf . How do your results differ from the previous bullet point You have just shown the aggregation property of homothetic preferences. 3. Exchange in an Open Economy. Now we will look at trade patterns between two countries, say France and Germany. Agents in both countries have preferences over two goods – say cars and wine – described by: U(xc, xw) = x 1 3 c x 2 3 w (2) where xc (xw) denotes consumption of cars (wine). Let E G, EF denote the endowments of Germany and France, respectively. (You can interpret these endowments as production levels at a given point in time, assuming they are fixed). EG = (EGc , E G w ) = (10, 10) EF = (EFc , E F w ) = (10, 30) which means that Germany and France are endowed with the same number of cars, but France is endowed with more wine than Germany. (a) Compute the autarky relative prices pGc /p G w , p F c /p F w in the two countries. 2 (b) Draw relative demand for both countries on the plane (xc/xw, pc/pw). 3 Indicate the en- dowment points and autarky prices. (c) Compute the free-trade world relative price pTc /p T w, and indicate it in the same graph. (d) For each country, compute the optimal quantities consumed at the world relative price (normalize pw = 1 so that pc = pc/pw). 2Hint: remember that in autarky the total consumption of a country must be equal to its endowments. 3Hint: Cobb-Douglas preferences are homothetic. What does this imply for two countries that differ only in their endowments 3 (e) Compute imports and exports of each good for each country. What can you say about comparative advantage and trade patterns (f) Do consumers gain from opening to trade