Big Earth and District 13 are two producers of neodymium, a rare earth. If they agree to restrict output, each firm earns $100 million per year. If both firms expand output, each firm earns $50 million per year. If one firm restricts output and the other firm expands output, the firm that expands output earns $150 million per year and the other firm earns only $30 million per year. Assume that Big Earth and District 13 will compete infinitely, with each firm following a grim trigger strategy. Which of the following statements is TRUE?
A) If d = 0.50, Big Earth is indifferent between agreeing to restrict output and expanding output.
B) If d = 0.40, Big Earth would be better off restricting output.
C) If d = 0.90, Big Earth is indifferent between agreeing to restrict output and expanding output.
D) If d = 0.75, Big Earth would be better off by expanding output.

Question

Quizplus · Accepted Answer

Under the grim trigger strategy, if one firm cheats (expands output), the other firm will also cheat in all future periods. Therefore, if Big Earth restricts output and District 13 expands output, Big Earth earns only $30 million per year, which is less than the $50 million it would earn if it also expanded output. On the other hand, if Big Earth also expands output, both firms earn only $50 million per year. Therefore, in this scenario, neither firm has an incentive to cheat. 
The critical discount factor (d) at which the firms are indifferent between restricting output and expanding output is:
100 + 100d = 150d + 30
d = 0.5

Therefore, for d = 0.50, choice A is true: Big Earth is indifferent between agreeing to restrict output and expanding output.

Big Earth and District 13 Are Two Producers of Neodymium