Crude oil is transported across the globe in enormous tanker ships called Very Large Crude Carriers (VLCCs). By 2001, more than 92% of all new VLCCs were built in South Korea and Japan. Assume that...

Crude oil is transported across the globe in enormous tanker ships called Very Large Crude Carriers (VLCCs). By 2001, more than 92% of all new VLCCs were built in South Korea and Japan. Assume that the price of new VLCCs (in millions of dollars) is determined by the function P 5 180 2 Q, where
  (That is, assume that only Japan and Korea produce VLCCs, so they are a duopoly.) Assume that the cost of building each ship is $30 million in both Korea and Japan. That is,
 30, where the per-ship cost is measured in millions of dollars.

(a) Write the profit functions for each country in terms of
  and either

Find each country’s best-response function.

(b) Using the best-response functions found in part (a), solve for the Nash equilibrium quantity of VLCCs produced by each country per year. What is the price of a VLCC? How much profit is made in each country?

(c) Labor costs in Korean shipyards are actually much lower than in their Japanese counterparts. Assume now that the cost per ship in Japan is $40 million and that in Korea it is only $20 million. Given c_Korea
= 20 and c_Japan
= 40, what is the market share of each country (that is, the percentage of ships that each country sells relative to the total number of ships sold)? What are the profits for each country?