The Coase Theorem, named after Nobel laureate Ronald Coase, states that in the presence of an externality, private parties will arrive at an efficient outcome without government intervention. According to the theorem, if trade in an externality is possible and there are no transaction costs, bargaining among private parties will lead to an efficient outcome regardless of the initial allocation of property rights

The Coase theorem is a method of tackling the inefficiency caused by an externality, by awarding property rights to the externality to one party and allowing the parties concerned to bargain their way to an efficient solution. In the case of a negative externality such as pollution, the property right to pollute could be awarded to the polluter, and the victim of the pollution would have to offer to pay to get the polluter to reduce their output. Alternatively, the property right to clean air/water/whatever else is being polluted, could be awarded to the victim, so the polluter would have to offer to pay the victim to be allowed to pollute.

Consider the situation where we have a firm, firm A, producing some good in a competitive market that causes some pollution as a result of its output. Another firm, firm B, which produces a different good in a different market, is directly harmed by this pollution. It could be something like A being a factory and B being fisheries, and the factory pollutes the water and reduces the number of fish.

Anyway we consider the market for firm A. We said that it was a competitive market so it is aprice taker , it faces a horizontal demand curve at the market price, Pc, and can produce as much output as it likes at this price. As the market price is constant and does not vary depending on the output the firm produces, the marginal revenue is also equal to the price. Assume as well that firm A faces an upward sloping (private) marginal cost curve, the more output it produces, the greater its marginal costs.

Firm A will produce up to the point where its marginal revenue equals its private marginal costs, here MR=PMC at Qc, the competitive output quantity.

However also on that diagram is a social marginal cost curve (here ‘society’ includes firm A and firm B), this is higher than A’s PMC curve because it includes the cost of the externality (the pollution) on firm B. By producing at Qc, firm A is producing output above the social optimum. This is because the joint benefit as a result of this output is simply the total revenue gained by firm A (Pc x Qc), firm B does not get any benefit. But the joint social cost is greater. The cost to firm A is (Pc x Qc), and the cost to firm B caused by the externality is ((SCc – PC) x Qc), making the total social cost (SCc x Qc). As (SCc x Qc) > (Pc x Qc) then there is a net loss incurred by this level of production.

The Coase solution offers us two options, either we could

i) Award firm A the right to pollute or

ii) Award firm B the right to clean