Extending the previous problem, suppose China decides to enter the VLCC construction market. The duopoly now becomes a triopoly, so that although price is still P = 180 - Q, quantity is now given by Q...

Extending the previous problem, suppose China decides to enter the VLCC construction market. The duopoly now becomes a triopoly, so that although price is still P = 180 - Q, quantity is now given by

Q = q_Korea
+ q_Japan
+ q_China. Assume that all three countries have a per-ship cost of $30 million:

c_Korea
= c_Japan
= c_China
= 30.

(a) Write the profit functions for each of the three countries in terms of

q_Korea, q_Japan, and q_China, and c_Korea, c_Japan, or c_China. Find each country’s best-response rule.

(b) Using your answer to part (a), find the quantity produced, the market share captured [see Exercise S8, part (c)], and the profits earned by each country. This will require the solution of three equations in three unknowns.

(c) What happens to the price of a VLCC in the new triopoly relative to the duopoly situation in Exercise S8, part (b)? Why?