Private ownership with a single, non-overlapping exclusion right
Under this legal rule, there is a single individual owner of the upstream owner (or group of owners who act as a single owner). The upstream owner can charge users a price P for the right to extract the resource, and can exclude those who do not pay this fee.
Let N be the number of users that the owner allows to exploit the resource. Each individual downstream firm once again compares its marginal private benefit with private marginal cost. For any N, the marginal private benefit accruing to each downstream firm is again simply the individual benefit b(N), which is equal to the average benefit:
We again assume that this is positive but declining with N. Once again, the average benefit curve is the aggregate demand curve or willingness to pay curve for usage rights. That is, the aggregate demand curve is:
The upstream owner's revenue (and profit) from selling usage rights is:
Choosing the number of users to maximise this profit yields:
But since we also have B'(N*) = 0, this means that N° = N*. The profit- maximising outcome under single ownership is also the efficient outcome, which maximises the sustainable benefits of extraction.
Why is private ownership efficient here? As we showed in the previous section, under the open access rule, each user imposes an unpriced negative externality on the other users and this led to overexploitation. Under private ownership with non-overlapping exclusion rights, however, overexploitation reduces the upstream owner's profit. The pursuit of profit induces the owner to set a usage fee of:
which is exactly equal to the external cost (which was previously unpriced), evaluated at the efficient N. The usage fee is exactly equal to the efficient Pigouvian tax. Each downstream user pays a fee so that the revenue gain to the upstream owner just offsets the loss to the upstream owner from allowing another user to enter. In other words, the external effect still exists, but it is no longer Pareto relevant: the single upstream owner completely internalises it and it is now priced efficiently. In this instance, the 'invisible hand' and the pursuit of profit combined with an appropriate legal rule solves the tragedy of the commons. This shows that it is not competition and the unfettered pursuit of profit per se that are the sources of the original efficiency. The source of the problem lies in overlapping usage rights.