Government can reallocate resources away from private goods toward public goods, usually through

Efficient Provision

Pareto optimality (also referred to as Pareto efficiency) is a standard often used in economics. It describes a situation where no further improvements to society's well being can be made through a reallocation of resources that makes at least one person better off without making someone else worse off. If resources are not allocated in a Pareto-efficient manner, then it would be possible through reallocation to provide more of some good(s) to at least one person, making that person better off, without making any other person feel less well off. If all members of society who enjoy a public good are paying an individualized price equal to the marginal benefit they each receive at the level (quantity) provided, and if the sum of these marginal payments is balanced against marginal delivery cost, then no individual can be made better off, such as by paying less and retaining more surplus benefits, without making another individual worse off. If one individual paid less, either someone else would have to pay more to make up the deficit at the margin, or the quantity provided would decline below the Pareto-efficient level such that the collective benefit of the lost unit(s) would exceed the (marginal) cost of their provision. The Lindahl equilibrium is then Pareto optimal, generating a level of provision that is efficient if each individual reveals and pays his/her true marginal value.

Samuelson proved that the efficient level of provision of the public good is where the sum of individual marginal benefits equals the marginal cost of provision. In a two-person world, where each individual pays his/her marginal benefit, the public good is then provided at an efficient level and individual prices (IP1 and IP2, respectively, for each person) are established at an equilibrium level of the good, n*. The graph below illustrates this outcome (Figure 1). If people offer less than their marginal value, the equilibrium quantity produced will be lower than optimal; if people offer more than their marginal value, they would be paying above their marginal benefit for the quantity produced. When the sum of marginal benefits equals marginal cost, the consumer's surplus generated becomes a net benefit that individuals would like to obtain and retain; in this way, the Lindahl approach might generate an incentive for individuals to offer a marginal price that is equal to their marginal value, which then establishes an equilibrium quantity in society (n*). Generally, if all individuals attempt to free ride by waiting for someone else to provide the good, this ubiquitous free-riding strategy would prevent any provision, and there would be no consumers' surplus for anyone to enjoy.

Despite the work of Lindahl, Samuelson, and others, much of the public-good literature of the early twentieth century did not support the conclusion that public good allocations could be Pareto efficient through private decision making, because of the presence of free riders. Consumers will underreport their preferences via willingness to pay under a set of decision rules that explicitly ties consumers' offers to the quantity of the public good produced, resulting in the public good being underprovided relative to the Pareto-efficient point. Experiments conducted in both the field and lab settings explore the role incentives play to overcome free-riding behavior, potentially raising the prospects of Pareto-efficient provision of the good.

3.1 Sources of inefficiency

For social capital to increase Pareto efficiency, the decentralized equilibrium without social capital must not be Pareto efficient in the first place. Social capital can only have a beneficial effect in a second-best world. Deviations from first-best outcomes arise for a variety of reasons including externalities and free-riding, imperfect information and enforcement, imperfect competition, and the like. For social capital to be beneficial, it must therefore resolve or compensate for one of these sources of inefficiency. Secondly, whatever the source of inefficiency, there are only a limited number of ways by which social capital – or any other mechanism – may improve upon a decentralized equilibrium. First, it may resolve a coordination failure in an economy that has multiple Pareto-ranked equilibria. Second, it may alter individual incentives so as to replace the decentralized equilibrium with a superior one. Third, it may affect the technology of social exchange, for instance by opening new avenues for the circulation of information.

From these two preliminary observations, it is immediately obvious that social capital will never be the only possible solution to inefficiency. There always exist alternative mechanisms to solve coordination failure, improve individual incentives, and upgrade the technology of social exchange – such as contracts, vertical integration, state intervention, or redefinition of property rights. Of course, there are many circumstances in which social capital is a less expensive or simpler institutional solution, but it is important to recognize that it can never be the only one.

These observations have immediate implications regarding empirical investigation. Suppose social capital improves efficiency by solving a coordination failure problem. For this to occur, the economy must have multiple Pareto-ranked equilibria. Social capital provides the leadership or coordination device necessary to select a superior equilibrium among the many possible ones. Suppose further that the researchers have multiple observations of such economies, some with social capital and some without. Since nothing precludes these economies from achieving a high equilibrium without social capital, it is inherently difficult to test its effect. Furthermore, social capital may arise endogenously as an institutional response to an inferior equilibrium. To the extent that social capital does not always succeed in moving the economy to the better equilibrium, one could have the paradoxical situation in which economies with social capital are on average at a lower equilibrium than those without. This is a standard difficulty with multiple equilibria but it is not always adequately recognized in empirical work.

Even when there is a single equilibrium, social capital never is the only possible way of improving efficiency by altering incentives or technology. Identifying the effect of social capital requires that the researcher adequately control for other possible institutional solutions. Here too, self-selection is a concern.

4.2.1 Intertemporal efficiency

The basic static conditions implied by Pareto efficiency can be extended to an intertemporal setting in a straightforward fashion through the dating of commodities. That is, final goods and productive factors are distinguished by time as well as by the type of good. For private goods, distributional efficiency requires that each pair of individuals has the same marginal rate of substitution between any pair of commodities, including the same good consumed at different points in time. The common marginal rate of substitution must be equal to the economy's marginal rate of transformation between the pair of commodities. The necessary conditions for a Pareto-efficient allocation of a public good are somewhat more complicated. In particular, efficiency obtains when the marginal rate of transformation is equal to the summation of individual marginal rates of substitution over both time and individuals [Sandler and Smith (1976)].

As demonstrated in the previous section, the efficiency conditions for the use of long-lived assets require that the marginal value of the flow of services from the asset is equal to the marginal value of the asset, and that the marginal rate of return to each asset is the same. The basic condition of equal returns to each asset is independent of any ethical criterion. That is, given any social welfare function, if the intertemporal condition is not satisfied, then there exists a better path for the economy to follow, where better is defined in terms of the chosen social welfare criterion.

A market allocation will be intertemporally efficient given standard neoclassical conditions about the convexity of production and preference sets and a complete set of markets, including future markets for each dated commodity and a full set of contingent markets for each state of the world. Arbitrage activity by asset owners seeking to maximize the present value of their portfolio would ensure that the total return to each asset is equal. The future markets enable the economy to establish the proper initial price for each asset [Dasgupta and Heal (1979)]. In the absence of futures markets, it could be some time before an initial error is discovered and corrected. The absence of contingent markets would prevent the efficient allocation of risk. The exact impact on the pattern of natural resource use depends upon the source of uncertainty. For example, uncertainty about the timing of the development of a substitute for the resource can lead to more rapid depletion while uncertainty about the size of the resource stock can lead to less rapid depletion [Fisher (1981)].

The existence of a complete set of futures, risk, and capital markets is essential to the efficient allocation of any long-lived asset and is not specific to interactions between resource use and the environment. The open access to environmental assets and the public good characteristics of environmental amenities are important sources of intertemporal market inefficiencies derived from resource–environmental interactions. Because of the open-access and public-good aspects of the environment, the environmental costs of resource use are not fully internalized in private decision making. This market failure results in both direct intertemporal inefficiencies and static misallocations with indirect implications for intertemporal allocation. In general, one would expect that environmental assets would be undervalued and, therefore, over-exploited.

The static failure of the market to capture the current environmental costs of natural resource use induces greater extraction of natural resources than would occur if all costs were covered by the resource price. This static inefficiency also affects the entire time pattern of resource extraction. The intertemporal bias in the pattern of resource extraction created by market imperfections, including externalities, depends upon the rate of change in the market imperfection over time relative to the rate of discount [Sweeney 1977)]. A simple example is the case of a static environmental effect with a constant marginal cost so that the rate of change in the market imperfection is zero. In this case, if the rate of discount is positive and the environmental cost is external to the market, then the market depletes the resource more rapidly than socially desirable because the present value of the market imperfection is greater in the present than it is in the future.

In addition to the dynamic implications of static inefficiencies, there are several direct sources of intertemporal inefficiency that are associated with the interaction between natural resource use and the environment. Many of the environmental effects of resource use are long-lived and cumulative in nature – the climatic impact of carbon dioxide emissions will be felt long after the consumption of fossil fuels has ended. In the case of cumulative effects, there is a dynamic cost of the externality that captures the present value of any future environmental damage caused by current emissions. For example, if D(P(t)) denotes the value of the environmental damage of an accumulation of pollutant P at time t, then the shadow price of the resource should include the term

∫t∞e−δ(s−t)D′(P(s)) ds,

which represents the present value of the present and future marginal environmental damage caused by the use of the resource [Schulze (1974)].

This value is greater than the present value of the marginal damage of the current stock of pollution, D′(P(t))/δ, whenever the marginal damage of pollution increases with the level of pollution and the level of pollution is increasing over time. In the models of the previous section, this cumulative effect of natural resource use is captured in the shadow price of the resource – note the equivalence of this term with the second term on the right-hand side of eq. (25) above. Note also that the correct valuation of the environmental damage depends upon the entire future path of pollution. The persistence of pollutants can imply that economic incentive policies do not have an informational advantage over direct controls since it is not possible to determine the optimal tax (or number of tradeable permits) without solving for the optimal path for environmental quality [Griffin (1987)].

The open access to the environment means that the benefits of the regenerative capacity of the environment are not appropriable. Consequently, there are no market incentives for investment in the assimilative capacity of the environment nor for the development of technologies that use the environment less intensively. Commoner (1972) presents evidence that changes in production processes were the most significant factor in the increase in environmental degradation in the post-World War II period. For example, in the USA between 1949 and 1968, the use of fertilizer nitrogen increased by 648% while population increased by only 34% and per capita output increased by only 11%. Hence there has been a very significant increase in the use of nitrogen fertilizer per unit of output. Research and development efforts are guided by market forces and if environmental resources are undervalued, then R&D activities will be allocated inefficiently and technological progress will be oriented toward more extensive use of the environment and, in turn, the depletion of natural resources will be too rapid.

Other intertemporal inefficiencies may arise because future generations do not participate in the market. The general nature of these problems is the inability to conduct trades across generations. Future generations may prefer a different mix of capital, resource, and environmental assets than the mix of assets bequeathed to them by the present generation. It is possible that they may desire to exchange material wealth for environmental amenities. The present generation might be willing to accept the trade but cannot because of the temporal barrier. Such a situation arises when development is irreversible and there is uncertainty about future preferences [Fisher and Krutilla (1974)].

The public-good nature of an environmental asset over time raises questions about the effect of discounting on the intertemporal allocative efficiency. Sandler and Smith (1976) have argued that discounting can result in Pareto inefficiency in the intertemporal allocation of long-lived public goods such as environmental assets. Cabe (1982) establishes that the proper rate of discount on future services is the marginal rate of transformation for the numeraire good between the current period and the period in which the services are provided. He argues that the result obtained by Sandler and Smith is due to their implicit assumption of a numeraire with a marginal rate of transformation equal to unity and that this assumption is unrealistic in a growing economy. Sandler and Smith (1982) agree that the proper discount factor is the intertemporal marginal rate of transformation for the numeraire but argue that a value of unity is realistic for a commodity that serves as a standard of value. In any case, the market rate of discount is not necessarily the socially optimal rate of discount.

In summary, because of the open-access and public-good characteristics of environmental assets, the interaction between resource use and the environment poses significant problems for achieving an efficient intertemporal allocation even in the presence of a complete set of futures, risk and capital markets for privately owned commodities. While a variety of outcomes is possible, it is generally expected that a market allocation would deplete natural resource stocks too rapidly and that environmental degradation would be too great.

16.1.2 Modeling Household Decision Making: The Collective Model

The basic axiom of the collective approach is Pareto efficiency: Whatever decision the household is making, no alternative choice would have been preferred by all members. Whereas this assumption is undoubtedly restrictive, its scope remains quite large. It encompasses as particular cases many models that have been proposed in the literature, including:

“Unitary” models, which posit that the household behaves like a single decision maker; this includes simple dictatorship (possibly by a “benevolent patriarch,” as in Becker, 1974) to the existence of some household welfare function (as in Samuelson, 1956).

Models based on cooperative game theory, and particularly bargaining theory (at least in a context of symmetric information), as pioneered by Manser and Brown (1980) and McElroy and Horney (1981).

Model based on market equilibrium, as analyzed by Grossbard-Shechtman (1993), Gersbach and Haller (2001), Edlund and Korn (2002), and others.

More specific models, such as Lundberg and Pollak's “separate spheres” (1993) framework.

On the other hand, the collective framework excludes models based on noncooperative game theory (at least in the presence of public good), such as those considered by Ulph (2006), Browning et al. (2010), Lechene and Preston (2011), and many others, as well as models of inefficient bargaining a la Basu (2006).

The efficiency assumption is standard in many economic contexts and has often been applied to household behavior. Still, it needs careful justification. Within a static context, this assumption amounts to the requirement that married partners will find a way to take advantage of opportunities that make both of them better off. Because of proximity and durability of the relation, both partners are in general aware of the preferences and actions of each other. They can act cooperatively by reaching some binding agreement. Enforcement of such agreements can be achieved through mutual care and trust, by social norms and by formal legal contracts. Alternatively, the agreement can be supported by repeated interactions, including the possibility of punishment. A large literature in game theory, based on several “folk theorems,” suggests that in such situations, efficiency should prevail.3 At the very least, efficiency can be considered as a natural benchmark.

Another potential issue with a collective approach to inequality issues is of a more conceptual nature. By definition, the collective approach is axiomatic; it assumes specific properties of the outcome (efficiency), and leaves aside the specific process by which this outcome has been generated. It has sometimes been argued that one should judge differently situations that generate the same allocations (and the same utility levels) but which are reached by different processes. In that case, the collective approach has to be further specialized, and this may be (and has been) done in several directions.4

Finally, an obvious but crucial advantage of the collective model is that it has been by now fully characterized. We have a set of necessary and sufficient conditions for a demand function to stem from a collective framework (Chiappori and Ekeland 2006); exclusion restrictions have been derived under which individual preferences and the decision process (as summarized by the Pareto weights) can be recovered from the sole observation of household behavior (Chiappori and Ekeland, 2009a,b). To the best of our knowledge, this is the only model of the household for which similar results have been derived.5

The next section describes the basic model. We then discuss the conceptual issues linked with intrahousehold inequality, first in the case where all commodities are privately consumed, then in the presence of public goods, finally for the case of domestic production. We then discuss the determinants of intrahousehold allocations followed by a section on identification of preferences and the sharing rule. Finally, we discuss issues related to identification. In the following section we give an overview of empirical findings and then we conclude with a brief discussion of future directions of research.

7.4.4. The Basic Equations

Our method uses the first-order conditions for Pareto optimality to solve for the optimal consumption of each trader i in terms of the consumption of some particular trader, say Trader 1. We then use the feasibility constraint to solve for Trader 1 's consumption. The fact that we can do this only implicitly is not too much of a bother.

Let κi = λ1/λi. From Eq. 7.3 we get that

(7.7)u′i(cti(σ))u′1(ct1(σ))=κi(β1βi)t∏s∈S(ρs1ρsi)nts(σ)

Sometimes it will be convenient to have this equation in its log form:

logui(cit(σ))ui(cit(σ))=logκi+tlogβ1βi−∑snst(σ)(logρisρs−logρ1sρs)

We can decompose the evolution of the ratio of marginal utilities into two pieces: the mean direction of motion and a mean-0 stochastic component.

logμ′i(cti(σ))μ′1(ct1(σ))=logκi+tlogβ1βi-t∑sρs(logρsiρs-logρs1ρs)-∑s(nts(σ)-tρs)(logρsiρs-logρs1ρs)=logκi+t(logβ1-Iρ(ρ1))-t(logβi-Iρ(ρi))-∑s(nts(σ)-tρs)(logρsiρs-logρs1ρs)

The mean term in the preceding equation gives a first-order characterization of traders' long-run fates.

Definition 7.3. Trader i's survival index is si = logβi − Ip(pi). Then

(7.8)logμ′i(cti(σ))μ′1(ct1(σ))=logκi+t(S1-Si)-∑s(nts(tρs))(logρsiρs-logρs1ρs)

1.2 Finite Economies

The most obvious social choice property satisfied by a Walrasian mechanism is Pareto efficiency. Indeed, as discussed in Section 4.3, for economies with just one “representative” agent, or alternatively with several identical agents who all receive the same consumption vector, Pareto efficiency offers a complete characterization of the Walrasian mechanism under standard continuity, convexity, and aggregate interiority assumptions. Beyond this special case, however, standard textbook examples with two consumers and two goods demonstrate that Pareto efficiency alone is insufficient to characterize the Walrasian mechanism. Nevertheless, once one allows lump-sum redistribution, then most Pareto efficient allocations can be characterized as Walrasian equilibria. The main exceptions are extreme or “oligarchic” allocations in which some agents are so well off that they cannot benefit even from free gifts of goods that would otherwise be consumed by agents outside the oligarchy. Also, even such oligarchic allocations are compensated Walrasian equilibria with lump-sum transfers. These and some related results are presented in Section 4.

Characterizations of Walrasian equilibria without lump-sum transfers remain much more elusive, however, especially for economic environments with a fixed finite number of agents. First Section 5 presents conditions sufficient to ensure the existence of Walrasian equilibrium. Then Section 6 considers characterizations that apply to one economic environment with a fixed set of agents having a fixed type profile. Next, Section 7 considers characterizations with a fixed set of agents but a variable type profile. To conclude the results for “finite economies” with a finite set of individual agents, Section 8 allows the number of agents to vary as well as their type profile. Included are asymptotic characterizations such as the Debreu–Scarf Theorem, which hold when the number of agents tends to infinity.

2.2.3 Libertarian Theory

Probably the most widely used decision rule in economic theory is the Pareto criterion, which is most often applied to efficiency and political feasibility (e.g., in bargaining theory). It has also been applied to equity, for instance by a common-sense conception of justice. In libertarian theory, the baseline is that individual freedom prevails except where others may be harmed. Thus, this ethic is in the same line as Pareto superiority saying that there is an improvement in welfare if one or more persons are made better off due to change in resource use as long as the other persons are at least as well off as before. A strict interpretation of libertarian theory is that an act is only immoral if anyone is worse off because of it.

Robert Nozick's theory is the best-known statement of libertarian thought. The theory can be summarized in three principles: justice in appropriation, justice in transfer, and justice in rectification. A distribution of goods is just if it is the end result of an unbroken chain of just transfers, beginning from a just original appropriation. If these conditions are not satisfied, justice in rectification requires that we should establish the distribution that would have occurred if all unjust links in the chain had been replaced by just ones.

The first principle is essentially a finder's keepers principle, where the basic idea is that anyone has the right to appropriate, exploit, and enjoy the fruits of any unowned piece of nature. The principle of just transfers says that the outcome of any voluntary transaction between two or more individuals is just. It is assumed that there is no coercion. If individuals agree on a contract that will benefit all, there is no reason to stop the contract. The only reason to invalidate the contract is if anyone uses its power to make the nonagreement state worse for other parties than it would otherwise have been. The last principle is probably the main weakness of the theory, as identifying the point in time where the earliest violation occurred and thereafter the counterfactual chain of just transfers may be rather indeterminate.

1.2.3 Pareto Criterion

In economics, a commonly used criterion for evaluating and comparing situations is the Pareto Criterion. A situation is defined a Pareto Optimum (PO) if from there no agent’s situation can be improved without reducing the payoff of someone else at the same time. Note that this criterion does not include a broader judgment regarding the desirability of an outcome including some redistribution. A situation where one agent controls all available resources or receives the entire payoff in a given setup, while the rest of the group have or receive nothing, nevertheless is Pareto-optimal according to that definition, just as is a situation where all agents control or receive equal shares. If a situation is not Pareto-optimal, if it is Pareto-inferior compared to another Pareto-superior one, then, according to the definition, at least one agent’s payoff can be improved without a concurrent reduction in anyone else’s payoff. If the individually optimal decisions lead to an outcome that is a PO, we assume the degree of conflict to be relatively low. If individually optimal decisions lead to a Pareto-inferior outcome, in turn, the degree of conflict is assumed to be relatively high, as agents’ interests in others’ decisions and their preferred choices do not concur.

What are two characteristics that differentiate private goods from public goods?

When a competitive market achieves allocative efficiency it implies that?

What two conditions must hold for a competitive market to produce efficient outcomes?

Which of the following conditions does not need to occur for a market to achieve allocative?