Assignment of Property Rights

Another understanding of optimality situation is that there is an omitted market i.e. market for pollution. Externality problem arises because steel firm is facing 0 price for pollution. In order to create market for pollution, property rights can be assigned either to steel firm or fishery firm. Price of pollution traded is q and fishery firm has property right to have clean water. Therefore, profit maximizing conditions can then be written as:
Steel firm’s = PSS – CS (S, x) –qx (1)
Fishery firm’s = PFF – CF (F, x) – qx (2)