Author:Vitaliano, Donald F.

    The advent of optimal tax theory with Mirlees' (1971) seminal contribution has led to the eclipse of earlier models of public finance such as the benefit principle and the utility sacrifice theory of taxation. Musgrave's (1959) treatise devotes an entire chapter to utility sacrifice theories of taxation, which date back to the 19 (th) century utilitarian tradition of Bentham and J.S. Mill. Proponents of progressive taxation such as Edgeworth (1897) and Cohen Stuart (1889) relied heavily on diminishing marginal cardinal utility. (1) Edgeworth characterized it as the hedonic theory of taxation. Modern undergraduates are taught that, "...individual utility is not now considered to be a cardinally measureable magnitude. Even if it were, utilities could not be compared among separate individuals. This fact alone prevents the principle [of utility sacrifice taxation] from having any 'scientific' basis." (Buchanan and Flowers, 1987, p. 54) This paper contradicts that assertion and makes operational a U.S. income tax rate structure based on a cardinal utility function drawn from the emerging 'Happiness' literature.

    Revival of interest in hedonic tax theory is justified by recent empirical evidence. Weinzierl (2014) has conducted an in depth survey of attitudes toward tax policy in the United States, although his framing of the issue does not rely on the cardinal utility sacrifice principle. When confronted with a choice between the dominant optimal tax framework and the equal sacrifice principle, "...a large majority of individuals appear to place a substantial value on an alternative--Equal Sacrifice--that rejects the conventional policy implications." (p.3) Respondents were presented with an array of tax distributions reflective of alternate policies, ranging from Rawlsian (highly redistributive) to a poll tax (equal amount per household), and asked to rank them. Further, Weinzierl cites a body of evidence that actual tax rate schedules are consistent with the equal sacrifice principle (ibid, p.5). Nor does he find much support for the Rawlsian idea of favoring the least well-off. (2) Equal sacrifice is appealing from the perspective of horizontal equity, a widely accepted criterion of tax fairness, while at the same time it addresses vertical equity--unequal treatment of persons not equally circumstanced. The apparent popularity of equal sacrifice might be due to its perceived relationship to horizontal equity.

    This paper employs published estimates of a cardinal utility function to construct a revenue neutral U.S. personal income tax for 2010. The average rate structure varies from roughly 5% at the lowest income quintile to 17% at the highest percentile (millionaires).


    Let u = household utility (utils), y = income, T = taxes. Under equal absolute tax sacrifice each household is asked to yield the same total amount K of utility:

    u(y) - u(y - T) = K (1)

    Vitaliano (1973) shows that under criteria (1), the required tax structure depends on:

    y * u'(y) / [(y-T) * u'(y -T)] > 1 (2)

    where the primed terms are first derivatives (marginal utility).

    If (2) 1 a regressive tax. This result and that given below for equal proportional utility sacrifice holds for all three of the accepted methods of measuring the degree of progression: average rate progression, liability progression and residual income progression (Vitaliano, 1977).

    Expression (2) may be readily seen to be the product of the abscissa and ordinate along the marginal utility of income curve, analogous to the product of price and quantity along a demand curve. If that product is a constant, the elasticity of marginal utility is 1, and proportional taxation is called for. An inelastic marginal utility curve calls for progressive taxation, and an elastic curve requires regression. An alternate formulation of utility sacrifice taxation calls for each household to yield the same fraction or proportion of their total utility. (3) This may be defined as:

    u(y) - u(y -T) = k u(y) (3)

    In this formulation, k is the proportion of utility to be sacrificed by each household (0

    Progression, proportionality or regression will be required depending upon the following (ibid.):

    y u'(y) / [(y-T) * u'(y -T)] * [1 - k] >1 (4)

    which is identical to (2) except for being multiplied by [1-k]. A unit elastic marginal utility implies y * u'(y) = [(y-T) * u'(y -T)], and since [1 - k]


    Apart from those who reject out of hand the idea of utility measurement, the chief obstacle historically to implementation of the hedonic theory of taxation has been the absence of an empirical estimate of the cardinal relationship between income and utility. The skepticism about the measurement of utility expressed in the quote above by Buchanan and Flowers has been the dominant view in mainstream economics for the past one hundred years. It was first stated by Pareto, and reiterated by such luminaries as Hicks, Samuelson and Houthakker: observed choice behavior by individuals or households only allows inferences about what is preferred and not preferred, that is, ordinal utility, not the level of utility or satisfaction. Since the modern Happiness literature specifically asks respondents to state their level of satisfaction on a numerical scale, it now is possible to estimate the level of satisfaction or cardinal utility derived from income, a job, one's health or marriage, for example. Thus the reported happiness of household i is denoted hi, which is related to utility ui by h = f(ui) + vi, where f( ) is the household's utility function and vi a random error term independent of the circumstances affecting true utility (Layard, Mayraz and Nickell, 2008, p. 1848). In this formulation hi is the answer to a happiness survey question, and the utility function f( ) is assumed common to all individuals while the error term captures the idiosyncratic aspect of human behavior.

    The two most relevant pieces of the Happiness...

To continue reading