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.

Compute these three quantities under each of the following regulatory/legal regimes.

1. Consumers are awarded a transferable property right to clean air. The firm must reach a negotiated agreement with consumers before any production can begin. The firm and the consumer reach a contract that specifies two terms: an allowable maximum level of pollution x, and the amount A of a payment that the polluting firm must make to the consumer.

2. Same as (1), except property rights are awarded initially to the polluting firm.