Consider a Stackelberg duopoly: Firm 1 chooses their quantity q1 first; Firm 2 observes q1 and then chooses their quantity q2. The market price is p = 30 - q1 - q2. Firm i's costs are Ci = 5qi. Firm i aims to maximize profits πi = (p - 5)qi.
a.) Find the subgame-perfect Nash equilibrium quantities in the game described above.
Suppose now that initially, before Firm 1 chooses their quantity, Firm 2 can publicly decide whether or not to invest in a technology that reduces their costs to zero, i.e., Firm 2's cost function becomes C2 = 0. Firm 1's cost function remains unaffected, i.e., C1 = 5q1. The technology costs 50. After the investment decision, the game proceeds as in part (a) (except with the new cost function for Firm 2, if they chose to invest).
b.) Does Firm 2 invest in the technology in the subgame-perfect Nash equilibrium of the game?