Two rms, called Polluter 1 and Polluter 2, produce good A. The production of A adversely affects the prots of a third rm, called Victim, which...

Two firms, called Polluter 1 and Polluter 2, produce good A. The production of A

adversely affects the profits of a third firm, called Victim, which produces the good

V .

1. Two firms, called Polluter 1 and Polluter 2, produce good A. The production of Aadversely affects the profits of a third firm, called Victim, which produces the goodV. The profits of the three firms are as follows, Where in denotes Polluter 1’s profit’s,7r2 Polluter 2’s, and 7r” Victim’s. 7r1 =6A1 —A§ 1T2 : 16A2 — 2.4%711,, = 12V — 3V2 — CA2 where c > 0 and A : A1 + A2. Suppose the government recognises that the Polluters’ production of A imposes anegative externality on Victim, and to try to remedy this, mandates that Victim cancharge the Polluters a price of P for every unit of A that they produce. Once thiscompensation scheme is in place, the government observes a total of A = 4 beingproduced. Find 0, and the A1 and A2 that are produced under the compensationscheme. (Assume all three firms are price-takers (i.e. they take P as given)).