efficient provision of public goods
working together ain't easy


Public goods are often overlooked, yet we owe big part of our lifestyles to their stable provision. Also taken for granted is the social cooperation required to achieve stability in the consumption of collective goods. This can be attributed to the blind faith most people have on collaboration occurring simply when individuals share the same interests. This essay will show this is not the case. To do so, I will present an account of the development of the theory of public goods and show why public goods are likely to be inefficiently provided. Furthermore, I will discuss how these theories of public goods can improve our understanding of collective action problems significantly.

Samuelson initially distinguished public goods as those that are non-rivalrous, that is when the use of a good by an individual does not reduce the available supply for the rest of the public1. This feature is also called ‘jointness of supply’. Given that non-rivalrous goods force all individuals to consume the same amounts, the optimal provision occurs at a level of consumption different than that of a rivalrous good, where each individual can consume the number of goods they prefer. The optimal condition for the consumption of private goods occurs when every individual’s marginal rate of substitution is equal to the marginal rate of transformation. Samuelson showed that the demand schedules for goods with jointness of supply do not aggregate horizontally, as is the case with private goods, but vertically. Therefore, equilibrium occurs where the sum of the marginal rates of substitution is equal to the marginal rate of transformation. The shift in optimal conditions is intuitive. The public good is nonrivalrous; therefore, a social planner would require producers to take into consideration the sum of all the consumer’s preferences.

By illustrating a distinct optimal condition for non-rivalrous goods, Samuelson demonstrated that private markets cannot supply public goods efficiently. As decentralised pricing systems will optimise the provision of public goods to the level where the marginal consumer’s marginal rate of substitution is equal to the marginal cost, it will inevitably converge to a provision below the social marginal rate of substitution. Samuelson went on to say that not even voting systems will be able to address this problem given that voters, who are all assumed to be selfish, will have an interest in underrepresenting their real preference for the public good. Thus, Samuelson hinted at the idea of the ‘free-rider’, a concept that although it had long permeated the collective action literature, was only named ten years later by Buchanan2. The threat of free-riding is perhaps the underlying concept that challenges successful collective action. The free-rider problem is a form of market failure that allows individuals to benefit from resources without contributing to their provision. The possibility to consume a good without paying for them incentivises people to defect from any collaborative scheme; thus, under providing the public good3. Attributing to Samuelson’s contribution, Downs illustrated the free-rider in how “each man finds it advantageous to refuse to pay for such indivisible benefits” in the case of the provision of national defence 4. Downs also drew from the free-rider problem to explain rational ignorance and rational abstention5.

In 1959, Musgrave argued that it is the exclusion principle rather than jointness of supply what differentiates public goods from private goods. Namely, he stipulated that public goods were those that once produced, were immediately available to everyone regardless of whether they contributed or not. Head demonstrated that the critical condition behind Samuelson’s rule was excludability and not non-rivalry6. Contemporary conceptions of public goods now include both the exclusion principle and jointness of supply. Pure public goods are those that exhibit the two conditions in their totality. For example, lighthouses are unable to exclude anyone from using them, and the provision to a single individual does not reduce the provision for everyone else. Thus, the two properties are continuums. Exclusion costs can describe levels of exclusion, as is the case with the construction of gated fences around public parks that are meant for contributors only. The traffic caused by an increase in vehicles in public roads is an example of crowding, a deterioration in jointness of supply7.

A defining moment in the discussion of collective action problems was when Olson opened his ‘The Logic of Collective Action’ with the assertion that no rational individual will contribute to a public good unless the group is small, there is coercion, or there are selective incentives8. To demonstrate what is now known as the ‘zero contribution thesis’9, Olson used Musgrave’s definition to determine a good’s publicity according to their exclusivity8. By use of the exclusion principle, Olson went beyond this to demonstrate the ubiquity of the free-rider problem and made further precise predictions for the provision of collective goods. He still recognised the usefulness of rivalry as a property of public goods, but he did not consider marginal rates to be as significant as group features, such as the number of members or preference and income heterogeneity510.

The idea that groups tend to provide collective goods when all of the participating members share the same interest in its provision is the composition fallacy that Olson exposed with his group paradox. He argued that larger groups are less likely to provide for themselves where gains from collective action are reduced when the number of members in the group increase8. Non-rivalrous goods will not present this provision and will incentivise groups to grow in members given that it will lower the required contribution per individual. Larger groups will also reduce the perceived individual benefit of a public good; therefore, contributors will have a higher incentive to defect and become free-riders.

An additional claim within the group paradox is that the larger the group, the higher the under-provision of the public good. That is, as groups increase in members, the amount of the supplied good grows further away from the optimal level of provision. As shown above, in the discussion of the Samuelson rule, the optimal level of provision is where the public good is provided at the level where the social marginal rate of substitution meets the marginal rate of transformation. Olson’s group paradox claim follows the suboptimality of the Samuelson condition when it becomes apparent that best responding individuals ignore how their contribution ignore how their contribution benefits others given that their best response is where the marginal rate of substitution meets the relative price of the public good. These ignored benefits can be quantified by

\[\sum_{j \neq i}^n MRS_{Gy}^i\]

Where \(MRS_{G_y}^j\) indicates the superscript’s marginal benefit from the public good relative to its price; thus, simply stating the sum of the marginal rates of substitution of all the individuals except one. As the ignored benefits grow with the number of group members, Olson’s claim holds11.

Olson also advanced other claims regarding collective action outcomes that involve the group’s asymmetry in preference and size such as the exploitation hypothesis, which postulates that members with larger endowments will tend to bear a disproportionate burden when supplying a collective good. Olson believes in this tendency given that heterogeneity in potential rewards will inevitably lead to some participants having higher incentives to contribute which others will take as an opportunity to free-ride8. Therefore, heterogeneous groups are also more likely to overcome collective action problems.

As Olson tried to capture the mechanics of every collective action problem with eight simple maxims, his book posed a challenge for researchers to find the conditions and exceptions to his rules11. Hence, multiple studies have surfaced in the decades since the book’s publication to show deviation to Olson’s conditions. Chamberlin, Oliver and Marwell have pointed out that Olson’s group paradox only holds when the good is rivalrous, and they find that the exact opposite is more likely to occur when dealing with a pure public good, meaning that they are more likely to be provided when large groups organise1213. More recently, Hennig-Schmidt et al. have shown evidence that the size of the group is only as crucial as the marginal per capita return on contributions to the public good and that the interaction of these two variables is capable of predicting the size of contributions better than the size of the group14. Furthermore, the exploitation hypothesis is challenged by a novel addition to the theory of public goods15. In addition to the principle of exclusion and the jointness of supply, a good can also be characterised by the function that determines the level of provision given the contributions of the members in the group. This feature is also called the good’s ‘aggregation technology’. In the case of a weakest-link public good, the amount provided is determined by the smallest contribution16. For example, in the case of a global pandemic, the prescribed collective action is to quarantine. If anyone decides to defect then the viral infection will continue to threaten the group; therefore, the smallest contribution has the impact on determining the total negative utility for the group members. The exploitation hypothesis does not hold with weakest-link public goods because those who were previously free-riders will now have to contribute in order to raise the amount of collective good supplied17.

According to the zero contribution thesis, large groups will only overcome collective action problems when there are selective incentives or coercion. Selective incentives refer to the possibility of structuring rewards or punishment so that group members have additional purposes of contributing. Olson argued that very often the gains obtained from public goods are the appended by-products of a private benefit. He illustrated this provision with the case of the American Medical Association where doctors receive a non-excludable benefit from lobbying but only do so because they are interested in private benefits such as copies of medical journals and admission to medical conferences8. Punishment is an alternative to the positive selective incentive; however, this is also hard to achieve given that punishment treatments can incur costs without returns. Nevertheless, experimental studies have shown that, against predicted rational behaviour, individuals are often willing to punish free-riders18.

In order to understand the origin of coercive institutions as a means of ensuring the provision of public goods, it is relevant to discuss the role of political entrepreneurs. Political entrepreneurs attempt to capture the surplus existing in the margins between the collective value of the good and the cost of providing it and do so by possessing the factors of production19. Through taxation, political entrepreneurs can raise funds required to provide the public good. However, without the credible threat of sanctioning, group members will not be compelled to contribute, therefore requiring the political entrepreneur to possess the powers to coerce individuals into paying sanctions. Sanctioning costs can be higher than the benefit of organising the provision of a public good, but if it is only required occasionally, it can still leave the political entrepreneur with substantial payoffs in the long run20.

By now, it is not too hard to see how an understanding of public goods theory can create a justification for the state. Thomas Hobbes argued that “freedom in commons means ruin for all,” and therefore “mutual coercion mutually agreed upon” was required, this is the essence of his famous Leviathan10. David Hume believed that the state emerged organising the public defence from foreign invasion and Adam Smith believed the role of the state is to enable a safe conduit for the invisible hand to guide self-interested cooperation. Both theorised purposes of the state can be understood as a collective action to provide public goods.

Supporters of the state assert that public goods should be provided for free given that the marginal cost of a non-rival good is zero. Hence, it can be more efficient for the state to provide public goods than for the markets to do so21. On the other hand, privatisation has been argued to be the best solution to help combat the depletion of rivalrous goods. Such a situation, also known as the ‘tragedy of the commons’, occurs when consumers ignore the common good of all users and maximise short term extraction at the expense of the healthy replenishment of the common good. Privatisation would incentivise property right holders to maintain a steady supply of the good therefore internalising externalities.

Ostrom argued that privatisation is hard when the good is non-stationary, given that it is hard to keep track of the amounts and to define what owning them means22. For example, it is hard to follow a school of fish and say which fish belongs to whom. For these reasons, these non-rivalrous goods tend to be owned in common. Ostrom put together a compendium of decentralised governance systems around the world that were providing these rivalrous public goods, also called common pooled resources. After reviewing all these cases, Ostrom put together design principles for the successful governance of common pooled resources. In summary, collective action problems are solved when the local users design their own rules and enforce them themselves using graduated sanctions. These rules define who has rights to consume from the rivalrous good and assign costs proportionate to the gains effectively23. As these systems were able to beat the collective action problem even though there were incentives to free-ride, she considered the dichotomy between public good provision by the state or by the markets to be sterile.

Ostrom also tried to explain experimental evidence of non-selfish behaviour such as that of subjects that often contribute between 40 and 60% of their endowment in public good games22. These and other empirical results suggest that perhaps self-interest is not the only motivator1824. An explanation could be that there are multiple types of individuals, among them are the selfish rationals but also individuals that value norms highly enough to willingly punish or to cooperate conditionally to the belief that a sufficient amount of the rest of participants will also contribute. The existence of these types could be explained by social evolution theories whereby certain emotions induce individuals to follow the behaviour that has proven successful in guaranteeing the survival of their ancestors.

The problem of collective action has incited discussion over centuries, but now during the time of a global pandemic, a collapsing global order and rising climate temperatures, understanding what makes us work together for the common good is more important than ever before. As of today, there is no definite theory of collective action. There are multiple threads of research discovering the secrets to collaboration, some of it with the potential to shine a new light into our human nature.

  1. Samuelson, Paul A. 1954. ‘The Pure Theory of Public Expenditure’. The Review of Economics and Statistics 36(4): 387. 

  2. Desmarais-Tremblay, Maxime. 2017. ‘Musgrave, Samuelson, and the Crystallization of the Standard Rationale for Public Goods’. History of Political Economy 49(1): 59–92. 

  3. Baumol, William J. 2004. ‘Welfare Economics and the Theory of the State’. In The Encyclopedia of Public Choice, Springer, 937–940. 

  4. Downs, Anthony. “An economic theory of democracy.” (1957): 260-276. 

  5. Dougherty, Keith L. 2003. ‘Public Goods Theory from Eighteenth Century Political Philosophy to Twentieth Century Economics’. Public Choice 117(3/4): 239–53.  2

  6. Head, John G. 1962. ‘Public-Goods and Public-Policy’. Public Finance-Finances Publiques 17(3): 197–219. 

  7. Buchanan, James M. 1965. ‘An Economic Theory of Clubs’. Economica 32(125): 1– 14. 

  8. Olson, Mancur. 1965. The Logic of Collective Action Public Goods and the Theory of Groups. Cambridge, Mass.: Harvard University Press. http://site.ebrary.com/id/10314321 (May 26, 2020).  2 3 4 5

  9. Ostrom, Elinor. 2000. ‘Collective Action and the Evolution of Social Norms’. The Journal of Economic Perspectives 14(3): 137–58. 

  10. Bowles, Samuel, and Herbert Gintis. 2013. A Cooperative Species: Human Reciprocity and Its Evolution. 1. paperback print. Princeton: Princeton Univ. Press.  2

  11. Sandler, Todd. 2015. ‘Collective Action: Fifty Years Later’. Public Choice 164(3–4): 195–216.  2

  12. Chamberlin, John. 1974. ‘Provision of Collective Goods As a Function of Group Size*’. American Political Science Review 68(2): 707–16. 

  13. Marwell, G., Oliver, P. E., & Prahl, R. (1988). Social networks and collective action: A theory of the critical mass. III. American journal of Sociology, 94(3), 502-534. 

  14. Weimann, J., Brosig-Koch, J., Heinrich, T., Hennig-Schmidt, H., & Keser, C. (2019). Public good provision by large groups–the logic of collective action revisited. European Economic Review, 118, 348-363. 

  15. Cornes, Richard. 1993. ‘Dyke Maintenance and Other Stories: Some Neglected Types of Public Goods’. The Quarterly Journal of Economics 108(1): 259–271. 

  16. Hirshleifer, Jack. 1983. ‘From Weakest-Link to Best-Shot: The Voluntary Provision of Public Goods’. Public choice 41(3): 371–386. 

  17. Sandler, Todd. 2016. ‘Strategic Aspects of Difficult Global Challenges’. Global Policy 7: 33– 44. 

  18. Fehr, Ernst, and Simon Gächter. 2000. ‘Cooperation and Punishment in Public Goods Experiments’. The American Economic Review 90(4): 980–94.  2

  19. Laver, Michael. 1980. ‘Political Solutions to the Collective Action Problem’. Political Studies 28(2): 195–209. 

  20. Frohlich, Norman, Joe A. Oppenheimer, and Oran R. Young. 1971. Political Leadership and Collective Goods. Princeton University Press. 

  21. Hardin, Russell. 1996. ‘Economic Theories of the State’. In Perspectives on Public Choice, ed. Dennis C. Mueller. Cambridge University Press, 21–34. https://www.cambridge.org/core/product/identifier/CBO9780511664458A009/type/bo ok_part (May 24, 2020). 

  22. Ostrom, Elinor. 1990. Governing the Commons: The Evolution of Institutions for Collective Action. Cambridge University Press.  2

  23. Agrawal, Arun. 1999. Greener Pastures: Politics, Markets, and Community among a Migrant Pastoral People. Duke University Press. 

  24. Gächter, Simon, and Benedikt Herrmann. 2009. ‘Reciprocity, Culture and Human Cooperation: Previous Insights and a New Cross-Cultural Experiment’. Philosophical Transactions of the Royal Society B: Biological Sciences 364(1518): 791–806.