The public smoking of cigarettes generates costs to society from second-hand smoke, therefore, cigarette production imposes costs on people who do not smoke. Moreover, private consumption of cigarettes can start apartment building and wild fires that also impose costs on non-smokers. Luckily, fire extinguishers can help prevent the spread of fires.

Suppose that the government can institute either a tax on cigarette producers, or a subsidy to cigarette producers, to bring the private production costs in line with social costs. Identify where the socially optimal equilibrium would be.