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 . 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)).
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