Valuing Public Goods

Philip E. Graves
Department of Economics UCB 256
University of Colorado
Boulder, CO 80309-0256

Revised: August, 2002
May, 2003

[Note: A close variant of this paper appears in Vol. 46 of Challenge: The Magazine of Economic Affairs (September/October 2003).  Authorization to reproduce or otherwise use all or part of this paper must be requested at M.E. Sharpe Inc., Rights & permissions Dept., 80 Business Park Drive, Armonk, NY 10504]


Economists believe that optimal levels of public goods are produced at the levels that a perfectly functioning private market would produce, if it were able to exist. The condition conventionally thought to achieve this outcome is to sum vertically the marginal willingness to pay of households affected by the public good and to equate that aggregate marginal benefit to the marginal cost of provision, at a given income. However, the traditional economic framework fails to yield the proper levels of public goods because there will always be a concomitant input market failure, resulting in initial income levels that are non-optimally low. Moreover, under independence, that income would have virtually all been devoted to public goods (environmental quality being emphasized here), yielding a possibly severe under-valuation and under-provision of them. Potential extensions are discussed.

JEL classification: C91, D12, D81

Keywords: Decision making; Choice behavior; Public Goods; Willingness-to-pay; Willingness-to-accept, benefit-cost analysis, cost-benefit analysis

I. Introduction

Economists, philosophers, and environmentalists have starkly contrasting ways of thinking about environmental values. In economics, everything revolves around the choices imposed on us by the existence of scarcity. Since we cannot have everything we want, trade-offs are inevitable. Economists believe that if we think hard about those trade-offs (using benefit-cost analysis) that we will make better decisions than if we do not. In the extreme case of perfect information, thinking about the benefits and costs should, it is argued, lead to "perfect" decisions; if we had either more or less environmental quality, we would be worse off. Even among economists, however, there is very spirited debate about whether we do the calculations at all right.

Philosophers and environmental ethicists find much to criticize about the economists' paradigm. Their worldview often finds the approach of the economist to be too human-centered, arguing that human preferences alone might be inappropriate for a variety of reasons. Or, we might just be too ignorant to know meaningfully the long-run consequences of our actions (perhaps destroying ourselves, after destroying everything else), and so on.

There is much merit in both the views of economists (scarcity matters) and the views of environmentalists and philosophers (other things matter, too). The broad range of things the latter groups might ideally like to do does not, however, provide much specific practical guidance about what to do now with the limited resources we have available. So, even economists that are skeptical about the accuracy of benefit-cost analyses believe economic tools are useful in helping to prioritize the many projects that environmentalists advance, identifying the "more important" things to do first (a principle point of Lomborg 2001). This resulted in codifying economic efficiency as the method by which such decisions are to be made when, in 1981, Reagan signed Executive Order 12291, which explicitly required achievement of economic criteria in adopting regulatory actions.

But, the story I wish to relate is not a rehash of the largely irreconcilable views of economists and their critics. Rather, the goal is to establish that the economists, themselves, have failed to get the proper mechanism to yield the socially optimal levels of environmental goods, even if all of the unwieldy measurement problems were overcome. Hence, following Executive Order 12291, as economists currently interpret that, results in substantial under-valuation of pure public goods, with environmental quality being emphasized here.

Section II lays out, in very accessible terms, how economists have traditionally viewed the correct amount of environmental quality to be determined. This section follows closely, at a quite readable level, the famous paper by economist Paul Samuelson (1954). In Section III, it will be shown that, even if we have perfect information and demand revelation (the most favorable possible conditions), following the approach of Section II results in the under-provision of environmental goods. Indeed, plausible numbers suggest that the extent of the error is very large. The Section III presentation represents an intuitive version of more technical manuscripts (Flores and Graves 2002, Graves 2003b) which, in addition to providing formal proofs and graphs, also more fully relate the idea to the existing literature. Section IV concludes the paper, discusses the potential importance of the observations made here, and provides some additional implications.

II. The Economists' Approach to Valuing Environmental Goods

Environmental goods are, generally, a subset of a general class of goods called "public goods." The distinction between public goods and private goods has nothing directly to do with whether they are publicly provided, although it turns out that they will have to be. Rather, being a pure public good hinges on two critical properties: 1) A public good is non-rivalrous in consumption (e.g. your breathing of the clean air or looking at the scenic view, does not affect my ability to do so), and 2) A public good is also non-excludable in consumption (e.g. we cannot be prevented from seeing the view or breathing the air).

Two important problems stem from those properties. First, it will never be profitable to produce public goods privately, because the producer who incurs the cost of production cannot prevent the consumer from using the good freely (it is non-excludable). So public goods provision is accordingly the most important, perhaps the only important, role of government (e.g. police protection, national defense, legal institutions, along with the environmental goods of specific focus here, come to mind). The government must be in charge of supplying public goods, since it will not be profitable for the private market to provide them.

Second, how is the government to decide how much to provide? The economists' view is that government interventions should replicate, as closely as possible, what a perfectly functioning private market would do, if it could exist.In a competitive private market for an ordinary good, people face prices that determine how much they would like to buy or sell. Demanders will buy the good as long as the added (or "marginal" in the jargon of economics) benefit they derive from the good exceeds its price. Indeed, they will wish (individually, hence collectively) to buy the good right up to the point where their declining marginal values (the more you have of anything the less an additional unit is worth) equal the price. To stop short of that would be to fail to do something that could make the demanders themselves better off.

Suppliers, similarly, will supply the good as long as they receive more for their good than its (marginal) cost of production. They, too, will want to supply right up to the point where their marginal costs equal the price, obtaining maximum profit.

The market-clearing price then has the property that peoples' marginal values of all private goods just equal the marginal costs (of foregone other goods) of those purchases. Additionally, the net benefit of having the good versus doing without it is as large as possible at this output level (the sum of consumer and producer is maximized). As Adam Smith would have expressed it, the competitive market outcome maximizes "the wealth of nations," giving us the most of the private goods we value. Note that the "appropriate question" then is at what prices will the quantity produced exactly balance marginal benefits and marginal costs for private goods.

In the case of public goods the "appropriate question" changes. We no longer ask "how much will be bought and sold at various prices and what price equates those?" Rather, we now want to ask "how much will adding more of this good be worth to everybody, since we all get it once it is produced, and at what level will the aggregate marginal value from all consumers just equal the marginal cost?"

For ordinary private goods, then, one adds "horizontally" the demands of everybody for, say, broccoli, and at the market outcome the marginal value of broccoli will equal the marginal cost of broccoli; the right amount is produced, given peoples' preferences. Were we to produce a smaller amount of broccoli, additional broccoli would be worth more to people than it would cost (in foregone other goods) to produce, so we could make ourselves better off by producing more. If we, instead, produced more broccoli than the equilibrium amount, the added costs would exceed the added benefits and we would be making ourselves worse off. We can have, in short, too much of a good thing, even environmental quality.

In the case of public goods, the seemingly parallel treatment is to add "vertically" the demands for, say, an improvement in CO2 levels or the saving of an endangered species, since everybody benefits (non-rivalrously) from such activities. Adding up what everybody is willing to pay and comparing that to the marginal cost of getting that improvement tells us whether we want to do it or not, and how much of it to do for activities that are continuously variable. We would want to keep cleaning up the air, for example, until aggregate marginal benefit (decreasing) equals the marginal cost (increasing) of further clean up.

However, there is an additional problem with applying the preceding methodology to the provision of public goods that is very serious as a practical matter. It will be very difficult to figure out what any individual's true marginal willingness to pay is, since they will have an incentive to lie when asked to contribute, knowing that if everybody else pays enough to get it, they cannot be excluded. This is the well-known "free rider" problem in output markets that has been addressed elsewhere (see Clarke 1971, Groves and Ledyard 1977). We will assume that the demand revelation problem caused by free riders in the output market has been solved in what follows. Since this problem is unlikely to be solved in practice, the extent that current provision levels of environmental goods falls short of the socially optimal levels is likely to be still larger.

The apparent conclusion, with perfect demand revelation, is that we as a society would get the right amounts of all goods, public and private, if we follow the preceding approach of vertically summing the (true) marginal values for the public goods. At such an optimum, if we were to increase the levels of the public good, we would be worse off, since the added (marginal) costs in terms of foregone other private goods that we also care about would exceed the added (marginal) benefits of the improved environment. While beset with many practical problems of implementation that are fiercely argued about, the preceding way of thinking has dominated economics for a half-century.

III. The Conventional Methodology Undervalues the Environment

I argue in this section that the preceding approach to determining how much environmental quality to produce will always produce an amount that is below the true social optimum. Moreover, the sense in which this is so should be clear to anyone with even minimal exposure to economics.

At the very heart of how economists think is the notion that we work to get the things that we want. Leisure is itself a very desirable good, yet we give up leisure by working in order to acquire the goods we want. In a market system, apart from philanthropy or theft, we must supply inputs to get the outputs that we want. For ordinary private goods, individuals choosing to work harder or at more lucrative occupations will receive the income that allows them to get the goods they desire. Indeed, rational individuals will balance their goods demands with their leisure demands, so that the utility gain from goods purchased with the after-tax wage from the last hour worked exactly balances the utility value of the foregone leisure to get those goods.

But, consider the case of people who care relatively little for such private goods but have instead very strong demands for saving species or air quality improvements, or habitat preservation. By the very nature of such public environmental goods, income generated by individual decision-makers cannot affect their consumption. The levels of public environmental goods are determined collectively because they are non-excludable, hence non-profitable to provide privately. This problem was recognized on the output market, but any time there is an output public goods market failure, there will also be an input market failure, a failure to generate the right amount of income!

Those caring about the environment (everybody to varying degrees) will generate too little income, because the marginal benefit of generating the income, in terms of getting the public goods you care about, is effectively zero, while the opportunity cost of foregone leisure is large and positive. So rational people, those whose behavior economists think about, would just increase leisure and ordinary goods consumption, the variables they can affect (in extreme cases "dropping out," like hippies of earlier generations).

Environmentalists are also likely to be disdainful of individuals working hard to make large incomes, because environmentalists do not get to buy what they want if they generate more income...and they have little admiration for the preferences for private goods possessed by those who do generate the large incomes. But, people are really more alike in their desires to earn income than it would seem from observed data. If strong environmentalists could buy what they really want by doing so, they would have generated more typical incomes, by altering both labor supply in the short run and human capital investment or occupation in the longer term.

So economists, in using benefit-cost analysis to value public goods, are implicitly starting out with a presumed optimal level of income that is, in fact, sub-optimal. If people could actually buy public goods like they buy private goods, they would have generated more income. But how much empirically important is this likely to be? I believe that the observation made here has great importance for a number of reasons.

Consider first the case of narrowly defined environmental quality. Freeman (2002, p. 126) argues that the annual costs of all major environmental laws enacted since Earth Day in 1970 were $225 billion in 2000. Suppose that current U.S. incomes are a mere one percent lower than they would have been, without the "free riding" in the labor markets by those who would like to buy more environmental goods. To be sure, ardent environmentalists, through labor market and human capital investments, might potentially generate far more income than their current income (which they spend on the few private goods that interest them and on "buying" leisure by working less) were they able to buy the environmental good as ordinary goods can be bought.

Current GDP is approximately ten trillion dollars. So, that one percent of income amounts to $100 billion dollars all of which would have been spent on environmental quality. Thus, our current expenditure, under very conservative assumptions, would be over forty percent too low. If one were to argue that incomes could plausibly be understated by 2.5 percent, spending on all of our environmental initiatives should, on efficiency grounds, be twice what it currently is. This expenditure level would buy a much nicer environment than we currently have, and the numerical example seems somewhat conservative.

IV. Summary and Further Thoughts

There is great conflict among households in all countries over how much environmental quality we collectively should produce. Those desiring ordinary marketed goods generate the income to acquire them. But, those who are frustrated by their inability to buy the environmental goods that they want, regardless of the incomes they generate, have few options. They will be expected to adjust their leisure and ordinary goods upward (variables they can affect), with some just "dropping out," while others retain weak, flexible attachments to the labor force to acquire their limited desires for private goods. And, some might become environmental activists, rather than pursuing a more lucrative career, in the hopes of being able to have an impact that way. And a few, the deeply frustrated, become eco-terrorists, burning a Vail Associates mid-mountain restaurant, spiking a tree, or engaging in other acts that most people think terribly wrong. While not excusing such acts, social antagonisms would be greatly diminished if we could all buy what we really want of everything if we generate the income to do so.

The arguments presented here indicate that the benefits in the numerators of economists' benefit-cost analyses are currently much too small. There is a potentially large amount of missing income, income that had benefits greater than the leisure and goods opportunity costs, if only people could buy the environmental public goods they want. And, under independence, nearly all of that income would have gone in the numerators of those benefit-cost analyses, being spent on environmental public goods.

Additionally, many environmental projects are of a very long-term nature. Were such projects able to be purchased, as are investment projects yielding larger future ordinary goods flows, much additional income that would be earned would be saved and invested in long-term environmental projects. Hence, another implication of the failure to generate income when you cannot buy what you want, is that the social discount rate that is currently used to evaluate long-term projects is too high.

Moreover, since only saving for environmental public projects is affected, failure to solve the "missing income" problem (getting the numerators right in a benefit-cost analysis) provides a rationale for using a lower interest rate for environmental projects, at least until we get the numerators right.While environmentalists have long argued that typical discount rates used in project analysis discriminate against the environment, the preceding provides a reason, for applying a lower rate, under the status quo, to long-term environmental projects (e.g. reduced CO2 emissions).

It is important to think about what should be done, as to public goods provision, if the "supply revelation problem" discussed here cannot be resolved. If we do not generate the missing income, could the conventional methodology discussed in Section II be a 2nd Best rule? Clearly not, because the labor market responses are unavailable to contribute to overall marginal willingness to pay, due to the free rider problem in that market. Households will give up their leisure and private goods to pay the taxes for the incremental environmental goods and to pay the higher prices for less-polluting private goods. But, there will be continued free-riding, until the unique optimum optimorum is attained, among an infinite number of apparent optima at various levels of input market free-riding. That is, at any point short of zero free riding, the "true" social marginal value is greater than the apparent one, because the socially optimal level of income is not being earned.

Hence, it would be optimal to increase the amount of public goods provided from an initial, apparently perfectly determined, quantity under the conventional methodology. In consequence, the households (faced with a tax equal to their marginal willingness to pay and paying higher prices for less-polluting cars, etc.) will adjust their leisure downward, and it will make them better off. They will be "forced" to do something they would have liked to do anyway, as long as they could get everybody else to do it!

The preceding paragraph hints at a problem discussed in detail in Graves 2003b. A robust finding in economics is that decision-makers often exhibit a much smaller dollar willingness to pay (WTP) for an item than the minimum amount that they claim to be willing to accept (WTA) to part with it (see Horowitz 2002 for a survey of 45 studies). This finding has been sometimes attributed to an "endowment effect" (see Kahneman, et al. 1990, Twersky and Kahneman 1991) in somewhat ad hoc, non-utility-based discussions. While there is likely to be merit in this—and perhaps other—explanations for the WTA-WTP gap, the fact that the WTA-WTP gap is by far the largest for public goods, suggests the importance of the arguments presented here. The non-generated income would add to the WTP, greatly reducing the gap, and suggesting that it is WTA, as currently measured, that is of relevance even for increments to the public good, for it more closely approximates properly measured WTP.

In sum, both economists and environmentalists should be in agreement that we are currently devoting far too little of our resources toward provision of environmental public goods. There remain many other areas of disagreement, and environmentalists and philosophers will doubtless continue to believe that when humans are making the decisions, other species and their eco-system habitats are unlikely to be properly considered. But such issues might best be taken up after major steps have been taken, steps that we can all agree on, to incorporate the observations made here into real-world environmental goods provision.


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