ONLY QUESTION 2 and 3 need to be answered
Question 1: The Optimal Tariff Rate (13 points) Suppose home country Hogwarts is a big country and is a net importer of Bezoar. The demand for Bezoar in the home country is @ = 80 - p. The domestic supply is @ = 2p - 10 and the foreign country's export supply is Q = 3p -6. (a) Find the free trade equilibrium, i.e., the equilibrium world price, quantity of domestic demand, quantity of domestic supply, and the quantity of imports. (2 points) (b) Suppose the home country decides to impose a tariff of $t per unit on imports of Bezoar. Derive the new equilibrium, express the following as formulas of t, the world price, the domestic price, the quantity of domestic demand, domestic supply, and the quantity of imports. (4 points) (c) Explain the three changes in national welfare. Write down a mathematical expression for the total change in national welfare as a function of the tariff rate t, in comparison with the free trade scenario. (4 points) (d) Give an analytical or mathematical argument for why the optimal tariff is greater than zero. (1 points) (e) Calculate the optimal tariff rate {*. (2 points)Question 2: Who could benefit from a positive tariff? ( 10 points) Now we continue to use the set up in Question 1 to try to understand who could benefit from a positive tariff. In this question, we will look at the preferred tariff rate of the individuals in Hogwarts. For simplicity, suppose three are only three individuals, Ron Weasley, Harry Potter, and Draco Malfoy. These three are consumers of Bezoar, and we assume that they share the consumer surplus equally. The ownership of the domestic producing firm, Hogwarts Bezoar Tech, is split among the three. Poor Ron Weasley does not own any shares, Harry Potter owns 20% of the firm, and the rest of the ownership belongs to Draco Malfoy. This ownership split creates income inequality in their world. (a) What will be tariff rate preferred by Ron Weasley tRw ? Explain the intuition in one sentence. (2 points) (b) Calculate the total consumer surplus CS and the total producer surplus PS , as functions of tariff t. (2 points) (c) Suppose one person's utility is the sum of his share of CS and his share of PS. Calculate the utility for Mr. Potter and for Mr. Malfoy. What is the tariff rate preferred by Mr. Potter tup? And toy for Mr. Malfoy? (2 points) (d) AmongtDM . tup, tRw, which one is the highest? Is it the same as *? Explain in one sentence why it is the same (or not). (2 points) (e) By the theory of electoral competition, policy will converge to the one preferred by the Median voter. Who has the median tariff preference? Thus what will be the tariff rate picked by the Hogwarts government? (2 points)Question 3: Is optimal tariff rate optimal? ( 10 points) In this question we continue our discussion in Question 2 but consider a slightly different setting. Here we assume that (i) Mr. Malfoy owns 100% of Hogwarts Bezoar Tech and the other two gentlemen owns nothing; (ii) Mr. Malfoy himself does not consume Bezoar! Thus we only have two consumers, Mr. Potter and Mr. Weasley. (a) What is the preferred tariff rate for each individual now? Suppose the government follows the median voter rule, what tariff rate will the government pick? Suppose Mr. Malfoy is filthy rich that he could buy off the government, will the tariff rate change then? (4 points. ) (b) We have not considered possible responses from the foreign country. Suppose the foreign country could set positive tariff rates on imports from Hogwarts as well. We may use a PD (prisoner dilemma game) to understand this strategic situation: Hogwarts\\Foreign country Free trade Positive tariff Free trade (10, 10) (-10,20) Positive tariff (20, -10) (-5,-5) Note: This table represents the same information as Table 10-3. According to the table, what do you think Hogwarts will choose if the foreign country chooses "free trade"? What will Hogwarts choose if the foreign country chooses "positive tariff"? Therefore, what do you think will be two countries' choices in the equilibrium? Is it a desirable result? (4 points) (c) The situation in (b) represents a single period of time. In practice, how can countries avoid the (Positive Tariff, Positive Tariff) result over a multi-period game? (2 points)
