Polluting emissions generate a negative externality. The total external costs of emissions are described by the following function: EC(M) = 3/8M². The true benefit of pollution arising to the polluter (unknown to the government) is described by the following function: BT(M) = 10M - 7/8M².

However, there is uncertainty about the actual marginal benefits of pollution. The government believes (wrongly) that the benefits of pollution are described by the following function: BG(M) = 5M - 3/4M².

1. Identify the maximum level of pollution from the true benefit function and the socially optimal level of emissions.
2. Identify the pollution target that the government would set according to the information it has about the marginal benefits of pollution.
3. Suppose there is just one polluting firm. The government sets an overall pollution target (enforced by means of command-and-control regulation) based on its information about the marginal benefit of pollution (as computed in point (b). Provide a graphical representation of the welfare loss with respect to the social optimum that is caused by imperfect information about the marginal benefits of pollution
4. Instead of an overall pollution target, the government could opt for the introduction of a Pigouvian tax. Compute the tax that the government would set according to the information it has about the marginal benefits of pollution.
5. Compute the level of pollution that would (actually) emerge by applying this Pigouvian tax.
6. Compute the welfare loss that emerges when setting a Pigouvian tax (based on incorrect information about the MB) with respect to the social optimum and compare this welfare loss (graphically and numerically) with the one generated by the command-and-control regulation.