Positive Externality

Positive Externality in Health and Health Care

In health economics, a positive externality arises when a person or organisation acts on the benefit it receives itself while part of the gain goes to others, as when treating one person's infection protects the partners they might have infected, or vaccinating young children lowers the rate of disease among unvaccinated adults. Because the decision-maker weighs only its private benefit, less of the beneficial activity takes place than would be chosen if every benefit were counted. The practical questions are which benefits are truly external, how large they are at the margin and whether an economic evaluation counts them. Medical research is a second large source, because knowledge spreads to people who did not pay for it. The general idea is on the externality page, and the harmful mirror case on the negative externality page.

The gap between private and social benefit

Arthur Pigou set out the idea in The Economics of Welfare, first published in 1920. He described cases in which marginal private net product falls short of marginal social net product because incidental services are performed for third parties from whom it is technically difficult to exact payment, and he counted resources devoted to scientific research as the most important of them. In modern notation the wedge is written as follows.

$$MSB(Q) = MPB(Q) + MEB(Q)$$

where $Q$ is the quantity of the activity, $MSB(Q)$ is the marginal social benefit of one more unit, $MPB(Q)$ is the marginal private benefit to the person who decides, which traces their demand curve, and $MEB(Q)$ is the marginal external benefit that goes to third parties.

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

$$MPB(Q_m) = MC(Q_m) \qquad MPB(Q^{*}) + MEB(Q^{*}) = MC(Q^{*})$$

where $MC(Q)$ is the marginal cost of the last unit, $Q_m$ is the market quantity and $Q^{*}$ is the socially efficient quantity. With a positive external benefit and no external cost, $Q_m$ falls short of $Q^{*}$, and the welfare lost on the units never produced is the area between marginal social benefit and marginal cost over that range.

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

where $DWL$ is the deadweight loss from underprovision. With linear demand and marginal cost and a constant marginal external benefit $b$ per unit, the area is a triangle equal to one half of $(Q^{*} - Q_m)$ multiplied by $b$.

Which benefits count as external

In health the line between benefits the decision-maker keeps and benefits that go to others is hard to draw. Five kinds of benefit are often mixed together, and only some belong in the marginal external benefit.

• Lower risk of infection for other people. In the HPTN 052 trial of 1,763 couples in which one partner had HIV-1 and the other did not, Cohen and colleagues found only 1 of 28 linked transmissions in the group that started antiretroviral therapy early, a hazard ratio of 0.04, and concluded that early treatment brought both personal and public health benefits.
• Health and wellbeing of family members. Al-Janabi and colleagues describe health spillovers in which care for one person benefits family carers, for example by relieving them of demanding caring work. They credit Culyer with the concept of the caring externality, which public intervention in health care may internalise.
• Knowledge from research. Arrow argued that no legal arrangement can make information a thoroughly appropriable commodity, because its productive use is bound to reveal it at least in part, and he expected a free enterprise economy to underinvest in research, more so for basic research.
• Savings to collectively financed budgets. Where care is tax-funded, illness averted in other people saves public money that the person who acted never receives.
• Benefit to the decision-maker. A vaccinated person's own protection is already in the private benefit and does not belong in the external benefit.

Measuring marginal external benefit in health

A subsidy or an evaluation needs the external benefit of one more unit at the relevant margin, usually an estimate of benefit to others multiplied by a value per unit. The external benefit of infection control changes with how much of it is already under way.

Whitney and colleagues give early surveillance evidence of indirect benefits. After a pneumococcal conjugate vaccine for young children was licensed in the United States in 2000, the 2001 rate of invasive pneumococcal disease in children under two was 69 per cent below baseline, and rates fell among adults too, by 32 per cent at ages 20 to 39 and 18 per cent at 65 or over. The authors said the vaccine may be reducing disease in adults. Brisson and Edmunds noted that most economic evaluations of vaccination programmes used models that cannot take into account these indirect effects of herd immunity, which a dynamic transmission model captures. How the external benefit of a vaccine changes as coverage rises is shown on the vaccination externalities page.

Research spillovers are measured as a return on public spending. Sussex and colleagues found that each additional GBP 1 of government and charity medical research spending in the United Kingdom was associated with an additional GBP 0.83 to GBP 1.07 of private sector research and development spending. They estimated that this spillover implies a real annual rate of return of 15 to 18 per cent, and around 24 to 28 per cent once earlier estimates of the health gain from public research in cancer and cardiovascular disease were added.

Worked example with influenza vaccination bought at pharmacies (illustrative)

All numbers are illustrative. Adults in a town who are not offered free vaccination can buy a seasonal influenza dose at a pharmacy. Demand gives a marginal private benefit of $MPB = 40 - 0.002Q$ in GBP per dose, where $Q$ is doses a season, and the price, equal to marginal cost, is GBP 12 per dose.

1. Find the market quantity. Marginal private benefit falls to GBP 12 when 0.002 multiplied by the quantity equals 28, so $Q_m = 14{,}000$ doses.

2. Classify the benefits per dose. The vaccinated person's own protection is private and already in the demand curve. An analyst estimates GBP 4.00 for the health of household members and other contacts who avoid infection, GBP 1.00 for NHS treatment avoided in those contacts, GBP 2.00 for working days the employer does not lose and GBP 1.00 for the reassurance relatives feel, a caring externality. The marginal external benefit is 4.00 + 1.00 + 2.00 + 1.00, which is GBP 8.00 per dose.

3. Find the efficient quantity. Marginal social benefit is 48 minus 0.002 multiplied by the quantity, which equals GBP 12 when 0.002 multiplied by the quantity equals 36, so $Q^{*} = 18{,}000$ doses.

4. Measure the welfare loss. The shortfall is 18,000 minus 14,000, or 4,000 doses, and with a constant external benefit the loss is a triangle.

$$DWL = \frac{1}{2} \times 4000 \times 8 = 16000$$

where 4,000 is the number of doses not given, 8 is the external benefit in GBP per dose and the result is GBP 16,000 a season.

5. Change what counts. An analyst who counts only the contacts' health and the NHS saving, the items inside a health and NHS perspective, uses GBP 5.00 per dose. Marginal social benefit then equals GBP 12 when 0.002 multiplied by the quantity equals 33, giving 16,500 doses. The measured loss is one half of 2,500 multiplied by 5, or GBP 6,250 a season, about two fifths of the first estimate.

6. Correct the market. A subsidy of GBP 8.00 per dose lowers the price to GBP 4 and raises uptake to 18,000 doses, at a cost of 8 multiplied by 18,000, or GBP 144,000 a season. Of that, 8 multiplied by 14,000, or GBP 112,000, goes to people who would have been vaccinated anyway, a transfer whose funding cost is discussed on the Pigouvian subsidy page.

7. Interpret. The efficient quantity, the welfare loss and the subsidy all rest on the classification in step 2. The example also holds the external benefit constant, which rarely suits transmission, where the protection of contacts depends on how many of them are already immune.

Positive externalities in economic evaluation and HTA

In a cost-effectiveness analysis an external benefit is counted only if it falls inside the perspective chosen. The NICE manual (PMG36, section 4.2.7) 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. Section 4.2.9 states that productivity costs should not be included, and under section 4.2.10 benefits to other government bodies enter only evaluations agreed with the Department of Health and Social Care. Infections averted in contacts and NHS treatment avoided can therefore enter the reference case if the model captures them, while gains in work output, reassurance and knowledge spillovers belong in a societal perspective or a cost-benefit analysis.

Al-Janabi and colleagues note that health effects from reduced transmission would usually already be counted, because they accrue to potential patients, and they deal instead with family effects that pass through social and psychological routes. For those, the spillovers a new technology generates and the spillovers lost with the care displaced to fund it both matter, which they express with two multipliers.

$$\frac{\Delta c}{\Delta h_p} \times \frac{m_d}{m_i} < k_p$$

where $\Delta c$ is the incremental health care cost, $\Delta h_p$ is the incremental health benefit to patients, $m_i$ is the ratio of total health benefit, to patients and their families, to patient health benefit for the new intervention, $m_d$ is the same ratio for the health benefit displaced, and $k_p$ is the threshold ratio expressed in patient health forgone. When the two multipliers are equal, the conventional rule gives the same decision. With illustrative values, a patient-only ratio of GBP 24,000 per QALY with $m_i = 1.2$ and $m_d = 1.05$ becomes 24,000 multiplied by 1.05 and divided by 1.2, or GBP 21,000. Carer effects are covered on the carer page.

Responses to a positive externality

Pigou argued that the State could remove such a divergence through extraordinary encouragements, of which bounties are the most obvious, and he saw the patent laws as aiming to bring private and social net product closer together for inventions. Arrow added that patents support invention by creating property rights, and that to the extent they succeed the information is underused, so he concluded that optimal allocation to invention would need government or another agency not governed by profit and loss to finance research, a role long accepted in medicine.

For infections, the main instruments are a subsidy set at the marginal external benefit, provision free at the point of use, and mandates, discussed under vaccination policy.

Positive externalities, public goods and spillovers

A positive externality is a by-product of an activity chosen for private reasons. A public good is non-rival and non-excludable, so that once it exists nobody can be kept from using it. In health economics a spillover is any effect beyond the person treated, and once an evaluation counts family spillovers they are part of the outcome, no longer an omitted externality. Market failure is the wider category, of which positive externalities are one source, with the efficiency benchmark set out under welfare economics.

Common misreadings

Most errors come from counting the wrong benefits or valuing them at the wrong point. They recur in subsidy debates and in evaluations.

1. Treating any beneficial activity as a positive externality. A service that improves its user's health has a private benefit. An externality needs a benefit to someone else that the user does not weigh.
2. Counting the user's own benefit twice. The protection of the person vaccinated or treated is already in the demand curve.
3. Using an average where a marginal value is needed. The efficient quantity depends on the external benefit of the last unit, which for an infection can be small once most people are immune.
4. Leaving the benefit out because it is hard to value. Omitting herd protection or knowledge spillovers sets their value at zero, which is itself an assumption.

Sources

• Al-Janabi H, van Exel J, Brouwer W, Coast J. A framework for including family health spillovers in economic evaluation. Medical Decision Making. 2016;36(2):176-186. https://doi.org/10.1177/0272989X15605094
• Arrow KJ. Economic welfare and the allocation of resources for invention. In: The Rate and Direction of Inventive Activity: Economic and Social Factors. Princeton: Princeton University Press; 1962:609-626. https://www.nber.org/chapters/c2144
• Brisson M, Edmunds WJ. Economic evaluation of vaccination programs: the impact of herd-immunity. Medical Decision Making. 2003;23(1):76-82. https://doi.org/10.1177/0272989X02239651
• Cohen MS, Chen YQ, McCauley M, et al. Prevention of HIV-1 infection with early antiretroviral therapy. New England Journal of Medicine. 2011;365(6):493-505. https://doi.org/10.1056/NEJMoa1105243
• 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
• 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
• Sussex J, Feng Y, Mestre-Ferrandiz J, et al. Quantifying the economic impact of government and charity funding of medical research on private research and development funding in the United Kingdom. BMC Medicine. 2016;14:32. https://doi.org/10.1186/s12916-016-0564-z
• Whitney CG, Farley MM, Hadler J, et al. Decline in invasive pneumococcal disease after the introduction of protein-polysaccharide conjugate vaccine. New England Journal of Medicine. 2003;348(18):1737-1746. https://doi.org/10.1056/NEJMoa022823