A firm operates and produces pollution that only harms an individual, Bob. The firm and Bob both ...

If the firm has the right to pollute, then Bob can bargain with the firm. Bob will pay the firm up to the point where his per unit payment to reduce the pollution equals the marginal benefit he receives from pollution. This will be the efficient level of pollution. If Bob has the right to have no pollution, then the firm will pay to pollute until this cost equals the marginal benefit of a unit of production. This will result in the efficient level of pollution. Thus, no matter which party owns the property right, the efficient level of pollution will result.

Perfect