Two firms produce identical widgets.

The price function is P (q) = (150 − q) + and the cost to produce q widgets is C(q) = 120q − 2 3 q 2 for each firm.
(a) What are the profit functions for each firm?
(b) Find the Nash equilibrium quantities of production.
(c) Find the price of a widget at the Nash equilibrium level of production as well as the profits for each firm.
(d) If firm 1 assumes firm 2 will use it’s best response function, what is the best production level of firm 1 to maximize it’s profits assuming firm 1 will then publicly announce the level. In other words they will play sequentially, not simultaneously