Two firms (Firm 1 and Firm 2) compete by simultaneously choosing output over an infinite horizon. Let qnbe the Nash equilibrium output from part 1(c)ii. Let qcbe half of the monopoly output, qc= qm/2. Consider the following grim trigger strategy:

set q = qcin the first period of the game or if both firms produced qclast period and in every previous period;

set q = qnotherwise - that is, if either firm has chosen any output other than qcin any previous period.

i. If both firms were to use this strategy, what profits would they each earn, c? (2 marks)

ii. If Firm 1 were to deviate from the grim trigger strategy, what is their optimal deviation output, qd, and what profit would they earn, d? (3 marks)

iii. For what discount factors (patience levels), , is this strategy sustainable (ie constitutes a subgame perfect Nash equilibrium)? (3 marks)

iv. Explain in words the meaning of your answer in part 1(e)iii. (2 marks)