Two firms are located adjacent to one another and each imposes an ex- ternal cost on the other: the detergent that firm 1 uses in it’s laundry business makes the fish that firm 2 catches in the lake taste funny, and the smoke that firm 2 uses to smoke its caught fish makes the clothes that firm 1 hands out to dry smell funny. as a consequence, each firms profits are increasing it its own production and decreasing in the production of its neighboring firm. in particular, if q1 and q2 are the firms’ production levels then their per-period (stage game) profits are given by
vi(qi, qj)=(30−qj)qi −qi2
(a) draw the firms’ best response functions and find the nash equilibrium of the stage
for i ∈ {1, 2}.
game. how does this compare to the pareto optimal stage-game profit levels?
(b) for which levels of discount factors can the firms support the pareto optimal level of quantities in an infinitely repeated game?