Department of Economics University of Michigan Winter 2020 Economics 441 Econ 441: International Trade Prof. Dominick Bartelme Winter 2020 Problem Set 4 March 17, 2020 Due on Tuesday, April 21 by midnight (11:59 pm) via Canvas. You are required to submit your answers in a single PDF file. Please, write your full name and umich id on your problem set. Please, pay attention to the organization of your answers. Always keep the order of the questions, write legibly, and clearly indicate what you are doing. Please staple your answer sheets together. Don't forget: the grader can only give you credit if they can read and comprehend what you have written. After derivations that need several steps, always mark your final answer clearly: put a box around it, underline it or highlight it. You should aim for brief, concise explanations. 1 Optimal Import Tariffs This question asks you to work through an example of optimal trade policy when an importing country wants to manipulate its terms of trade. Consider an importing country that faces a foreign export supply curve XS = a + b P , where XS is the export supply, P is the price that foreigners recieve for their exports, a is a negative constant1 and b is a positive constant. Recall that foreign exports equal domestic imports M . 1. Write down the formula for the optimal tariff (as a percent of the price) t/P (Hint: see lecture). 2. Find the elasticity of the foreign export supply curve \u000fS (P ) for an arbitrary value of P . Express your answer both in terms of Xs and a alone, and in terms of P , a and b alone. 3. Is \u000fS increasing, decreasing, or constant in the domestic imports M (hint: in equilibrium, XS = M )? What does this imply for how small and large importers should set their import tariffs? 4. Explain the intuition behind your answer to part 3. 1 Interpretation: at a zero price, foreigners want to import from us. 1 Department of Economics University of Michigan 2 Winter 2020 Economics 441 Subsidies in Strategic Trade Policy This question asks you to show that the optimal unilateral subsidy in the strategic trade policy setting is always positive. We will take the example of Boeing and Airbus used in lecture, with all the same parameters. 1. The E.U. government's objective is to maximize domestic profits less the cost of the subsidy. Write down the E.U.'s maximization problem as a function of the chosen quantities of Airbus and Boeing, QA and QB . Hint: see the lecture notes. 2. Substitute the price and the optimal quantities, given the E.U. subsidy, in the expression above to find the E.U. maximization problem as a function of sA , a, b and c. Assume the U.S. does not subsidize. Hint: see the lecture notes. 3. Differentiate the government objective with respect to sA . Hint: use the product rule of differentiation. 4. Show that the optimal subsidy is positive (Hint: assume a > c and explain why this makes sense) . 5. Give the intuition for part 4. 2