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 isQ=80p

. The domestic supply isQ=2p10

and the foreign country's export supply isQ=3p6

.

(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 ratet

. (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 WeasleytRW

? Explain the intuition in one sentence. (2 points)

(b) Calculate the total consumer surplusCS

andthe total producer surplusPS

, 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 byMr. PottertHP

? AndtDM

for Mr. Malfoy? (2 points)

(d) AmongtDM

,tHP

,tRW

, which one is the highest? Is it the same ast

? 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)