23.01.23 · economics / market-failure

Externalities and public goods

draft3 tiersLean: none

Anchor (Master): Mas-Colell, Whinston & Green, Microeconomic Theory; relevant academic sources

Intuition [Beginner]

A factory dumps waste into a river. The factory owner pays only the cost of production, not the cost of polluted water downstream. Downstream residents bear that cost. This is a negative externality: a cost imposed on third parties who did not choose to incur it.

The opposite also occurs. A beekeeper's bees pollinate a neighbouring orchard, increasing the farmer's yield. The beekeeper receives no payment for this service. This is a positive externality: a benefit conferred on third parties who did not pay for it.

When externalities exist, the private cost (or benefit) of an action diverges from the social cost (or benefit). The market produces too much of goods with negative externalities and too little of goods with positive externalities. The price signal, which normally coordinates individual self-interest with social welfare, fails.

Related to externalities are public goods -- goods that are non-rival (one person's use does not reduce availability to others) and non-excludable (it is impossible or costly to prevent non-payers from using them). National defence, street lighting, and clean air are classic examples. Because no one can be excluded, individuals have an incentive to "free ride" -- enjoy the good without paying. If enough people free ride, the good is underprovided or not provided at all, even when everyone would benefit from it.

Visual [Beginner]

Negative Externality (Pollution)

  Price
    |          S_private
    |         /
    |        /          S_social
    |       /          /
    |      /          /
  Pm |--- / ---------/------ Market equilibrium
    |    /          /
    |   /          /
  P* |----------- / -------- Socially optimal
    |            /
    |           /
    +------------------------ Quantity
         Q*      Qm

  Qm > Q*: Market overproduces.
  Deadweight loss = triangle between S_social and S_private
                    from Q* to Qm.


Public Goods and Free Riding

  Good is non-excludable:
    Person A pays ----> Good exists
    Person B pays nothing ----> B enjoys good anyway
    Person B's incentive: don't pay, still benefit.
    Result: good is underprovided.

Worked Example [Beginner]

A coal plant produces electricity sold at $0.10/kWh. Each kWh also causes $0.03 in health damages from air pollution. The plant does not pay these health costs.

Quantity (kWh)	Private MC	Social MC	Demand Price
100	$0.06	$0.09	$0.14
200	$0.08	$0.11	$0.12
300	$0.10	$0.13	$0.10
400	$0.12	$0.15	$0.08

Market equilibrium: Private MC = Demand, so Q = 300 at P = $0.10. Social optimum: Social MC = Demand, so Q = 200 at P = $0.12.

The market overproduces by 100 kWh. The deadweight loss from the externality is the area between the social MC and demand curves from Q = 200 to Q = 300.

A Pigouvian tax of $0.03/kWh would internalise the externality by shifting the private MC up to equal the social MC, moving the market to the socially optimal quantity.

Check Your Understanding [Beginner]

Formal Definition [Intermediate+]

An externality exists when an agent's utility or production function depends directly on the choices of another agent, not mediated through market prices. Formally, if agent $i$ 's utility depends on agent $j$ 's consumption $x_{j}$ :

$u_{i} = u_{i} (x_{i}, x_{j})$

and this dependence is not reflected in any price, then there is an externality.

The social marginal cost of production is:

$S M C = P M C + M E C$

where $P M C$ is private marginal cost and $M E C$ is marginal external cost. The socially optimal quantity equates social marginal cost with marginal benefit (demand):

$S M C (Q^{*}) = M B (Q^{*})$

The market equilibrium equates private marginal cost with marginal benefit:

$P M C (Q_{m}) = M B (Q_{m})$

When $M E C > 0$ (negative externality), $Q_{m} > Q^{*}$ and the market overproduces.

Pigouvian tax: A per-unit tax $t = M E C (Q^{*})$ imposed on the producer shifts the private cost curve upward to equal the social cost curve, internalising the externality. The tax revenue equals the external cost at the optimal quantity.

Coase theorem: If property rights are well-defined and transaction costs are zero, private bargaining will internalise the externality regardless of who holds the initial rights. The allocation is efficient; only the distribution of surplus changes.

Public goods

A good is purely public if:

Non-rival: $x_{i} = X$ for all $i$ -- one agent's consumption does not reduce the amount available to others.
Non-excludable: It is impossible or prohibitively costly to prevent any agent from consuming the good.

The Samuelson condition for the optimal provision of a public good is:

$i = 1 \sum n M B_{i} (Q^{*}) = M C (Q^{*})$

The sum of all individuals' marginal benefits must equal the marginal cost of provision. Because individuals have an incentive to understate their true willingness to pay (free riding), private provision yields less than $Q^{*}$ .

Mechanisms for public good provision: Governments can provide public goods funded by taxation (forced contribution eliminates free riding). Alternatively, mechanisms like the Clarke-Grooves (VCG) mechanism can truthfully elicit willingness to pay, though these are rarely implemented in practice due to complexity.

Key Concepts [Intermediate+]

Externality: A cost or benefit affecting a third party not involved in the transaction. Not reflected in market prices.
Negative externality: External cost. Leads to overproduction relative to the social optimum.
Positive externality: External benefit. Leads to underproduction relative to the social optimum.
Social cost: Private cost plus external cost. The full cost of an activity to society.
Pigouvian tax: A tax equal to the marginal external cost at the optimal quantity. Internalises the externality by aligning private and social costs.
Cap-and-trade: A system that sets a total limit (cap) on an activity (e.g., emissions) and distributes tradable permits. Combines regulation with market incentives.
Coase theorem: If property rights are clear and transaction costs are zero, private bargaining resolves externalities efficiently regardless of the initial allocation of rights.
Public good: Non-rival and non-excludable. Subject to free riding and underprovision by private markets.
Free rider problem: Individuals who benefit from a good without contributing to its cost. Leads to underprovision of public goods.
Tragedy of the commons: Overuse of a common-pool resource (rival but non-excludable) because no individual bears the full cost of their use.
Samuelson condition: The optimal quantity of a public good equates the sum of all individuals' marginal benefits to marginal cost.

Exercise 1. A factory emits pollution costing downstream residents $5 per unit of output. The factory's private marginal cost is $10 + Q, and the marginal benefit of output is $30 - Q. Find the market equilibrium, the socially optimal quantity, and the Pigouvian tax that would correct the externality.

Exercise 2. Three individuals have marginal benefits from a public good of $M B_{1} = 20 - Q$ , $M B_{2} = 15 - Q$ , $M B_{3} = 10 - Q$ . The marginal cost of providing the good is $M C = 15 + Q$ . Find the socially optimal quantity. If the good were left to private provision, how much would be provided?

Academic Perspectives [Master]

Neoclassical view

The neoclassical tradition treats externalities as a deviation from the competitive ideal that can be corrected through well-designed policy instruments. Pigou (1920) proposed per-unit taxes on negative externalities and subsidies for positive externalities. The approach assumes the government can measure the marginal external cost accurately -- a non-trivial requirement.

Cap-and-trade systems, formalised by Montgomery (1972), achieve the same efficient allocation as Pigouvian taxes under ideal conditions, but the permit allocation determines the distribution of surplus. The equivalence breaks down when uncertainty is introduced: Weitzman (1974) showed that taxes outperform permits when the marginal benefit curve is steep relative to the marginal cost curve, and permits outperform taxes when the reverse holds.

Coasean / institutional view

Ronald Coase (1960) challenged the Pigouvian orthodoxy by arguing that the standard analysis was incomplete. If transaction costs are low, the affected parties can bargain to an efficient outcome without government intervention. The famous Coase theorem states that the initial assignment of property rights does not affect efficiency -- only the distribution of surplus.

Coase himself emphasised that transaction costs are rarely zero in practice, making the theorem less a policy prescription than a framework for analysis: the real question is whether government intervention reduces transaction costs more than it creates new inefficiencies. This insight launched the field of law and economics.

Critics note that the Coase theorem requires bilateral (or few-party) externalities with clear causation, well-defined property rights, and low bargaining costs -- conditions rarely met for environmental problems involving millions of polluters and millions of affected parties.

Austrian school

Austrian economists are generally sceptical of Pigouvian taxation on epistemic grounds. Hayek's knowledge problem applies: the government cannot calculate the optimal tax because the relevant information (individuals' marginal damages) is dispersed and tacit. Any tax rate is necessarily arbitrary.

Austrians prefer property rights solutions: if property rights to clean air, clean water, and quiet are clearly defined and enforceable through common law, the affected parties can negotiate solutions. In the Austrian view, the externality problem often stems from poorly defined property rights (e.g., the government allowing factories to pollute public waterways) rather than from a market failure per se.

Critics respond that property rights approaches are impractical for diffuse externalities like climate change, where causation is global and cumulative.

Marxian perspective

Marxian economists view environmental externalities not as accidental market failures but as systematic features of capitalist production. The drive to accumulate capital and maximise profit creates pressure to externalise costs onto workers (occupational hazards), communities (pollution), and future generations (resource depletion). The "free" use of nature as a sink for waste is treated as a subsidy to capital.

From this perspective, Pigouvian taxes and cap-and-trade do not address the underlying structural dynamic. They may mitigate specific harms but cannot resolve the systemic tendency toward environmental degradation, which requires confronting the growth imperative itself.

Critics note that this analysis struggles to explain why some capitalist economies have achieved significant environmental improvements (e.g., reductions in air pollution in wealthy nations) while some non-capitalist economies have experienced severe environmental degradation (e.g., the Soviet Union).

Ecological economics

Ecological economists, following Herman Daly, argue that the neoclassical framework treats the environment as an externality to be internalised rather than as the biophysical foundation of the economy. They advocate steady-state economics: an economy that operates within ecological limits, rather than one that treats environmental constraints as correctable deviations from an infinite growth path.

Historical Context [Master]

Pigou (1920): Arthur Pigou's The Economics of Welfare introduced the concept of divergences between private and social costs and proposed corrective taxes. The Pigouvian tax remains a central policy instrument.
Coase (1960): "The Problem of Social Cost" challenged Pigouvian analysis by showing that, under zero transaction costs, private bargaining achieves efficiency regardless of the initial allocation of rights. One of the most cited papers in economics.
Hardin (1968): "The Tragedy of the Commons" argued that common-pool resources are inevitably overexploited. Hardin's solution was either privatisation or state control. The essay provoked decades of research.
Ostrom (1990): Elinor Ostrom's Governing the Commons showed that communities can manage common-pool resources sustainably through local institutions, contradicting Hardin's pessimism. Ostrom received the Nobel Prize in 2009.
Samuelson (1954): Paul Samuelson formalised the theory of public goods and derived the Samuelson condition for optimal provision. His paper "The Pure Theory of Public Expenditure" founded the modern public goods literature.
Weitzman (1974): Martin Weitzman's "Prices vs. Quantities" compared the efficiency of Pigouvian taxes and cap-and-trade under uncertainty, providing the theoretical foundation for modern environmental policy design.
Montgomery (1972): Formalised the equivalence of cap-and-trade permits and Pigouvian taxes under ideal conditions, establishing the theoretical basis for emissions trading.
Stern Review (2006): Nicholas Stern's report on climate change applied externality theory to the largest collective action problem in history, estimating the social cost of carbon and arguing for immediate, aggressive mitigation. The report reignited debate over discount rates and intergenerational equity.

Bibliography [Master]

Coase, R. H. (1960). The problem of social cost. Journal of Law and Economics, 3, 1-44.
Hardin, G. (1968). The tragedy of the commons. Science, 162(3859), 1243-1248.
Montgomery, W. D. (1972). Markets in licenses and efficient pollution control programs. Journal of Economic Theory, 5(3), 395-418.
Ostrom, E. (1990). Governing the Commons: The Evolution of Institutions for Collective Action. Cambridge University Press.
Pigou, A. C. (1920). The Economics of Welfare. Macmillan.
Samuelson, P. A. (1954). The pure theory of public expenditure. Review of Economics and Statistics, 36(4), 387-389.
Stern, N. (2006). The Economics of Climate Change: The Stern Review. Cambridge University Press.
Weitzman, M. L. (1974). Prices vs. quantities. Review of Economic Studies, 41(4), 477-491.