Overlapping and conflicting property rights

Property rights and property law play a key role in facilitating the creation of economic value. One key function of private property rights is the creation of incentives for internalising both positive and negative externalities. This privatisation of social costs and benefits reduces opportunities for - and incentives for - free-riding. This free-riding can manifest itself in very different ways. This section examines the most well-known benefit of private property rights: the virtues of single versus multiple usage and exclusion rights.

The key economic issues involved in overlapping or multiple usage and exclusion rights are best illustrated by the following simple example. Consider an economic asset, from which a valuable but depletable resource can be extracted. The asset replenishes itself in each period, but the extent of replenishment depends on the amount that is depleted in each period. The sustainable aggregate benefit of extraction is defined to be the (constant) aggregate benefit that can be obtained each year into the indefinite future.

Suppose that there are a large number of identical downstream firms which may extract the resource and use it as an input into production. To simplify matters, suppose that each firm either extracts one unit of the resource, or none. Let N denote the number of firms extracting at each point in time. This number N will be determined endogenously by the institutional arrangements that are in place.

Individual and aggregate extraction costs are normalised to zero. The individual and aggregate benefits of extraction vary with the number

Individual benefits

Figure 7.3.1 Individual benefits

of firms using the asset. The individual benefit in each period to each firm using the asset is b(N), with b(N) > 0, b'(N) < 0 and b"(N) < 0. Individual benefits as a function of N are shown in Figure 7.3.1. These properties of the individual benefit function reflect the assumption that the i ndividual benefit to each firm of using the asset is decreasing in the number of firms. This negative congestion-type externality could occur for a number of reasons. For instance, as more firms extract the resource, the likelihood of each firm being able to extract resources with an acceptably high quality could decline. Alternatively, in the more general case where there are positive extraction costs, for a given level of resource quality, per unit extraction costs could rise with the number for firms.

The aggregate benefit is:

At first, as more firms extract the resource, B(N) rises with N, so the social marginal net benefit B'(N) = b(N) + Nb'(N) > 0 for some N > 0.

However, as the number of firms N rises, at some point the sustainable benefit begins to decline, and thus the net present value of aggregate benefits also declines. This happens because the change in the marginal social benefit is:

Since there is a level of N where b(N)=0 [ and so B(N)=0 as well ], there must a point where we reach the maximum sustainable benefits of extraction, which we denote by B*. Let N* be the number of firms at which the maximum sustainable aggregate benefits of extraction are reached. That is,

Aggregate benefits

Figure 7.3.2 Aggregate benefits

B* = B(N*), with B'(N*) = 0, B'(N) > 0 for N < N* and B'(N) < 0 for N > N*. This is shown in Figure 7.3.2.

The economic question surrounding legal rules governing usage rights here is straightforward: what is the legal rule which provides incentives for the maximum sustainable aggregate benefits to be achieved? Consider the following three legal rules:

  • 1. Open access with overlapping usage rights: Under this arrangement, there are no restrictions on the usage rights of any firm.
  • 2. Private ownership with a single excluder: Under this arrangement, there is a single owner who can charge users a price P for the right to extract the resource, and who can also exclude those who do not pay this fee.
  • 3. Private ownership with multiple excluders. Under this arrangement, there are n > 1 upstream owners indexed by i = 1,...,n each of whom is permitted to charge users a price Pi for the right of downstream firms to extract the resource. Further, any one of the upstream owners can exclude a user who does not pay the fee Pi. Thus, each downstream firm must pay a total fee of P = ^n P, which is the sum of the individual fees charged by each owner.
 
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