Eliminating pollution completely implies that production has been reduced to zero. Thus, it would not be a rational decision to reduce the output to zero to eliminate pollution completely.
Government must strike balance between the benefits arise from output and pollution cost associated with output.
Firms must be compelled to operate where Marginal social benefits are equal to marginal social cost.
Margnal social benefit = Marginal social cost.
Or
Marginal Benefit of output = Marginal Cost of pollution arising from output.
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