For the purpose of these exercises, let the firm's profits be given by P(x) = 20x - x^2, and let damages be given by D(x) = 2x^2.

You are asked to describe equilibrium outcomes for this economy under several alternative regulatory and/or legal regimes. For each of the situations described below, compute the following quantities:

Level of output x

Producer surplus, which equals profits, plus the net effects of any taxes, subsidies, or side-payments agreed to under the terms of a contract with the consumers; and Net damages to the consumer, likewise net of any payments made to or received from the polluting firm or the government.

3. A regulator imposes a unit Pigovian tax on pollution at the level t=2 per unit.

4. Same as (3), but the government returns to tax revenues collected to the consumers.

Can someone explain this to me?