Once upon a time in the land of America, there lived triplet brothers named Tom, Dick, and Harry Class. They were 45 years old, had virtually the same aptitude (skill), and were raised in the same home. Each was married and had two children. All three were employed as carpenters making $25 per hour, working 50 weeks a year.

While they were almost identical in most respects, they had somewhat different preferences and values. For example, Tom, who worked 20 hours a week, had a different work ethic from his brothers, Dick and Harry, who each worked 60 hours per week. Neither Tom’s nor Dick’s wives worked, while Harry’s wife worked 40 hours per week as an office manager making $50,000 per year (the same hourly rate as her husband). Tom and Dick spent all of their income, and were relying on Social Security to take care of them when they retired. Harry and his wife, on the other hand, saved most of her after-tax income over many years, gradually accumulating $300,000. They invested this money in bonds and real estate that produced $25,000 a year in interest and rental income. This was the income of each family:

Family income

Despite their different priorities, the Class families were close; so much so that when a new housing tract was developed in their community, they each bought an equal-priced home on the same private street. Theirs were the only houses on the street.

One day the brothers decided to pool their funds for the purpose of improving their street. Concerned about crime and safety, and desirous of a more attractive setting for their homes, the three families decided to: install a gate at the street’s entrance to deter burglars; add lighting for safety and additional security; repave the street’s surface to repair damage; and install landscaping to beautify the approach to their homes. The work was done for a total cost of $30,000.

The brothers were quite happy with the outcome and felt the $30,000 was a worthy expenditure given the benefits provided each family. But when it came time to divide up the bill, the problems began.

Harry thought it would be simple to divide the bill. Since the benefits to each family were equal, each brother should pay one-third, or about $10,000. But Tom and Dick objected. “Why should we pay the same as you?” they said. “You make much more money than we do.” Harry was puzzled. “Why is that relevant?” he asked. “My family makes more money than yours does because my wife and I work long hours and we earn extra money on our savings. Why should we be penalized for working and saving?” Harry looked at Tom and said, “I’m no smarter or more talented than you are. If you and your wife worked harder and saved more you would make as much as my family does.” To which Tom replied, “I don’t work more because I value my leisure time more than I value money. And I don’t save because I prefer the gratification of consumption today more than I will when I’m too old to enjoy it.” Tom was adamant. How could Harry, who was clearly “rich,” ask him to pay the same amount, when it was obviously harder for him to do so?

Dick thought for a moment, and then said, “I’ve got an idea. Our aggregate income is $250,000, and $30,000 is 12 percent of that amount. Why don’t we each pay that percentage of our income? Under that formula, Tom would owe $3,000, I would owe $9,000, and Harry would owe $18,000. Since I make three times as much as Tom, I would pay three times as much. Harry, who makes twice as much as me and six times as much as Tom would pay two times as much as me and six times as much as Tom.”

“No,” said Tom. “No?” Dick and Harry responded in unison. “Why not? What do you propose instead?” asked Harry. Tom was ready with his answer. “Paying the same percentage of our income is not fair. Instead, Harry, you pay $23,450; Dick, you pay $6,550; and I will pay nothing. This is the only fair division.” Dick was surprised at how completely arbitrary this proposal was. He was also surprised at how disproportionate it was, but since his suggested share was significantly less than under his own proposal, he didn’t object. Harry, however, was stunned. “You call that fair?! I make only two times as much as Dick, but you want me to pay three-and-a-half times as much as he does. I make six times as much as you but you expect me to pay almost 80 percent of the total cost while you pay nothing. And this is despite the fact that each of us is receiving the exact same benefits. Where did you get such a crazy idea?” he asked. “From no less an authority than the federal government,” said Tom as he pulled out a gray booklet. “It’s all right here in the irs tax tables. Under the current tax code, here is what each of us paid in income taxes last year:”1

Income taxes last year

“By an amazing coincidence, our total taxes paid were exactly equal to the $30,000 expended on our street improvements. This is the progressive income tax system all U.S. taxpayers live under, and I don’t see why the Class families should be different. In fact, I believe all future pooling of funds should be divided in this way.” “I’m in,” said Dick. So, by a vote of two to one, the cost of the street improvements was divided as follows:

costs divided

Also by a vote of two to one, all future pooling of funds was to be divided up the same way.

Like all parables, the story of the Class brothers is designed to illustrate a moral principle. In this tale, Harry is required to pay a disproportionate amount of the cost and value of the benefits he derives from his “mini-society,” simply because his family works harder than the families of the society’s other members. The moral question is: Is Harry being treated fairly? If not, how should this affect our thinking about progressive taxation?

In the United States, the payment of taxes is effectively a “pooling of money” by the nation’s citizens to fund the services of government. These services include, but are not limited to: the national defense, infrastructure, the judicial court system, police and fire protection (delivered at the federal, state, and local levels), education (delivered at the state and local level), the general administration of government, and support for truly needy citizens. Deciding how much money should be appropriated for this pool and how it should be spent is almost always a subject of contentious debate. The same is true when deciding how taxes should be apportioned. As to the latter, the debate inevitably devolves into an argument over fairness and economic efficiency.

The primary source of federal tax revenues (excluding Social Security and Medicare taxes) is a progressive tax on the earned income of individuals.2  This essay will make the case that the progressive income tax is plainly inequitable. It will also review the alternatives to progression in an effort to identify the most equitable (or least inequitable) tax system.

Factors that determine income

America’s free enterprise system provides an environment in which the substantial majority of its citizens can realize their fullest earnings potential. Within that environment, individual economic outcomes are the product of a combination of three elements: aptitude, work effort, and choice of occupation.

Aptitude.3 For the purposes of this essay, aptitude is broadly defined as the capacity to produce, or to earn income. For the most part, it comes from circumstances of birth and is distributed unequally. Aptitude may be derived from innate talents (cognitive, musical, artistic, athletic, etc.) or physical attributes (appearance, dexterity, possession of senses, etc.). Or it may be acquired from lessons learned from parents and other life experiences. Aptitude emanating from circumstances of birth (either innate or acquired) can be significantly enhanced by individual effort applied to strengthening one’s skills (see “Work Effort” below). Aptitude is measured from low to high in accordance with the monetary value placed on it in the marketplace. This is a measure of earning power and is not in any way an indication of an individual’s intrinsic worth as a human being. For most people aptitude is the most significant determinant of income. But it has to be understood as capacity; aptitude does not produce income until it is combined with individual effort.

“Paying the same percentage of our income is not fair. Instead, Harry, you pay $23,450; Dick, you pay $6,550; and I will pay nothing.”

Work effort. For any given level of aptitude and occupation, work effort plays the decisive role in determining income, and in many cases may result in persons with lower aptitudes earning more than their higher-aptitude peers. For the purposes of this essay, the term “work effort” includes not only the number of hours worked, but also the intensity of the effort applied during those hours. As noted above, it also includes work effort applied to strengthening one’s skills.

At every level of aptitude and in every profession, whether the pay is in salary or hourly wages, there are workers who outperform their peers in each hour worked. They do this by performing tasks more quickly; focusing on the tasks more intently; finding and completing additional tasks that need to be done; and using some of their leisure time practicing or training to become more skilled. These people get more raises, larger bonuses, and more promotions than their peers. Thus, greater work effort can produce higher income whether the person is paid by the hour or earns a salary.

In addition to producing higher income in its own right, work effort applied to strengthening one’s skill — resulting in “learned” or “enhanced” aptitude — can make a substantial contribution toward increasing income. The “rough” carpenter who spends nights and weekends developing the skills necessary to qualify as a more highly valued “finish” carpenter will move up the wage scale by doing so. Professional athletes, musicians, singers, and other performers can enhance their innate aptitudes substantially through extensive practice, and a great many are renowned for having done so. A classic example is Hall-of-Famer Jerry Rice, who is generally recognized as the best wide receiver in nfl history. He was one of the highest paid players in pro football for twenty years, an achievement largely credited to his intense practice and workout regimen. Perhaps the most effective way of enhancing aptitude is through increased study in school. Whether it is grade school, high school, vocational school or college, for any particular tier of aptitude, those who study the most almost always get the best grades, matriculate to the best colleges, and secure the best jobs.

Choice of occupation. Choice of occupation is also important in determining income. Had Bill Gates decided to finish Harvard and become a high school math teacher, he almost certainly would have been successful, but he would not have become a multi-billionaire.

Earned income is determined by a mix of the three factors described above, and the relative contribution of each varies by individual. Understanding the primary determinants of income and the implications of each for tax policy are essential to designing the most equitable tax system. Surprisingly, the literature contains only infrequent and oblique references to this crucial aspect of tax theory.

Alternative income tax systems

There is a consensus among economists and tax theorists that the best tax system is one that strikes the optimum balance between economic efficiency and equity. An efficient tax system is one that does the least to distort the allocation of resources in the economy, thus maximizing overall production. Accordingly, taxes that might alter consumer or investor behavior should be eschewed. As to equity, there is virtually unanimous agreement among scholars that the tax system should be “fair.” Unfortunately, there is great disagreement as to which system best meets this criterion.

There are basically four systems of income taxation described in the literature:

A per-capita, or “head” tax, which would require each person to pay his or her per-capita share of the costs of government. (Technically a per-capita tax is not an income tax, but it is almost universally accepted as the most economically efficient tax system.)

A proportionate or “flat” tax, which would tax each dollar of income at a single rate. Embodied in virtually all proportionate tax proposals is a substantial broadening of the tax base through the elimination of most tax deductions, credits, and preferences, which has the benefit of simplifying the tax code and reducing the cost of compliance. The purest form of this system is a single-rate tax levied on all earned income from the first dollar, but different variations on this theme have been proposed.

A degressive tax, which is a proportionate tax only on income above a certain threshold or exemption. The exemption makes the system progressive, but typically much less so than a system of graduated rates.

A progressive tax, which taxes incremental income at higher marginal rates as income rises, resulting in an increase in taxes as a percentage of income as income increases.

Each of these systems will be examined as part of the analysis of progressive taxation.

The case for progression

Progression has been in use somewhere in the world for more than two thousand years. And it is safe to say the debate on its merits goes back just as far. At present, the substantial majority of nations employ some form of progressive taxation.

The first time a federal income tax was imposed in the United States was in 1861 as a means of financing the Civil War. The tax rates were decreased after the war and the income tax was allowed to expire in 1872. The concept of an income tax was legally quite controversial; so when a new income tax was levied in 1894, it was challenged in the courts, and in 1895 was found to be unconstitutional. It was not until 1913, with the ratification of the 16th Amendment to the Constitution, that the first constitutionally sanctioned income tax was enacted (which, incidentally, was progressive).

Throughout history, many arguments have been advanced both for and against the progressive income tax. One of the most comprehensive examinations of the subject in the 20th century was a book published in 1953 and reissued in 1963, The Uneasy Case for Progressive Taxation, by Professors Walter J. Blum and Harry Kalven of the University of Chicago Law School. This book is an exhaustive review of the prior literature on this topic, interspersed with the authors’ own analyses and critiques of the arguments presented. In their words, the book is, “an effort to explore what might be called the intellectual case for progression.”4 Another particularly useful source of information and analysis was a book-length article published in 1908 in the American Economic Association Quarterly, “Progressive Taxation in Theory and Practice,” by the noted economist and tax historian, Edwin R.A. Seligman.5

According to Blum and Kalven, “the most rigorous analysis of progression came only after the idea had become a political reality . . . whatever the reasons, it is clear that the political history affords little insight into the merits of the principle of progression.”6

The arguments in support of progression tend to fall into three main categories:7  economic efficiency, fairness, and reduction of income inequality.

Economic efficiency. The argument is that progressive taxation increases worker productivity, yielding greater economic efficiency and higher aggregate incomes. The study of the impact of tax policy on economic efficiency and growth has for centuries been a fertile ground for economists, who have produced numerous analyses on the topic without reaching clear consensus. Since the focus of this essay is on the issue of tax equity, the economic efficiency arguments will not be discussed beyond noting that logic and the weight of empirical evidence appear to favor less progression rather than more.

Fairness. The argument for progressive taxation on fairness grounds has three main strains.

  • The benefits principle. Taxes are payments made in return for government services and protections. People with higher incomes have disproportionately more to lose; therefore, they should pay disproportionately more for the protections afforded them by government;
  • Sacrifice theory and the marginal utility of money. Taxes are a burden on society that should be shared in an equitable manner. “Burden” is defined as the sacrifice made by the individual when he or she pays taxes. Since the marginal utility of a dollar declines as income rises, higher-income people should pay enough more in taxes to equalize their sacrifice relative to the sacrifice of lower-income peers.
  • Ability to pay. A fair tax system is one in which those with the greatest ability to pay should pay the most.

Reducing Income Inequality. In this view, inequality is a social injustice that can be remedied or mitigated by a progressive tax system. It is often proffered as an argument for basic “fairness,” but since proponents haven’t united around a specific principle of fairness in its support, we will consider it separately.

We will now examine each of the three fairness arguments in detail, then turn to the question of income inequality.

The benefits principle

The benefits principle of taxation holds that the government provides benefits to its citizens that should be paid for in taxes by each beneficiary in accordance with the value he or she receives from government services. As a basic foundation for taxation, the benefits principle — also called “give and take” or “quid pro quo” — has probably received more examination and comment than any other. As we will see, the statement of the principle — payment of taxes in return for benefits — lends itself to widely varying interpretations.

Historically, the use of the benefits principle to advocate progression relied on the “protection theory” of benefits, which asserts that the government’s primary function is the protection of property. The theory focuses on income as property, and analogizes the protections of government to an insurance company that insures property against loss. Those who cite protection theory as an argument for progression assert that individuals with higher incomes should pay a disproportionately greater share of the cost of government than lower-income individuals because the higher-income group would have disproportionately more to lose if the protections of government were withdrawn. Implicit in this interpretation of the principle is not just that the value of benefits received from the government increases as income increases, but that it increases more rapidly than the rise in income. As we will see, the statement of the principle — payment of taxes in return for benefits — lends itself to widely varying interpretations.

When examined carefully, the “protection theory” interpretation of the benefits principle falls short in five different ways.

First, the basic premise of the protection theory is flawed. Government protections extend to much more than property. The Founding Fathers made clear their vision for America in the Declaration of Independence when they spoke of the “unalienable rights” of all Americans to “life, liberty and the pursuit of happiness.” There is no basis for believing that a low-income person’s life is worth more or less to an individual (as contrasted with an insurance actuary, an economist, or a jury assessing damages in a wrongful death case) than the life of a high-income person. The same is true for liberty and the pursuit of happiness. The American military and other protective agencies and institutions of government exist to protect and preserve these rights for all Americans equally, regardless of how rich or poor they are.

Second, there is no persuasive support in the literature for the claim that higher-income people derive a disproportionately greater value from government protection of property than lower-income people. Some progression advocates have argued that government exists in large part to protect rich people from poor people, while poor people need no such protection. Thus, the value of the rich person’s protection is disproportionately greater than that afforded the poor. Perhaps this was true centuries ago in some feudal nations, but it is not now and never has been generally true in the United States. Others argue that insurance is priced according to risk as well as value, implying that high-value property is at greater risk of loss. While this notion has conceptual merit, it does not follow that property owned by high-income people is at greater risk than property owned by low-income people. In fact, the rich are more likely to engage in self-protection (e.g., build protective walls, install security systems, hire guards, etc.), which would result in reduced, not greater, risk. Seligman, Blum and Kalven, and others have examined the property protection arguments for progression and dismissed them as either untenably weak or without merit.

Third, this interpretation of the benefits principle overlooks the principle of marginal utility. If, as virtually all economists agree, the marginal utility of a dollar of income declines as income increases, then people would place a lower value on protecting their income as it rises. To accept protection theory as an argument for progression, one would have to assert that each additional dollar of income earned is worth more than the previous dollar of income, which is nonsensical.

Fourth, even if the protection argument had merit, it would, at best, argue for a proportionate rather than a progressive tax. To argue otherwise requires a belief that the price of property insurance increases faster than the value of the property (in this case, income), which is observably untrue. If the insurance analogy were applied, those with two times as much income or property would pay two times as much tax, which would be proportionate, not progressive. It’s no accident that “historically almost all exponents of benefit theory employed it to support proportion as against progression.”8  

Fifth, the analogy to an insurance company is specious. The costs of the military and police and fire departments are not equivalent to property and casualty insurance, in which the policy is priced in accordance with the value of the property insured. There is no material difference in the cost of protecting persons with high incomes or high-value property than that of persons with low incomes or low-value property. (In fact, the cost might be less, since persons with high income tend to reside in low-crime areas.) Accordingly, there would be no difference in the cost of these protections based on property value. Thus, under the protection theory, the fairest tax system would more logically be per capita.

A second interpretation of the benefits principle, and one that appears clearly to have more substance and more scholarly support, is that government benefits redound roughly equally to all people regardless of their income. More specifically, and as noted in the preceding paragraph, the value of benefits relating to life, liberty, and the pursuit of happiness, including the protection of property, is essentially the same for all citizens. Thus, each person should share the costs of government equally, in which case the fairest tax would be per capita. This is essentially what Harry proposed to his brothers as the fairest way of dividing the costs of their street improvements.

There is yet another interpretation of the benefits principle that is arguably superior to the others, because it comes closest to placing a true value on the benefits of government. This interpretation posits that the ultimate benefit of government is the overall well-being each person derives from its services.

The “Class Wars” parable imagined a society in which all of the members had the same aptitude. But in the broader society, aptitudes are distributed widely and unequally. This changes the picture substantially, as we can see by means of a simple thought experiment: Assume the society’s population has a normal (bell curve) distribution of aptitudes. Assume also that all of the persons in this society work exactly the same number of hours and at exactly the same intensity, resulting in incomes that correlate closely with aptitudes. In this hypothetical situation, and within each occupation, incomes would vary across a distribution curve almost identical to the aptitude curve. Accordingly, persons with more highly valued aptitudes would earn more income than their lower-aptitude counterparts, and thus derive greater value from government. It follows, therefore, that, all things being equal, higher-aptitude people should pay more in taxes than lower-aptitude people — not because they have more to lose (or to protect), but because they receive greater value from their government. Blum and Kalven touched obliquely on this concept when they noted:

Another approach [to the benefits theory] is more ingenious. It is founded on a double assumption: first, that the well-being of men, while not caused by the government, is dependent upon it in that government is a necessary condition for its existence; second, that the only aspect of well-being which is measurable is wealth or income and that it is therefore appropriate to take either of these as an index of the benefits flowing from government.9

It is noteworthy that this “ingenious” approach is entirely consonant with the “greater-value” interpretation of the benefits principle.

The greater-value interpretation of the benefits principle is at odds with the cost-sharing concept described above (which suggests a per-capita tax), inasmuch as it argues that higher-income people should pay a higher price for their benefits because they have received greater value from their government, largely because of a more highly valued aptitude (which is a gift at birth) or some other good fortune. The merit of this notion can be inferred by imagining that aptitudes could be purchased on the open market. If such a thing were possible, it is certain that the more highly valued aptitudes — those that would produce higher incomes — would be bid up to amounts in excess of the per-capita cost of government.

But how much more should higher-income people pay? The major fallacy in the use of the benefits principle as an argument for progression is the implicit premise that the value of government benefits increases more rapidly than income. Under the greater-value theory, since income — a proxy for well-being — is what each individual receives from the economic system, income is a reasonable measure of the value each individual receives from government. It is reasonable to conclude, therefore, that the fairest tax system is one in which each person pays tax in proportion to his or her income. It makes no difference whether the income is derived from aptitude (as defined), financial windfalls, random events, or privilege. In all of these cases, the tax should be levied in proportion to the value of the benefits received. Thus, a person who earns 10 times as much income as another would pay 10 times as much tax, while someone making 100 times as much would be taxed 100 times as much.

A new and important contribution to the debate over fairness emerged in the mid-19th century when proponents of proportionate taxation realized there were both practical and intellectual reasons for exempting a portion of income from taxation. The practical reason was simply the futility of taxing that portion of a person’s income that was needed for survival. To do so would be self-defeating, since the hardship imposed would deprive the state of production. The intellectual basis for the exemption, from the point of view of the state, emanated from the notion that income needed for subsistence constituted an expense of production, while income above this amount was “surplus” or “clear” income, i.e., net of production costs (an insight attributed to the economist David Ricardo). From the point of view of the taxed, government benefits only have real value when the taxpayer earns a surplus of income over what is needed for subsistence. Most scholars who supported a proportionate tax system concluded that taxing only clear income was both practical and fair to both the individual and the state. This enhancement to the benefits principle, which introduced a mild degree of progression by comparison to a pure proportionate tax (a tax from the first dollar of income), became known as a “degressive” tax. It is important to note that, among the proponents of the degressive tax, there was clear consensus that the income exempt from tax should be set no higher than the level of subsistence. To do otherwise would be arbitrary and in the opinion of many, inequitable.

The greater-value interpretation of the benefits principle stands as a rejection of a per-capita tax system and as a compelling case for either a proportionate or a degressive system.

Sacrifice theory and the marginal
utility of money

Sacrifice theory is perhaps the most historically prominent and persistent argument in favor of progressive taxation. Stated simply, the theory posits that the fairest tax is one that extracts from each taxpayer an equal or proportionate “sacrifice.” The theory rejects the quid-pro-quo notion that taxes are remitted in return for government benefits and instead treats taxes simply as a burden that must be shared in the most equitable way. Sacrifice theory is dependent upon the economic principle that holds there is a marginal-utility curve for money to the effect that the more money one earns, the less utility (or satisfaction) will be derived from the last dollar earned. Thus, if you plot a chart in which the vertical axis is units of marginal utility a person gets from money, and the horizontal axis is the amount of money the person earns, the curve will eventually have a downward slope. A downward slope indicates, for example, that an incremental $1,000 has greater utility to a person earning $10,000 a year than it has to someone earning $100,000.

The economic principle of marginal utility on which sacrifice theory depends is sound. However, there are several difficulties with the sacrifice theory itself that render it untenable as an argument for progression.

First, the basic premise of sacrifice theory is conceptually flawed. The notion that taxes are simply a burden that must be tolerated rather than a payment for benefits raises the question: Why would the citizens of a democracy vote to impose taxes on themselves if they did not expect benefits in return? And if the government does provide benefits (which of course it does), why would the payment of taxes be considered a sacrifice rather than a fair payment for value received? Did the Class brothers not receive benefits from their street improvements? If they did, what would be the logic of a tax based on proportionate sacrifice rather than one based on shared cost or value received? On conceptual grounds alone, sacrifice theory appears to be a very weak foundation for tax policy.

Second, the validity of the theory depends on more than just the existence of a downward sloping marginal-utility curve. For progression to be justified under a theory of equal sacrifice, the curve must not only decline, but decline more rapidly than income rises. In the view of British economist Arthur Pigou and others, there is no way to prove this is true:

All that the law of diminishing utility asserts is that the last ₤1 of a ₤1000 income carries less satisfaction than the last ₤1 of a ₤100 income does. From this datum it cannot be inferred that, in order to secure equal sacrifice . . . taxation must be progressive. In order to prove that the principle of equal sacrifice necessarily involves progression we should need to know that the last ₤10 of a ₤1000 income carries less satisfaction than the last ₤1 of a ₤100 income; and this the law of diminishing utility does not assert.10

Seligman credits the Dutch economist A.J. Cohen-Stuart with debunking the notion that there is a universal marginal-utility curve that dictates progression. Here Seligman summarizes Cohen-Stuart: “It is perfectly possible . . . to construct tables [curves] which lead not to progression, but to proportion and even to regression.”* 11

Third, the sacrifice argument for progression is dependent upon the additional assumption that the marginal-utility curves of all persons are essentially the same. While it is well accepted that marginal-utility curves will eventually slope downward, it is by no means true that all curves have the same slope. In fact, in comparing the marginal-utility curves of Tom, Dick, and Harry Class, there are any number of reasons why Harry’s marginal utility curve might decline less steeply than Tom’s and Dick’s. Imagine, for example, that Harry has a learning-disabled son who needs costly special education, or that Harry’s wife has an illness that requires expensive medication not covered by insurance. Or perhaps Harry has an obsession with saving enough money to send his two children to the best private secondary schools and universities. Now consider Tom’s and Dick’s situation: Knowing that Harry is the most industrious of the brothers and was unlikely to need their help, Harry’s parents made it clear that when they died they would leave all of their rather significant estate to the less industrious brothers, leaving nothing to Harry. In this event, Tom’s and Dick’s marginal-utility curves are affected by their knowledge that they don’t need as much income to secure their future. Thus, Tom’s and Dick’s marginal-utility curves may have steeper downward slopes than Harry’s, even though Harry earns much more income. Seligman calls this the “very core objection” to sacrifice theory:

The imposition of “equal sacrifices” on all taxpayers must always remain an ideal impossible of actual realization. Sacrifice denotes something psychical; something psychological . . . Two men may have the same income, which they may value at very different rates. The one may be a bachelor, the other a man with a large family dependent upon him; the one may be well, the other ill . . . the one may earn his income, the other may receive it as a gift . . . The attempt to ascertain a mathematical scale of progression, so as to avoid a charge of arbitrariness, is foredoomed to failure.12

This inability to prove the sameness of the marginal-utility curves of different people troubled Blum and Kalven to the point that they dismissed sacrifice theory as a theory on which to base a fair tax system:

The error lies in trying to translate money, which can be measured in definite units, into corresponding units of satisfaction or well-being. In the end satisfaction in the sense of happiness defies quantification. Utility is a meaningful concept; units of utility are not. It is in the face of this difficulty that, even waiving all other objections, the whole elaborate analysis of progression in terms of sacrifice and utility doctrine finally collapses.13

If there is no accurate way to draw any individual’s marginal-utility curve, there is no way to compare the curves of different persons. The only things that can be stated with confidence are that all persons have marginal-utility curves that are ultimately downward sloping and that the slopes of individual curves are determined by many factors in addition to income. And even if, as a general proposition, the curves are similar (as intuition would suggest), there are sufficient variations in them that sacrifice theory could not be applied without resulting in the inequitable treatment of an unacceptably large portion of the population.

Among people whose aptitudes are the same, the only way one person can earn more than a peer is by working harder.

Fourth, for a substantial (but indeterminate) number of workers — those who work because they need the money rather than because they enjoy it — the number of hours they choose to work is determined by the marginal utility of the income they earn from that work. Thus, for these workers, work effort has its own marginal-utility curve that is essentially the same as the marginal-utility curve for income. To illustrate: Harry’s family chooses to work 100 hours a week, while Tom’s family chooses to work 20 hours a week. Harry and his wife work these long hours because the marginal utility of the income produced from the extra hours is greater than the marginal utility of leisure (up to that point). Conversely, Tom’s family has decided to work only 20 hours per week because the additional utility of the income from the 21st hour is sufficiently low to him that he chooses to forgo it in favor of leisure. In this entirely plausible scenario, the marginal utility of one extra dollar to Harry might be equal to the marginal utility of one extra dollar to Tom. It is also plausible that the marginal utility of another dollar to Harry is even greater than it is to Tom, in which case, under its own logic, sacrifice theory would call for taxing Harry less than Tom. In either of these scenarios, taxing Harry at a higher marginal rate than Tom (as required by a progressive income tax) would be inconsonant with sacrifice theory, and by its own standard, inequitable.

Fifth, the application of sacrifice theory would be plainly unfair to the people in a society who work the hardest. Among people whose aptitudes are the same, the only way one person can earn more than a peer is by working harder. But progression has the perverse effect of reducing average, after-tax hourly wage or salary rates as work effort increases. Consider the Class brothers: While Tom’s average, after-tax hourly wage was $25 (he paid no tax), Dick’s was $22.82, and Harry’s was only $21.10 (this assumes the tax on Harry’s $75,000 in labor income was $11,725 or 50 percent of the family’s total tax of $23,450). To put this into perspective, imagine you are interviewing for a job. When you ask what the job pays, your prospective employer says, “Well that depends on how hard you work.” You say, “Good, because I am a hard worker.” To which the employer responds, “You don’t understand. If you work 20 hours a week, I will pay you $25 per hour. But if your family works 100 hours a week and has income from savings, I will pay you about $21 per hour. The more hours you work, the less average hourly wage I will pay you.” John Stuart Mill gave full voice to this apparent injustice when he denounced progressive taxation as “a penalty on those who worked harder and saved more than their neighbors” and a “mild form of robbery.”14

On the surface, sacrifice theory appears to be a respectable argument for progression. But on close examination, it seems clearly without merit as a rationale for a fair tax system. By far the most compelling condemnation of sacrifice theory is not the argument over the slopes of the marginal-utility curves, but the unfair penalty it would impose on the hardest working and most productive people in society.

Ability to pay

The notion of “ability to pay” is most often identified with Karl Marx (“from each according to his ability, to each according to his needs”), even though the basic concept was considered by scholars long before Marx was born. While the phrase says nothing about progression, it has often been used to advocate it.

Ability-to-pay has been the subject of considerable debate on definitional grounds alone. For example, a review of the literature on tax theory does not turn up a generally accepted definition of the word “ability.” What does “according to his ability&rdqquo; really mean? Does it mean (as some suggest) the financial wherewithal with which to pay taxes — which might come from either assets or income? Or does it mean the innate or learned ability to earn income, which would equate to aptitude? Both of these interpretations have been discussed in the literature. Either way, ability could as easily dictate proportion as it could progression. If the word means the financial wherewithal with which to pay taxes progressively, the basic concept lacks an underlying principle of fairness to support it. (Proponents of this meaning of ability-to-pay often draw on sacrifice theory for intellectual support, but as shown above, the application of sacrifice theory results in inequitable outcomes.) If the word ability means the innate or learned capacity to earn income, it is synonymous with aptitude, in which case, the greater-value interpretation of the benefits principle should be applied. This would lead to proportionate taxation.

Reducing income inequality

One of the most persistent arguments in favor of progressive taxation is that it reduces income inequality. For example, University of Chicago economist Henry Simons writes:

The case for drastic progression in taxation must be rested on the case against inequality — on the ethical or aesthetic judgment that the prevailing distribution of wealth and income reveals a degree (and/or kind) of inequality which is distinctly evil or unlovely.15

To be sure, inequality exists in the United States as it does to a greater or lesser extent in all other nations. But why should we care? If it is social justice we are concerned about, what is the evidence that the level of American inequality is unjust?

There are at least five methodologies used for measuring income inequality. The most commonly used measure is the “Gini coefficient,” developed by the Italian statistician Corrado Gini. The Gini coefficient is a method of measuring the statistical dispersion of (among other things) income, consumption, and wealth. The figure of merit for the Gini coefficient ranges from zero to 1.0, where zero equals total equality (all persons have identical incomes) and 1.0 equals total inequality (one person has all of the income). By this measure, the U.S. has higher income inequality than almost all other industrialized nations. In 2009, the U.S. Gini was .468, while the average Gini for the 27 European Union nations was .304, a ratio of 1.54:1. Interestingly, the per capita gdp in the U.S. in 2008 was $47,400, while the average per-capita gdp in the eu nations in that year was $32,900, a similar ratio of 1.44:1. The point is that strong economic performance can coexist with higher levels of income inequality (and vice versa).

It is important to note that the U.S. income figures cited above come from the Census Bureau, which uses what it calls “money income” (income before taxes, excluding the value of non-cash benefits). Money income is the income definition most often used when citing income inequality measures,16 even though this definition of income does not include many variables that might affect inequality and standard of living, such as transfer payments, taxes, employer-provided fringe benefits (primarily retirement benefits and health insurance, which can amount to as much as 30 percent of income17, capital gains, dividends, imputed rent from owner-occupied housing, size of household, increases in the value of home equity and other investments, etc. Consequently, the value of using money income to measure either standard of living or inequality is quite limited.

It has been widely reported that income inequality in the U.S. has been rising for “decades,” and by implication, that the rise is ongoing. These reports are arguably misleading. From 1967 to 2008 the Gini for money income rose from .397 to .468 (17.9 percent), about four-fifths of which occurred from 1967 to 1993. Roughly three-tenths of this increase occurred between 1992 and 1993 due to a change in the way data were collected. This change in methodology biased the Gini calculation upward. Accordingly, figures from the period before1993 are not directly comparable with the period from 1993 to the present. During the 16 years between 1993 and 2009, the Gini increased from .454 to .468 (3.1 percent), and from 2001 to 2009 there was virtually no change in income inequality as measured by the Gini coefficient.

The consensus view among economists is that the best measure of living standards over the long term is consumption.

A more comprehensive measure of income yields a very different picture. The Census Bureau’s so-called “15th measure of income” adds to money income, transfer payments, insurance supplements, capital gains, Medicare, Medicaid, net imputed return on equity in owned homes, and subtracts taxes. This measure indicates that inequality declined 1.8 percent during the last 16 years (1993 to 2009) from a Gini of .395 to a Gini of .388.

In any event, the consensus view among economists is that the best measure of living standards over the long term is consumption (determined not only by income but by savings, home ownership, borrowing, barter, region of domicile, and other factors), suggesting that consumption inequality is the inequality that counts the most. A 2005 study conducted by the Bureau of Labor Statistics found that in 2001 (the most recent year for which data are available) the Gini coefficient for consumption was .280,18 indicating that inequality with respect to this measure of U.S. living standards is relatively modest. It also appears that consumption inequality has barely changed in recent years. During the period 1986 to 2001, the consumption Gini went down slightly, from .283 to .280.19 Since the Gini for money income was virtually unchanged from 2001 to 2009, it is quite possible that the Gini for consumption was also relatively flat during that period; in which case, consumption inequality has not increased for 23 years or more. Support for this latter surmise comes from a 2010 study which concluded that “in the 2000s overall consumption inequality shows little change.”20

In addition to America’s substantial superiority in gdp per capita (which is a measure of the performance of the economy without regard to how income is distributed), the U.S. has a much higher standard of living than virtually all of the most advanced European and Asian countries. According to the Luxembourg Income Study (which uses a very comprehensive measure of income) median disposable personal income in the U.S. in 2002 was: 19.3 percent higher than Canada; 68 percent higher than Finland; 45 percent higher than Germany; 59 percent higher than Italy; 31 percent higher than Norway (despite its vast oil and gas wealth); 73 percent higher than Sweden; and 31 percent higher than the United Kingdom. It should be noted that the figures for gdp per capita and median income understate America’s advantage because the median age of America’s population (about 36.8 years) is about four years lower than the average of the median ages in Western Europe and almost eight years younger than Japan. Age (a proxy for experience) is one of the most significant contributors to income and is also, therefore, one of the most significant contributors to income inequality. In addition to higher median incomes, Americans have higher median net worths, which add further to the standard of living differential.

The U.S economy performed well in absolute and relative terms over the 25-year period from 1983 to 2008.

There is no question that until the recent recession, the U.S. economy performed well in both absolute and relative terms over the 25-year period from 1983 to 2008. During this period, real compound annual gdp growth in the U.S. was 3.3 percent, substantially greater than the growth of its G-7 counterparts, which on a weighted-average basis (using either population or gdp), grew only 2.3 percent per year. Thus, the U.S. economy grew 43 percent faster per year than the non-U.S. G-7 countries. Moreover, in the recent recession, the U.S. economy contracted less than the world’s other advanced economies. For example, U.S. gdp shrunk 2.6 percent in 2009, substantially less than the 4.1 percent contraction experienced in the Euro area. In 2010, the U.S. grew 2.8 percent compared with only 1.8 percent growth forecast for the Euro area by the International Monetary Fund.

Another common claim is that incomes in the U.S. have been stagnant for “decades.” But this claim is at odds with data from the Congressional Budget Office, which uses a measure of household income that, like the Luxembourg measure, is quite comprehensive, taking into account transfer payments, health and retirement benefits, profits from retirement accounts, imputed interest on owner occupied homes, differences in household size, and taxes paid. Using this more meaningful definition of income, from 1983 to 2005 real median household income in the U.S. rose by 35 percent, which can hardly be considered “stagnant.”

The presentation of these facts is not meant to suggest that income inequality causes higher living standards or gdp growth. But it is clear that it can co-exist with both high and low national living standards. Those who advocate redistribution of income on grounds of social justice should consider that America’s standard of living is higher and has grown faster than virtually all of the nations exhibiting lower measured inequality. This suggests that the most notable economic inequality in the world is that between Americans and the citizens of all other countries.

The most compelling argument against the use of the progressive income tax to redistribute income is simply that it is inequitable. Blum and Kalven noted that when the tax system is used to redistribute income,

the welfare of one group in a society has been increased at the expense of the welfare of a different group. Stated this way there is no “general” welfare; there is only the welfare of the two groups and the wealthy receive no counter-balancing benefits for their surrender of income or wealth.21

As contrasted with the benefits principle and sacrifice theory, each of which relies on conceptions that purport to enhance equity, income redistribution is simply a coercive transfer of wealth from one group to another without an equity principle to support it. Note that $13,450 of Harry’s income was “distributed” to Tom and Dick. (This is the difference between Harry’s one-third share of the cost of the street improvements ($10,000) and the $23,450 he was forced to pay.)

Ironically, a progressive income tax can even have the extraordinary effect of increasing rather than reducing income differences. Again, our parable is instructive: Assume that Harry’s boss is a construction foreman who works 40 hours a week at $37.50 per hour, thus earning $75,000 per year (which is the entirety of the family income). The foreman’s hourly rate is commensurate with his aptitude as a manager, while Harry’s $25 per-hour rate is commensurate with his aptitude as a carpenter. They both make $75,000 per year, but Harry does it working 60 hours per week and his boss does it working 40 hours per week. Under the current progressive tax system, Harry’s after-tax income will be $63,275 (after $11,725 in tax, which assumes that, since Harry’s labor income is 50 percent of his total family income, the tax attributable to him is 50 percent of the $23,450 tax paid by the family). His boss will take home $68,450 (after $6,550 in tax). Thus, a disproportionate amount of Harry’s income has been taken from him and redistributed, simply because his family worked harder.

As noted by Blum and Kalven, and illustrated by our parable, redistribution requires that money be taken from some and given to (or not taken from) others. What is the equity principle that justifies this taking? Redistribution has been justified by some as a means of rectifying social injustice in the economic system. But proponents of this view have not provided a convincing argument that such injustice even exists.22

There is no persuasive evidence that reducing income inequality will increase economic well-being for the majority of people; in fact, America’s superior median standard of living relative to the other advanced economies is evidence to the contrary.  

The case against progression

The strongest arguments against progression are the rebuttals to the arguments for progression. To wit: The pro-progression interpretation of the benefits principle is invalid because it depends on the untenable assumption that the value of government benefits increases more rapidly than the rise in income; on the surface, sacrifice theory is a respectable argument for progression, but on closer examination, it is clear that its application produces an inequitable outcome (this is most obviously so when applied to income derived from greater work effort); the ability-to-pay argument lacks an equity principle (other than sacrifice theory) on which to base a fair tax system; and redistributing income through a progressive tax system is inequitable.

These rebuttals to the arguments for progression, should be sufficient to settle the case. But there are other important reasons to reject progressive taxation.

Political irresponsibility. In 2008, the top 1 percent of taxpayers in America earned about 20 percent of all personal income and paid roughly 38 percent of federal income taxes; the bottom fifty percent of taxpayers currently pay only 2.7 percent of income taxes,23 and it is estimated that 46.9 percent of workers paid no federal income tax for the 2009 calendar year.24 Inasmuch as only a minority of taxpayers is affected by rises in tax rates, there is a built-in incentive for the majority to act in its self-interest, which opens the door to inequitable treatment of the minority.

Arbitrariness. Establishing a graduated rate scale and setting the top marginal rate on that scale are inherently arbitrary tasks. Scottish economist J.R. McCullough condemned this arbitrariness in the strongest of terms:

The moment you abandon . . . the cardinal principle of exacting from all individuals the same proportion of their income or their property, you are at sea without rudder or compass, and there is no amount of injustice or folly you may not commit.25

The progressive tax system rests on a very slippery slope, making the term “fair share” so subjective as to be an invitation to abuse. Did Harry’s brothers pay their fair share?

Fomenting dissension. One of the inherent characteristics of the U.S. system of government (and that of all Western nations) is the tension that exists between the political system (majoritarian) and the economic system (free enterprise). Most Western nations are experiencing the effects of this tension, which manifests itself in vigorous disputes over tax and welfare policies. Many of those who favor income redistribution assert that inequality foments dissension. Whether this is true or not, dissension is just as likely to be caused by tax laws that are deemed unfair by those being taxed. By its nature, a system that taxes people progressively without the support of an accepted equity-based principle may breed resentment, particularly when so many pay no tax at all. The deepest resentment will most likely be among those whose tax rates differ solely because of their work effort.

A new doctrine of fairness?

There is no perfectly fair tax system. But based on an examination of the various tax principles and theories described in the literature, together with a critical analysis of the arguments supporting and opposing progression, it’s possible to put forward a new doctrine of fairness. It is based on five principles:

  • The most equitable tax system is one based on the value of benefits received.
  • Income is the most equitable (or least inequitable) measure of the value of benefits; thus taxes should be levied in proportion to income. Well-being is the ultimate benefit of government and income is a reasonable proxy for well-being. Whether income is derived from aptitude (as defined), a financial windfall, a random event or privilege, it is fair (or less unfair) that it be taxed in proportion to value received. This principle serves as a rejection of a per-capita tax system and establishes the affirmative case for proportion.
  • Only “clear income” — defined as income above the level of subsistence — should be taxed. From the point of view of the state, an individual’s earned income up to the level of subsistence is effectively the government’s cost of production and should not be taxed. From the point of view of the taxed, government benefits only have real value after the taxpayer earns a surplus of income over what is needed for subsistence.
  • The progressive taxation of income from work effort is inequitable. Income is derived primarily from a combination of aptitude and work effort. All things being equal, people with high-value aptitudes earn more than those with low-value aptitudes. Each tier of aptitude (whether there be 100 or 10,000 such tiers) comprises a “mini-society” in which differentials in income between the members are derived almost solely from work effort. Under a progressive tax system, workers whose work effort is above the median in their aptitude tier will pay higher average taxes per hour than those below the median. As a result, at any one point in time, an unacceptably large percentage of the total work force will earn less average, after-tax income per hour than their peers, simply because they worked harder. This is inequitable on its face.
  • The progressive taxation of income from aptitude is inequitable. Whereas the most equitable tax system is one based on the value of benefits received from government; and whereas the value of government benefits does not increase more rapidly than income, there is no equitable basis for taxing income progressively. Thus, even if it were assumed that income was derived solely from aptitude, progression would be unfair.

Implicit in this fairness doctrine is that taxation in excess of a proportionate share of the value of benefits (defined as clear income) is an inequitable confiscation of property.

Critique of the doctrine

There are weaknesses in the logic of this doctrine that make the fairness of a proportionate or degressive tax system less than perfect. First, some have argued that the benefit derived from economic well-being (as measured by income) should be considered separately from the benefits derived from government protection of life, liberty, and property. This alternative view has induced some scholars (John Stuart Mill, for one) to suggest that two types of tax should be imposed: a proportionate tax to pay for economic well-being and a per-capita tax to pay for the protection of life, liberty, and property. Putting aside the measurement difficulties of such a scheme, if this alternative quid pro quo principle were applied, and the two tax rates were blended to reflect the different values of the benefits, the most equitable tax would be somewhere between per-capita and proportion. Thus, a proportionate or degressive tax as proposed, would favor lower-income persons at the expense of higher-income persons.

Second, a proportionate tax would only be fair if all income were derived from aptitude, when in fact a substantial portion of income is derived from work effort. The inequity of this is demonstrated in the Class Wars parable, in which Harry paid more than a per-capita share of the cost of the street improvements despite the fact that his benefits were exactly the same as his brothers. (Note that in this all-too-common circumstance, where both aptitudes and benefits are equal, even a proportionate or degressive tax is redistributive with respect to the hardest workers.) Thus, a proportionate tax favors people who work less over people who work more.

Third, the merit of the clear income theory is somewhat undermined with respect to hard workers. Again this can be seen in our parable: Using a degressive tax system and assuming the subsistence level of income was $25,000, Tom would not have to pay any tax, even though he could easily pay his share of a proportionate tax simply by working three more hours per week. Thus, the degressive tax favors people who work less at the expense of those who work more.

Since there is no perfectly equitable tax system, the goal must be to design the least inequitable system. This doctrine of fairness uses sound principles of equity to reject both the progressive and per-capita tax systems. At the same time, it establishes the affirmative case for a degressive system as being the least inequitable. Lastly, where the logic of the doctrine is flawed, in each case it errs on the side of taxing lower-income people less, regardless of the reason their income is lower.

Seeing income clearly

The flaw in virtually all of the intellectual arguments on the issue of the progressive income tax (both pro and con), is a lack of appreciation for how income is determined. Because of this, the crucial implications of the distinction between income derived from aptitude and income derived from work effort have been left out of the debate. When the importance of work effort is considered, the inequity of progression becomes clear.

While the title of Blum and Kalven’s book appears to indicate that the authors’ analysis led them to become uneasy proponents of progression, the reality is more nuanced (and more uneasy). At the conclusion of the book, they wrote:

The case for progression, after a long critical look, thus turns out to be stubborn but uneasy. The most distinctive and technical arguments advanced in its behalf are the weakest. It is hard to gain much comfort from the special arguments [in favor of progression], however intricate their formulations, constructed on the notions of benefit, sacrifice, ability to pay, or economic stability. The case has stronger appeal when progressive taxation is viewed as a means of reducing economic inequalities. But the case for more economic equality, when examined directly, is itself perplexing.

The authors seem to be saying that the only argument for progression that could not be dismissed was the value they ascribed to reducing income inequality. And even that argument left them “uneasy.”

But it is clear from a careful reading of the book that Blum and Kalven did not appreciate the implications of how income is determined, specifically the special nature of income derived from work effort. If they had, they almost certainly would have realized that taxing such income progressively is inequitable. In the event, their uneasy case for progression would have become an easy case for its rejection.

1 The tax figures were calculated by The Shapiro Group, a Los Angeles tax accounting firm. The marginal rates and brackets are those applicable for the 2010 tax year. These figures are for illustration purposes only. They do not include the effect of certain tax credits (which some would consider transfer payments) that exist in the law. If these credits were included, Harry would pay a tax of $22,600, Dick would pay a tax of $3,700 and Tom would receive a refund of $7,100.

2 There are several other types of taxes levied by federal, state, and city governments, including taxes on capital gains, dividends, estates, sales, and property. These tax systems are outside the scope of this essay.

3 As defined here, the term aptitude is similar to but distinct from other terms used in the literature to describe capacity to earn: 1) “endowment,” which, in this context, is synonymous with genetic inheritance and is, therefore, too limiting; 2) “faculty,” which, like aptitude connotes capacity to earn, but is also used in the literature to describe financial wherewithal; and 3) “ability,” which, like faculty, is used to describe either capacity to earn or financial wherewithal.

4 Edward Blum and Harry Kalven, The Uneasy Case of Progressive Taxation (University of Chicago Press, 1953.

5 Edwin R.A. Seligman, Progressive Taxation in Theory and Practice (Princeton University Press, 1908).

6 Blum and Kalven, 14.

7 Some advocates of progression argue that a progressive income tax is needed to offset the putatively regressive nature of the payroll “taxes” that fund Social Security and Medicare. The conflation of these revenue streams is ill-conceived, inasmuch as each has a different purpose. Income taxes are used to fund a broad range of government services as described above, while payroll levies are collected for the express purpose of providing income supplements and medical care during retirement. More specifically, Social Security levies are a form of forced savings, and Medicare levies are effectively prepaid medical insurance premiums. Neither of them finances government services per se. Since Social Security benefits when paid out are tied to the aggregate amount paid into the system by each beneficiary, it is inaccurate to call the levies regressive. In the case of Medicare, the amount paid into the system is proportionate to income while the benefits (paid health care) are essentially the same for each beneficiary; consequently, the system is redistributive.

8 Blum and Kalven, 38.

9 Blum and Kalven, 37.

10 Arthur C. Pigou, A Study in Public Finance (Macmillan, 1951), 85-86.

11 Seligman, 219. *An earlier version of this piece incorrectly stated that Seligman was quoting Cohen-Stuart when he was in fact summarizing Cohen-Stuart’s arguments.

12 Seligman, 222-223.

13 Blum and Kalven, 63.

14 John Stuart Mill, Principles of Political Economy with some of their applications to social philosophy, Vol. II (D. Appleton and Company, 1894), 99, 401.

15 Blum and Kalven, 72.

16 Gini coefficients cited herein come from The CIA World Fact Book 2010, the Census Bureau report on Income, Poverty, and Health Insurance Coverage in the United States: 2009 and other U.S. government publications, and Eurostat, the official statistical office of the European Union.

17 Bureau of Labor Statistics, “Employer Costs for Employee Compensation: December 2010.

18 David S. Johnson, Timothy Smeeding, and Barbara Boyle Toney, “Economic Inequality Through the Prisms of Income and Consumption,” Monthly Labor Review (Bureau of Labor Statistics, April 2006), available at http://www.bls.gov/opub/mlr/2005/04/art2full.pdf.

19 Johnson, et al., “Economic Inequality.”

20 Bruce D. Meyer and James X. Sullivan, “Consumption and income inequality in the U.S. since the 1960s” (2010) working paper, available at http://harrisschool.uchicago.edu/faculty/ web-pages/Inequality60s.pdf

21 Blum and Kalven, 75.

22 To be sure, there are people in America who are needy or disadvantaged, in some instances grievously so. For such people the most effective remedy would be through direct spending programs. But the funding for such programs should come from a tax system that is equitable.

23 Mark Robyn and Gerald Prante, “Summary of Latest Federal Income Tax Data,” Fiscal Fact 249 (Tax Foundation, October 6, 2010), http://www.taxfoundation.org/ news/show/250.html

24 Roberton Williams, “Who pays no income tax?,” Tax Notes (June 29, 2009), available at http://www.taxpolicycenter.org/UploadedPDF /1001289_who_pays.pdf

25 J. R. McCullough, A Treatise on the Principles and Practical Influence of Taxation, or the Funding System (The Lawbook Exchange Ltd., 2007), 143-145.

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