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Unformatted text preview: Seminar Paper: Tariffs and Imperfect Competition Petre, Page 1 Tariffs and Imperfect International Competition Introduction We examine an international trade problem where two countries’ governments simultaneously decide import taxes assuming each country has one firm producing one good. The governments want to maximize social welfare and the firms want to maximize profits given the tariff rate decided by the other government. We use a dynamical programming approach to simplify this problem into two steps, first solving the firm’s problem in terms of tariffs and then solving the governments’ problem given the optimal quantities found in the solution to the firms’ problem. The Model Consider two identical countries, denoted g = 1,2 . In each country, we have a government choosing an import tariff rate and one firm producing a good to sell on both the home and foreign markets. Firm g produces ℎ G for sale in country g and ¡ G for sale in country ¢ . Consumers can buy an identical good from either market. Their demand function is characterized by £ G ¤¥ G ¦ = § − ¥ G . Consumers in country g demand some quantity which is the sum of the quantity of the good made in that country plus the quantity exported from the foreign country, that is, ¥ G = ℎ G + ¡ ¨ where ℎ G is produced in country g and ¡ ¨ is imported from country ¢ . The firms face constant marginal costs, c, and no fixed costs. Thus, there total cost functions are © G ¤ℎ G , ¡ G ¦ = ©¤ℎ G + ¡ G ¦ . Since the governments are imposing an import tax ª G , firms will incur tariff costs on their exports. That is, firm g will pay ¡ G ª ¨ to government ¢ . Governments simultaneously choose their tariff rates, ª « and ª ¬ . Firms observe these tariff rates and simultaneously choose ¤ℎ « , ¡ « ¦ and ¤ℎ ¬ , ¡ ¬ ¦ . Payoffs for the firms are measured as profits and payoffs to the governments are measured as total welfare. Total welfare is the sum of the consumer surplus, the profit for the country’s firm and the tariff revenue collected by that country as explained in Appendix 1. Therefore, the firm’s problem is to maximize ­ G ¤ª G , ª ¨ , ℎ G , ¡ G , ℎ ¨ , ¡ ¨ ¦ . The firm wants to maximize profits, where profits are a function of both countries’ taxes, and quantity supplied by both firms in each country. Similarly, the government’s problem is to maximize ® G ¤ª G , ª ¨ , ℎ G , ¡ G , ℎ ¨ , ¡ ¨ ¦ . We break the analysis into two steps. First, we solve the firm’s problem for ¤ℎ G ∗ , ¡ G ∗ ¦ in terms of ª G and ª ¨ . Then, we use these optimal quantities supplied by both firms in their home and foreign markets to solve the government’s problem. Solving the government’s problem yields optional tariff rates, ª G ∗ ....
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