Question: Total pollution control cost functions for two firms are given respectively, as TC _ 1 = 4 0 + 2 4 ( q _

Total pollution control cost functions for two firms are given respectively, as

TC $_1 = 40 + 24 ($ q $_1)^2$

TC $_2 = 40 + 8 ($ q $_2)^2$

where q $_1$ and q $_2$ are the amounts of emission reduced by the firms. With no control, each firm omits $40$ units of emission. Assuming no significant transaction costs

Explain briefly cost $-$ effective allocation of control responsibility. Find how many units of emissions each firm will reduce under such an allocation

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