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Assume that two countries, A and B, produce steel for export markets. Steel from both countries is regarded by world buyers as perfectly substitutable (so that steel from each country has to sell at the same price in the world market). To make the analysis easier, assume that there is only one steel producer in each country. Assume also that the marginal cost of producing a ton of steel in country A is $10 and in country B it is $11.
(a) If the two countries' producers play a Bertrand game in the export markets, what would be the Bertrand-Nash equilibrium price of steel?
(b) Now assume that the two countries are engaged in Cournot competition in the steel export market. With this assumption, can you calculate the world price of steel if the world (inverse) demand for steel is given by p = 100 - X, where X is the total supply of steel into the world market. [Hint: write down first order conditions for profit maximization for each steel producer. This will give you two equations in two unknowns (which are each country's steel output). You can then solve for Cournot-Nash equilibrium output supplies.]
(c) Calculate shares of steel exports going to each country in the Cournot-Nash equilibrium. Now assume that country B decides to subsidize its country's steel export to the amount of $1 per ton. What will be the share of world exports of steel going to country B's manufacturer? What will happen to country A's exports of steel? What will happen to world price of steel?
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