Lump-Sum Tax

Lump-Sum Tax in Welfare Economics and Health Appraisal

A lump-sum tax is a tax set so that nothing the taxpayer does, whether working less or buying different goods, changes the sum owed. Because the bill cannot be reduced by any change of behaviour, it lowers what people can spend without changing the relative prices they face, and welfare economics treats it as the efficient benchmark against which real taxes are judged. Health economists meet the idea when they ask what a pound of public money for health care costs society, and when they weigh the welfarist argument that distribution belongs to the tax system and not to cost-benefit analysis. Real governments almost never levy one, so its value lies in the gap it reveals between the benchmark and the taxes that fund health services.

A tax bill that no choice can alter

Tax by Design, the report of the Mirrlees Review of the UK tax system, defines lump-sum taxes as taxes whose liability cannot be altered by any change in behaviour. Most taxes place a wedge between what a buyer pays and a seller receives, and people respond to the wedge. A lump-sum tax places no wedge, as the household budget constraint shows.

$$\sum_{j=1}^{n} p_j x_j = m - T$$

where $p_j$ is the price of good $j$, $x_j$ is the quantity of good $j$ bought, $n$ is the number of goods, $m$ is income before tax and $T$ is the lump-sum tax, a fixed amount that does not vary with any $x_j$ or with hours worked.

The tax moves the budget line inwards without changing its slope. Tax by Design separates the income effect of having less to spend from the substitution effect of facing different relative prices, and links the excess burden of a tax on earnings to the size of the substitution response. A lump-sum tax keeps the income effect and removes the substitution effect, so the money paid is the whole of the taxpayer's loss and the deadweight loss, or excess burden, is zero.

$$EB = L - R$$

where $EB$ is the excess burden of a tax, $L$ is the money value of the loss it imposes on taxpayers and $R$ is the revenue it raises. For a lump-sum tax $L$ equals $R$, while Tax by Design observes that for real taxes the costs to consumers and producers almost always exceed the revenue.

Mankiw, Weinzierl and Yagan note that with one representative consumer, who pays the whole tax bill in one form or another, and no market imperfection such as an externality, the planner does best by not distorting choices at all, which a lump-sum tax achieves. Hines notes that Harberger's deadweight loss triangles were calculated with tax revenue returned to consumers in lump-sum fashion, so the loss measured came from distorted choices and not from the payment of money.

Lump-sum transfers and the split between efficiency and distribution

Run in reverse, the device is a lump-sum transfer, a payment that no choice by the recipient can enlarge. The second fundamental theorem of welfare economics holds that, under strong conditions, any Pareto efficient allocation can be reached as a competitive equilibrium once purchasing power has been suitably redistributed, and Adler states the theorem as a market equilibrium at some prices with a lump-sum expenditure amount for each person.

Arrow's founding paper on medical care starts here. If the optimality theorems hold and real markets fit the competitive model, policy can confine itself to redistributing purchasing power, most simply through money taxes and subsidies, and leave allocation to the market. Arrow adds that in practice it is virtually impossible to find taxes and subsidies that do not harm the achievement of an optimal state, and that where the market differs significantly from the competitive model the separation becomes in most cases impossible.

The split supports a central welfarist position in health appraisal. Brouwer, Culyer, van Exel and Rutten describe applied cost-benefit analysis as giving an equal unit weight to each money gain or loss whoever receives it, with the initial distribution of income and wealth normally taken as given. Extra-welfarism, they write, may judge changes by additional ethical criteria and weight need explicitly, a route that equity-weighted analysis follows.

Adler sets out when unweighted analysis can be defended this way. If the decision maker in a non-tax body and the legislature share a utilitarian or isoelastic social welfare function, and the tax system is lump-sum, with zero administrative cost, no adverse incentive effects on labour supply or attributes such as health, and attributes that officials can observe, distributional weights are identical for everyone. He concludes that the absence of a lump-sum tax system, with the economic and political costs of tax reform, undercuts the objection that distributional concerns should be wholly relegated to the tax code.

Why real tax systems almost never use one

Tax by Design gives the practical reasons. A lump-sum liability could be tied to a characteristic the taxpayer cannot alter, such as age or some measure of inherent ability, but such characteristics are either undesirable as the sole basis for a tax bill or impossible to define or measure. The same lump sum for everyone is feasible, yet its lack of any link to ability to pay makes it politically unattractive, and the review cites public reaction to the UK community charge, the official title of the poll tax.

Mankiw, Weinzierl and Yagan add that a uniform lump-sum tax falls equally on rich and poor and so places a greater relative burden on the poor, and they describe the community charge levied from 1989 as deeply unpopular and quickly revoked. A government that could observe inherent ability could levy lump-sum taxes contingent on ability and reach equality with no efficiency cost. Real governments observe income and not ability, the problem Mirrlees formalised in 1971 to launch the second wave of optimal tax models.

Tax by Design states that most taxes alter behaviour and reduce both welfare and economic output, so tax-funded health services rest on taxes of that kind, and the lump-sum tax survives as the yardstick for how far each falls short.

The cost of a pound of public money for health care

Under a lump-sum tax each pound raised for a health programme costs taxpayers exactly one pound. Under real taxes it costs more, because the excess burden comes on top of the revenue.

$$\lambda = \frac{R + EB}{R}$$

where $\lambda$ is the cost to taxpayers of each pound of revenue, averaged over all the revenue raised, and $R$ and $EB$ are as defined above. A lump-sum tax gives $\lambda$ equal to one, and the marginal cost of public funds applies the same idea to the last pound raised.

The UK Green Book (2026) advises against counting the costs of raising public funds in most appraisals, because most proposals are funded from pre-determined departmental budgets and the overall level of spending is decided separately and in advance. Its one exception is the assessment of private finance options.

Within a fixed health budget this convention has the same effect as treating the money as if a lump-sum tax had raised it. A cost-effectiveness threshold then reflects the opportunity cost of spending inside that budget, and the excess burden of the taxes that filled it lies outside the comparison. The benchmark matters most in a cost-benefit analysis that sets public spending against benefits valued in money.

Lump-sum premiums, income transfers and health taxes

Insurance theory draws the same line. Nyman quotes Pauly's 1968 analysis of moral hazard, which assumed no significant income effects on the demand for medical care from paying a lump-sum premium. Nyman argued that part of the extra care bought under insurance is explained by income transfers that the healthy make, through the insurer, to the ill, and that this part should be excluded from the welfare loss as income transfers usually are.

Health taxes use lump-sum recycling as a modelling device. Allcott, Lockwood and Taubinsky compute an optimal sugar-sweetened beverage tax holding the US income tax at its status quo and assuming the revenue is distributed equally across all consumers as a lump-sum payment, and their appendix compares that case with revenue targeted to the poorest 10%. A soda tax of this kind is a Pigouvian tax, designed to change behaviour, so it sits at the opposite pole from a lump-sum tax.

Worked example with a vaccination programme funded two ways

The numbers are illustrative. A ministry appraises a vaccination programme costing GBP 800,000 a year, whose benefits a willingness-to-pay study values at GBP 860,000 a year, in a cost-benefit analysis that counts the cost of tax finance.

1. Lump-sum finance. 40,000 households each pay GBP 20, which raises 40,000 × 20 = GBP 800,000. Whatever else households change, their loss is exactly the GBP 800,000 they pay, so $\lambda$ is 1.000.

2. Excise finance. A tax of GBP 10 a unit is instead placed on a good with demand $Q = 120 - 2P$, where $Q$ is thousands of units a year and $P$ is the price in GBP, supplied at a constant GBP 10 a unit. Before the tax 120 − 2 × 10 = 100 thousand units are sold, and at the taxed price of GBP 20, 120 − 2 × 20 = 80 thousand. Revenue is 10 × 80,000, or GBP 800,000.

3. Excess burden. Each of the 20,000 units no longer bought was worth between zero and GBP 10 more to its buyer than its cost. The loss is the triangle 0.5 × 10 × 20,000, or GBP 100,000, so taxpayers lose GBP 900,000 and $\lambda$ is 900,000 / 800,000 = 1.125.

4. Verdict. With lump-sum finance the net benefit is 860,000 − 800,000 = GBP 60,000 a year. With excise finance it is 860,000 − 900,000, a loss of GBP 40,000 a year, and the programme fails.

5. Who pays. The GBP 20 is 0.2% of an income of GBP 10,000, since 20 divided by 10,000 is 0.002, but 0.04% of an income of GBP 50,000, since 20 divided by 50,000 is 0.0004.

The verdict turns only on how the money is raised. An appraisal that ignores the cost of tax finance has in effect adopted the lump-sum row, which the Green Book's fixed-budget reasoning supports but which is optimistic when the spending adds to taxation. The lump-sum option wins on efficiency while taking five times the share of income from the poorer household, the equity-efficiency trade-off in miniature.

Boundaries with neighbouring ideas

A Pigouvian tax is meant to change a choice and a lump-sum tax to leave every choice alone. Tax by Design names one other tax that should not change behaviour, a tax on pure economic rents, which falls only on the return above what a resource would earn in its next-best use. A fixed charge per prescription item ignores income, yet the total paid depends on how much care a person uses, so it acts as a price.

A uniform lump-sum tax ignores vertical equity, since people with very different ability to pay owe the same amount. The reverse instrument, a universal lump-sum grant paired with a flat marginal tax rate, belongs to the optimal taxation debate. The theory of the second best explains why removing one distortion among several need not raise welfare.

Limitations and common misreadings

The commonest misreading takes "lump-sum" to mean that people do not react to the tax. The definition concerns the liability, not the behaviour, and a lump-sum tax still has an income effect. Its efficiency comes from the absence of a substitution effect.

A second error treats lump-sum finance as fair because everyone pays the same, when an equal sum is a far heavier load on a low income. A third reads the Green Book's advice to leave out the cost of raising public funds as a claim that the taxes behind health budgets are lump-sum, when it is a rule about fixed budgets and the excess burden returns whenever a decision changes the total to be raised.

A fourth concerns distribution. The welfarist argument that unweighted cost-benefit analysis is neutral, because the tax system can redistribute at no cost, rests on lump-sum taxes and transfers that real tax systems lack, a point Arrow made in 1963 for medical care and Adler uses against the objection to distributional weights.

Sources

• Adler MD. 2013. Cost-Benefit Analysis and Distributional Weights: An Overview. Duke Environmental and Energy Economics Working Paper EE 13-04. https://www.gov.br/casacivil/pt-br/assuntos/governanca/regulacao/documentos/biblioteca-internacional/2013/cost-benefit-analysis-and-distributional-weights_-an-overview.pdf
• Allcott H, Lockwood B, Taubinsky D. 2019. Regressive sin taxes, with an application to the optimal soda tax. NBER Working Paper 25841. https://www.nber.org/papers/w25841
• Arrow KJ. 1963. Uncertainty and the welfare economics of medical care. American Economic Review 53(5): 941-973. https://www.aeaweb.org/aer/top20/53.5.941-973.pdf
• Brouwer WBF, Culyer AJ, van Exel NJA, Rutten FFH. 2008. Welfarism vs. extra-welfarism. Journal of Health Economics 27(2): 325-338. https://eprints.whiterose.ac.uk/id/eprint/3789/1/brouwerwb1.pdf
• Hines JR. 1998. Three sides of Harberger triangles. NBER Working Paper 6852. Published in Journal of Economic Perspectives 13(2): 167-188, 1999. https://www.nber.org/papers/w6852
• HM Treasury. 2026. The Green Book (2026). https://www.gov.uk/government/publications/the-green-book--2/the-green-book-2026
• Mankiw NG, Weinzierl M, Yagan D. 2009. Optimal taxation in theory and practice. NBER Working Paper 15071. https://www.nber.org/papers/w15071
• Mirrlees J, Adam S, Besley T, Blundell R, Bond S, Chote R, Gammie M, Johnson P, Myles G, Poterba J. 2011. Tax by Design: The Mirrlees Review. Oxford University Press for the Institute for Fiscal Studies. https://ifs.org.uk/sites/default/files/output_url_files/taxbydesign.pdf
• Nyman JA. 1999. The welfare economics of insurance contracts that pay off by reducing price. Discussion Paper 308, Center for Economic Research, University of Minnesota. https://conservancy.umn.edu/server/api/core/bitstreams/a5bf0296-3317-4e72-a0ed-753b517c443d/content