Negative Externality

Negative Externality in Health and Health Care

In health economics, a negative externality arises when a person or organisation acts on the costs it bears itself while part of the harm lands on others, as when second-hand smoke damages the health of non-smokers or heavy antibiotic use speeds the spread of resistant infections that later patients catch. Because the decision-maker weighs only its private cost, more of the harmful activity takes place than would be chosen if every cost were counted. The hard part in practice is deciding which costs are truly external and valuing them at the margin, and the answer changes the case for taxes and regulation and the results of an economic evaluation. Health care is itself one source. The general idea in both its forms is on the externality page.

The gap between private and social cost

Arthur Pigou set out the idea in The Economics of Welfare, first published in 1920. He described cases in which, owing to the technical difficulty of enforcing compensation for incidental disservices, marginal private net product exceeds marginal social net product, and one of them was the production and sale of intoxicants, which he said should be debited with the extra costs in policemen and prisons that it makes necessary. Elsewhere in the same chapter he noted that factory smoke in large towns inflicts a heavy uncharged loss on the community. In modern notation the wedge is written as follows.

$$MSC(Q) = MPC(Q) + MEC(Q)$$

where $Q$ is the quantity of the activity, $MSC(Q)$ is the marginal social cost of one more unit, $MPC(Q)$ is the marginal cost borne by the producer or consumer who decides, and $MEC(Q)$ is the marginal external cost that falls on third parties.

An unregulated market settles where marginal private benefit equals marginal private cost, while the efficient quantity is where it equals marginal social cost.

$$MPB(Q_m) = MPC(Q_m) \qquad MPB(Q^{*}) = MSC(Q^{*})$$

where $MPB(Q)$ is the marginal private benefit of the last unit, $Q_m$ is the market quantity and $Q^{*}$ is the socially efficient quantity. With a positive external cost and no external benefit, $Q_m$ exceeds $Q^{*}$, and the welfare lost on the extra units is the area between marginal social cost and marginal benefit over that range.

$$DWL = \int_{Q^{*}}^{Q_m} \left[ MSC(Q) - MPB(Q) \right] dQ$$

where $DWL$ is the deadweight loss from overproduction. With linear demand, linear marginal private cost and a constant marginal external cost $e$ per unit, the area is a triangle equal to one half of $(Q_m - Q^{*})$ multiplied by $e$. The externality may come from production, as with factory smoke, or from consumption, as with smoking or antibiotic use.

Which costs count as external

Health is where the line between costs the decision-maker bears and costs borne by others is hardest to draw. Four kinds of cost are often mixed together, and only some belong in the marginal external cost.

• Harm to other people's health. Illness in non-smokers exposed to second-hand smoke and injuries to other road users caused by drink driving are external in the full sense.
• Collectively financed costs. Costs that reach others through shared insurance, pensions and public budgets are external to the user, and savings to the same budgets offset them. Manning and colleagues found that once pension and nursing home savings were netted off, smokers probably paid their way at the cigarette taxes then in force, while alcohol taxes covered only about half of drinkers' costs to others.
• Harm to the decision-maker. Damage that smokers or drinkers do to their own health is a private cost in the standard model and does not by itself justify a corrective tax.
• Price effects on other buyers. When heavy demand raises a product's price, other buyers pay more and sellers receive the same extra amount on those purchases. Economists call this a pecuniary externality and treat it as a transfer, not a real resource cost.

The third category has been challenged. Gruber and Koszegi argued that if smokers are time inconsistent, discounting the step between this period and the next more heavily than steps between later periods, optimal policy should also depend on the internalities that smokers impose on themselves. They estimated that the optimal tax per pack of cigarettes would then be at least USD 1 higher than under the rational addiction model, in which only externalities imposed on others matter. An internality is a separate argument and is better reported as one.

Measuring marginal external cost in health

A corrective policy or an evaluation needs the external cost per unit at the relevant margin, usually the product of an epidemiological estimate of harm to others and a value per unit of harm. Valuation is often the weaker half.

For second-hand smoke, Oberg and colleagues used comparative risk assessment with data from 192 countries and estimated that exposure caused 603,000 deaths worldwide in 2004, about 1.0% of worldwide mortality, and 10.9 million disability-adjusted life years, with 28% of the deaths in children. Such a total in deaths and DALYs must be valued and divided by consumption, which gives an average cost per pack that equals the marginal cost only if harm rises in proportion to smoking.

For antimicrobial resistance, Shrestha and colleagues linked antibiotic consumption to later resistance in five pathogens and to the economic cost of that resistance. Their cost of resistance per standard unit consumed ranged between USD 0.1 and USD 0.7 by drug class in Thailand and between USD 0.1 and USD 0.6 in the United States, often more than the purchase cost of the drug. The shared stock of antibiotic effectiveness is also a commons.

Health services generate external costs too. Tennison and colleagues estimated that the NHS in England emitted 25 megatonnes of carbon dioxide equivalent in 2019, with 62% of the footprint coming from the supply chain. The damage falls on people outside any clinical decision, and needs a value per tonne before it can enter an analysis.

Worked example with second-hand smoke and a fiscal cost (illustrative)

All numbers here are illustrative, not estimates for any real market. Weekly demand for cigarettes in a town gives a marginal private benefit of $MPB = 12 - 0.001Q$ in GBP per pack, and the price is a constant GBP 6 per pack, with demand taken to reflect the smoker's own valuation of the health risk.

1. Find the market quantity. Marginal private benefit falls to GBP 6 when 0.001 multiplied by the quantity equals 6, so $Q_m = 6{,}000$ packs a week.

2. Classify the costs per pack. An analyst estimates harm to the smoker's own health at GBP 5, harm to non-smokers from second-hand smoke at GBP 1.50, extra tax-funded health care for smokers at GBP 1.00 and pension savings to others from earlier deaths at GBP 0.50. The GBP 5 is a private cost already reflected in demand, so it is left out of the external cost. The marginal external cost is 1.50 + 1.00 minus 0.50, which is GBP 2.00 per pack.

3. Find the efficient quantity. Marginal social cost is 6 + 2 = GBP 8. Marginal private benefit equals GBP 8 when 0.001 multiplied by the quantity equals 4, so $Q^{*} = 4{,}000$ packs.

4. Measure the welfare loss. The overproduction is 6,000 minus 4,000, or 2,000 packs, and with a constant external cost the loss is a triangle.

$$DWL = \frac{1}{2} \times 2000 \times 2 = 2000$$

where 2,000 is the number of excess packs, 2 is the external cost in GBP per pack and the result is GBP 2,000 a week.

5. Change what counts. An analyst who counts only second-hand smoke uses GBP 1.50, so marginal social cost is GBP 7.50, which marginal private benefit reaches when 0.001 multiplied by the quantity equals 4.5, giving 4,500 packs. The loss is one half of 1,500 multiplied by 1.50, or GBP 1,125 a week, a little over half the first estimate.

6. Correct the market. A tax of GBP 2.00 per pack, equal to the marginal external cost in step 2, raises the price to GBP 8 and cuts sales to 4,000 packs, raising 4,000 multiplied by 2, or GBP 8,000 a week.

7. Interpret. The externality, the efficient quantity and the corrective tax all rest on the classification in step 2. Netting off the pension saving follows the logic of Manning and colleagues. An internality would justify a higher tax, but it should be labelled as such and not as external cost.

Negative externalities in economic evaluation and HTA

In a cost-effectiveness analysis an external cost is counted only if it falls inside the perspective chosen. The NICE manual (PMG36, sections 4.2.7 and 4.2.9) sets the reference case perspective on outcomes as all relevant health effects, whether for patients or, when relevant, other people (mainly carers), and the perspective on costs as that of the NHS and personal social services. Under section 4.2.10, benefits to other government bodies, such as reduced crime, enter only analyses agreed with the Department of Health and Social Care and are presented separately. External harm that appears as ill health in other people can therefore enter in principle, while external costs outside health and the NHS budget belong in a societal perspective or a cost-benefit analysis.

Resistance shows how easily such a cost is dropped. Coast, Smith and Millar found no methodological justification for leaving it out, and expected it to go on being ignored because the costs are hard to measure. Shrestha and colleagues produced their per-unit estimates so that evaluations of antibiotics, diagnostics and vaccines could include it. A rapid diagnostic that cuts antibiotic use is undervalued when the cost is omitted, and a new antibiotic is overvalued if its extra use carries no resistance cost in the model. Paying for new antibiotics is covered under antimicrobial economics.

Responses to a negative externality

A Pigouvian tax set at the marginal external cost at the efficient quantity is the textbook response, and its design has its own page. Smoke-free laws act on quantity directly, and antibiotic stewardship acts on prescribing.

Coase argued that harm is reciprocal and that, if the pricing system works without cost, the outcome that maximises the value of production does not depend on who is legally liable. Most health externalities involve very large numbers of people, many of them future patients, so the bargaining route on the Coase theorem page rarely applies. Manning and colleagues noted that a tax might be raised for other reasons, such as reducing the number of adolescent smokers, and such reasons are better stated openly.

Positive externalities, internalities and market failure

A positive externality is the mirror case, an uncompensated benefit that leads to too little of an activity, and the transmission benefits of immunisation are on the vaccination externalities page. An internality is a cost a person imposes on their own future self. Market failure is the wider category, of which negative externalities are one source. A cost-of-illness estimate for drinking adds private, external and fiscal costs, so it differs from the marginal external cost a corrective policy needs, and the method is described under cost-of-illness studies.

Common misreadings

Most errors come from counting the wrong costs or valuing them at the wrong point. They recur in debate about health taxes and in economic evaluations.

1. Treating total social cost as external cost. Estimated totals of tobacco or alcohol harm usually include harm to users themselves, which the standard model treats as private.
2. Using an average where a marginal value is needed. The efficient quantity depends on the external cost of the last unit, which can differ from the average over current use.
3. Assuming any intervention improves on the market. The costs and side effects of the response still have to be weighed against the harm avoided.
4. Leaving the cost out because it is hard to value. Omitting resistance or emissions sets their value at zero, which is itself an assumption.

Sources

• Coase RH. The problem of social cost. Journal of Law and Economics. 1960;3:1-44. https://doi.org/10.1086/466560
• Coast J, Smith RD, Millar MR. Superbugs: should antimicrobial resistance be included as a cost in economic evaluation? Health Economics. 1996;5(3):217-226. https://pubmed.ncbi.nlm.nih.gov/8817296/
• Gruber J, Koszegi B. Is addiction "rational"? Theory and evidence. Quarterly Journal of Economics. 2001;116(4):1261-1303. NBER Working Paper 7507. https://www.nber.org/papers/w7507
• Manning WG, Keeler EB, Newhouse JP, Sloss EM, Wasserman J. The taxes of sin. Do smokers and drinkers pay their way? JAMA. 1989;261(11):1604-1609. https://pubmed.ncbi.nlm.nih.gov/2918654/
• National Institute for Health and Care Excellence. NICE technology appraisal and highly specialised technologies guidance: the manual (PMG36). Published 31 January 2022, last updated 13 October 2026. Sections 4.2.7, 4.2.9 and 4.2.10. https://www.nice.org.uk/process/pmg36
• Oberg M, Jaakkola MS, Woodward A, Peruga A, Pruss-Ustun A. Worldwide burden of disease from exposure to second-hand smoke: a retrospective analysis of data from 192 countries. Lancet. 2011;377(9760):139-146. https://doi.org/10.1016/S0140-6736(10)61388-8
• Pigou AC. The Economics of Welfare. London: Macmillan; 1920 (4th edition, 1932, consulted for Part II, Chapter IX). https://www.econlib.org/library/NPDBooks/Pigou/pgEW.html
• Shrestha P, Cooper BS, Coast J, et al. Enumerating the economic cost of antimicrobial resistance per antibiotic consumed to inform the evaluation of interventions affecting their use. Antimicrobial Resistance and Infection Control. 2018;7:98. https://doi.org/10.1186/s13756-018-0384-3
• Tennison I, Roschnik S, Ashby B, et al. Health care's response to climate change: a carbon footprint assessment of the NHS in England. Lancet Planetary Health. 2021;5(2):e84-e92. https://doi.org/10.1016/S2542-5196(20)30271-0