8.2 The distributive effects of regulating common property

Back to contents - Previous file - Next file

In this section, we investigate the distributive impact of regulating common property. We assume that regulation enhances income through the increased efficiency it is supposed to bring about in the management of the resource. We assume furthermore that this is correctly perceived by the agents concerned: they fully anticipate the gains associated with regulation. Otherwise, they may (wrongly) expect that regulation will decrease their expected income and they will oppose it.

Regulation with heterogeneous resource users

A well-known statement of the problem of heterogeneity in regard to collective action potential is due to Johnson and Libecap (1982) who analysed the cause of failure of cooperative mechanisms for catch restriction in the overcapitalized shrimp industry of Texas, USA:

Contracting costs are high among heterogeneous fishermen, who vary principally with regard to fishing skill. The differential yields that result from heterogeneity affect the willingness to organize with others for specific regulations. . . regulations that pose disproportionate constraints on certain classes of fishermen will be opposed by those adversely affected . . . Indeed, if fishermen had equal abilities and yields, the net gains from effort controls would be evenly spread, and given the large estimates of rent dissipation in many fisheries, rules governing effort or catch would be quickly adopted. .. For example, total effort could be restricted through uniform quotas for eligible fishermen. But if fishermen are heterogeneous, uniform quotas will be costly to assign and enforce because of opposition from more productive fishermen. Without side payments (which are difficult to administer), uniform quotas could leave more productive fishermen worse off' (Johnson and Libecap, 1982: 1006, 1010).

Treading the same way as Johnson and Libecap, Kanbur (1992) has recently attempted to demonstrate formally that, when agents are not identical and their differences get reflected in their assigning divergent (marginal) values to a natural resource, the income increment achieved through a co-operative agreement maximizing the sum of their payoffs will differ among them. Moreover, for some individuals there might even not be an increment at all: under certain conditions, co-operation will require some users to restrict exploitation and the others to intensify exploitation relative to the Nash equilibrium.

Since the example constructed by Kanbur is faulty, we present an alternative formulation of the problem from which it comes out that at the optimum the 'small' users (those with a lower level of exploitation of the CPR in the unregulated situation) may be worse off than in the decentralized, inefficient equilibrium. (In Kanbur's example, the opposite conclusion was attained: rather paradoxically, the technically more efficient (and large) users were losing when the optimal regulation without transfers was followed.) Consider two individuals, indexed I and 2, choosing harvesting efforts y1 and y2 that yield payoffs R. and R2, as given below:

(1), (2)

The payoff functions embody a negative externality: each individual's action affects the payoffs of the other individual adversely. They also contain an asymmetry in the parameters a1 and a2 to indicate that the marginal value of the action differs between the two individuals. One way to interpret the above equations is to construe the first term as private net benefits and the second term as a common social cost that depends on joint exploitation of a given natural resource. The Nash equilibrium values, superscripted by N. are thus:

(3), (4)

Assuming that a1 = 2 and a2 = 1, we obtain the following individual levels of exploitation and corresponding payoffs: y1N = 0.6, y2N = 0.2, R1N = 0.52, R2N = 0.06.

By contrast, the efficient solution requires that (R1 + R2) is maximized. With the above parameter values, it turns out that y2 must be equal to zero (y2C = 0): in other words, efficiency would require user 2 to be prevented from access to the resource. In that case, the efficient solution is obtained by maximizing R1 alone. Setting both y2 and R2 to zero, we then get: y1C = 1, and R1C = 1. A comparison of these two sets of results shows that individual 1 gains from regulation and that the total level of resource exploitation is actually increased. This apparently paradoxical outcome obtains because the comparative inefficiency of user 2 is so high (at the Nash equilibrium, the net income of user 2 is only 11% of that of user I while his comparative level of resource use is 1/3 ) that joint exploitation of the resource imposes considerable sacrifices on the more efficient user. Evidently, if heterogeneity in resource use efficiency is less, the room for conflict regarding regulation is considerably narrowed down. For instance, if all users are identical, they will all benefit from regulation. Or, if a1 = 2, and a2 = 1.8, y1N = 0.51, y2N = 0.46, R1N = 0.29, R2N = 0.17, while y1C = 0.36, y2C = 0.29, R1C = 0.38 and R2C = 0.23. In the latter case, therefore, both users increase their payoffs by moving from Nash to regulated equilibrium.

With regard to the illustration provided by Johnson and Libecap, an interesting question in the above analytical framework is what happens if regulation takes the form of a uniform quota imposed on all users. Such a solution may be appealing because of its inherent simplicity. In our example, when a1 = 2 and a2 = 1, we find that, at the regulated equilibrium, the uniform quota maximizing the sum of the two individual payoffs is equal to 0.27. The corresponding payoffs are, respectively, 0.32 and 0.09. Clearly, the most efficient user is worse offend the less efficient user is better off than under the Nash equilibrium situation (and, consequently, than under the unconstrained regulated equilibrium). This result also holds when a1 = 2, and a2 = 1.5 (the uniform quota is equal to 0.30, and the payoffs are respectively 0.33 and 0.20), yet there is some minimum level of heterogeneity in resource use efficiency below which it ceases to be true.

To conclude, the main implication one can draw from the analysis proposed here is that, where agents are heterogeneous, regulating the commons efficiently may cause conflicts of interest to erupt. Following the analysis proposed by Fernandez and Rodrik (1991), we now show that regulations that, once adopted, would be supported by a majority of users may in fact be opposed by a majority of the same users before it is implemented. Conversely, reforms that are detrimental to many e* post may appear ex ante as beneficial to a majority of voters. These will be adopted, but, once implemented, will be rejected and a return to the initial situation will occur. As a consequence, majority voting leads to a status quo bias. The rationale which underlies this counter-intuitive result is the following: in all reforms, there are losers and winners, some may know that they will win, but an important number of voters do not know what their own individual situation will look like after the reform. If their expected income is negative, they will vote against it. In other words, ex ante uncertainty about the identity of the winners from the reform may lead to its rejection, even though, if adopted, the reform would have benefited a large majority of people.

Regulation with uncertainty about the identity of the winners

Let us consider a simple example (for a fuller analysis, see Fernandez and Rodrik, 1991), in which all agents are risk-neutral and identical, except that a fraction of them anticipate that they will win, while the others are uncertain about their future, post-reform situation. Suppose, for instance, that regulation is achieved through (randomly) excluding some members, say n, from the collective ownership over the resource, increasing the collective income from Y to Y' with Y' > Y. (Other ways of regulating the resource can be easily imagined to fit in with the example below.) Let M stand for the minority of agents who know that they will not be excluded, with M < N - n, where N stands for the initial number of agents sharing collective ownership over the resource. It is evident that (n/N - M) represents the probability for an uninformed agent to be excluded by the regulation measures. His expected gain in income resulting from regulation is therefore equal to ( Y'/N - n) (N - M - n/N - M) - Y/N which may be positive or negative. If it is positive, the regulation is adopted, n users get excluded, and the (N - n) remaining users support the reform. If it is negative, then a majority of users oppose the regulation proposed, even if, ex post, (N- n) > N./ 2 (that is, even if, were the reform implemented against the will of a majority of users, ex post, a majority would vote for its continuation). In other words, 'there are reforms which, once implemented, will receive adequate political support but would have failed to carry the day ex ante. The argument does not rely on risk-aversion, irrationality, or histeresis due to sunk costs' (Fernandez and Rodrik, 1991: 1146).

To give a numerical example, suppose that the regulation considered reduces the number of users from 100 to 60, while the income per user increases from 10 to 20 units. Total income therefore rises from 1,000 to 1,200 units. Suppose also that thirty users know in advance that they will not be excluded. Ex ante, if such a reform is proposed to the users, seventy among them will oppose it since their expected gain associated with it is negative: (30/70) x 20 - 10 = 10/7 < 0. However, if the reform is implemented, the remaining users will oppose a return to the initial situation. Graphically, we have the situation represented in Figure 8.7.

The question may now be asked as to whether it is possible, when regulation increases the expected income of each user, that it will still be opposed by a majority of users and, therefore, be blocked. There are two different kinds of argument pointing to a positive answer to this question. The first one is based on risk-aversion, the other, on private information problems. In the following, we will develop these two arguments successively by first analysing the case where regulation takes place through the exclusion of some agents. Thereafter, we will analyse the case where regulation is achieved through appropriate taxation or through remuneration of the variable factor at its marginal productivity ('as if' the resource was managed by a capitalist).

FIG. 8.7. Ex ante and ex post gains of a regulation

Regulation with risk-aversion

In many instances, regulation through the individual reduction of each agent's level of effort alone, e.g. through the imposition of an appropriate tax scheme, is not possible. In those cases, regulation must take place through the exclusion of some former users, as in the example presented above. (Note that exclusion per se does not necessarily lead to the efficient level of exploitation. But exclusion may well be a necessary step before any other efficiency-improving measure is contemplated.)

In a first situation, let us assume that regulation does not increase (nor decrease) total income. Take the example of a fishery, and assume that each fisherman is entitled to operate only one boat. Suppose furthermore that the number of boats operated exceeds the efficient number, and that no taxes nor any side-payment can be made. In these circumstances, the only way to regulate the use of the resource is to exclude some fishermen, the remaining ones being then in a position to reap and share amongst themselves the benefits of such a measure through the increasing productivity of their boat.

Under these assumptions, one may ask the following question: will the fishermen agree to regulate the fishery by excluding some of them, if the selection of those to be excluded is uniformly random? The answer is negative if the fishermen are risk-averse. Total output is equal to Y and the total number of fishermen is equal to N. If, say, K agents are randomly selected for exclusion, each fisherman has a probability K/ N of being excluded and a probability (N - K/N) of staying in the fishery. If he is excluded, he gets nothing, while if he stays in the fishery, he gets Y/(N - K). His present income is equal to Y/N. If his utility function, U(.), is concave, so that U" < 0, the utility attached to a certain income of Y/N is, by definition, greater than the utility associated with any lottery yielding an expected income of the same amount, for example, a lottery giving an income of zero with probability K/N and an income of Y/ (N - K), with probability (N - K)/N. We can thus write:

The expected utility each fisherman gets from the exclusion scheme is always smaller than the current level of utility. This result is easy to check from Figure 8.8 in which E(U), the expected utility associated with the lottery involving the exclusion of K individuals, is measured by the vertical distance between the horizontal axis and the straight line OR at the initial (preexclusion) level of income Y/N.

FIG. 8.8. Impact of a random exclusion process on utility levels

Note that this result also holds even if the excluded fisherman is able to get some outside employment, provided his alternative income is sufficiently lower than his current income in the fishery. This is also true if the remaining fishermen would actually give him some side-payment to compensate for his being excluded, provided that the total sum of these side-payments is less than his current income (if equal, he will of course be indifferent, assuming no work disutility).

We have thus far examined the case where the expected gains from regulation are minimum since total income remains constant. If regulation implies an increase in total output, each agent will have to compare the increased productivity brought about by the regulation scheme with his degree of risk aversion and to choose whether or not to support the regulation scheme.

From the above analysis, we may conclude that the amount of support of a regulation scheme based on the random exclusion of some former users depends crucially on (a) the 'productive' effect of regulation, that is, the expected total increase in total output such a scheme is likely to lead to, (b) the possibility for the excluded former users to find some outside employment, and (c) the degree of risk-aversion displayed by the users group. In some cases, any regulation scheme based on random exclusion will be opposed by all fishermen, even if some side-payments are permitted. (The side-payment issue will be analysed in more depth in the following section.) Therefore, one may expect that, when regulation through exclusion must take place, exclusion will not be random but will be invariably directed towards a definite subgroup of members of the community. One may also expect that, when the group is homogeneous, exclusion will not always be resorted to and, as a result, overpopulation of productive units is likely.

Regulation with private information

As has already been hinted at above, if everything relevant to the problem is known to everybody, one can easily design a tax schedule such that exploitation of the commons

is Pareto-optimal. In the case where the proceeds of the taxes are siphoned off, say, by the central state, then every productive member of the community will be worse off. This is the result obtained by Martin Weitzman in his model described in Chapter 3. If, however, the proceeds are redistributed, one can always find a scheme of transfers such that every member of the community is better off, since the new situation Pareto-dominates the initial situation. One such scheme obtains when members receive a share of the tax proceeds proportional to the amount of variable factor they were applying in the initial situation (characterized by overexploitation).

In the following, we will follow John Roemer's terminology and call such an allocation a Nashdominator equilibrium, in the sense that it dominates the Nash equilibrium. On the other hand, the proportional equilibrium, in which tax proceeds are distributed proportionately to the amount of variable factor each member operates in the new (efficient) equilibrium, does not always Pareto-dominate the initial situation: under this distribution rule, some former users may be worse off and prefer the unregulated commons to the efficient proportional allocation. (This result actually follows from our modified version of Kanbur's model.) This also holds true for the equal-sharing equilibrium where tax revenues are distributed equally among the members, that is, on a per head basis. Of course, the three sharing rules described above differ only when the agents themselves are different. Otherwise, the three rules result in an identical outcome. One should also note that quotas (instead of taxes) support the proportional equilibrium: if agents agree upon individual quotas and these quotas are efficient, then the proportional equilibrium obtains.

Finally, these allocations can also be decentralized as a competitive equilibrium, in which the community establishes a firm which owns the commons, and runs them competitively by hiring labour and maximizing profits. Each agent supplies his own labour force, li, and owns a share tetai of the firm. The difference between the three equilibria bears upon the distribution of the shares: in the equal-sharing equilibrium, tetai = l/N, in the proportional equilibrium, H. = I`/~`l`, and, in the Nash dominator equilibrium, tetai is equal to the proportion of labour spent under the unregulated common property regime. In all these cases, the final allocation is Pareto-optimal (but does not necessarily Pareto-dominate the initial situation).

However, in many instances, the community or the traditional authority is not in a position to have all the information relevant to the problem: here again, phenomena of 'private information' may be encountered. Typically, preferences and private endowments are likely to be private information: only the agent concerned knows 'exactly' his preferences, skills, and endowments. The central authority will then ask the agents to announce their preferences and endowments, process these informations, and propose an allocation. The question is whether or not there exists some way of 'passing from the announced preference and endowments to an allocation that provides the proper incentives for agents to tell the truth and with the property that a Nash equilibrium for the game involves a vector of announcements for the fisherfolk that implements' (Roemer, 1988: 19) an equilibrium with some desirable properties, such as Pareto-efficiency. In such a case, the proposed allocation is said to be 'implementable in Nash equilibrium'. Under private information, John Roemer (1988) reaches two important results:

  1. 'There is no allocation mechanism that is Pareto-efficient, Pareto-dominates the common ownership equilibrium, and can be implemented in Nash equilibrium' (Roemer, 1988: 21).
  2. The proportional allocation is not implementable in Nash equilibrium.

Hence, in the presence of private information, if an efficient allocation has to be achieved, then, some agents will be hurt, and were they allowed to do so, they would veto the regulation scheme. Furthermore, whatever the agreed-upon allocation scheme, it cannot be achieved without a high degree of centralization. A central, neutral, and credible authority is needed to achieve an efficient allocation in the presence of private information. Or, agents have to be identical, in which case the private information problem disappears.