Social Status, Conspicuous Consumption Levies, and Distortionary Taxation

1 Introduction

Tax systems are very diverse in practice. While the United States relies mainly on income taxation, many countries in the European Union weight differentiated commodity taxation. Furthermore, developing countries usually impose differentiated taxes on luxury goods to prevent wasteful consumption. For example, in recent years, Mexico levied a luxury tax on several items; Australia levied tax on luxury cars, with a maximum tax rate of 33%; Hungary levied a luxury tax for real estate, yachts and cars whose value exceeded $150,000. Similarly, Russians with cars worth more than $90,000 will now have to pay as much as $4,000 a year in taxes on these vehicles.^[1] Although luxury taxes do not constitute a significant portion of tax revenues (ratio of luxury tax to overall tax revenue is 1% and 0.1% for Mexico and Australia, respectively), governments see them as a potential area for revenue raising. Sometimes luxury goods are consumed to achieve a better status in society. Veblen (1899) argued that people advertise their positions in a wealth hierarchy by consuming expensive products such as Rolex watches. Such individual behaviors set off a status-seeking game that wastefully allocates income for more “positional goods.” Thus, a positional externality occurs when new purchases alter the relevant context within which an existing positional good is evaluated. For example, as more individuals start wearing Rolex watches in a society, utility of those who already had Rolex watches will go down. Studies by Frank (1985), Seidman (1988) and Ireland (1994) show that if agents’ preferences are sensitive to a ranking based on the consumption of a particular good, the consumption of this positional good causes welfare loss. In order to seek higher status through conspicuous consumption, one has a lot of incentive to supply labor at a higher level, which can alleviate preexisting income-tax distortion. Accordingly, differentiated taxes on positional goods reduce this positive effect of conspicuous consumption on labor supply while simultaneously reducing positional externality by reallocating income for more “non-positional goods.” Therefore, the differentiated taxes in the existence of conspicuous consumption generate two opposite effects in a tax system.

Without arriving at definite conclusions and with still being open to debate even today, much has been written about the choice between differentiated commodity and income taxes for an optimal tax structure. The prominent work of Atkinson and Stiglitz (1976) and subsequent studies by Christiansen (1984) and Saez (2002) conclude that an optimal tax structure consists of only nonlinear income taxes without any commodity taxes under the condition in which utility is separable between commodities and leisure.^[2] Moreover, Kaplow (2006) shows that commodity taxation is still undesirable even if the preexisting income taxes are not as optimal as in reality. In other words, differentiated commodity taxes cannot supplement either optimal or non-optimal nonlinear income taxes. However, all the previous studies ignore status effect in a form of externality that the consumption of positional goods carries. The differentiated taxes on positional goods in this case can function as a corrective tool for cutting down wasteful consumption from the status-seeking race. In addition, these taxes also generate revenue that can be used to lessen preexisting income tax distortion. Such a budget-neutral tax reform shares some similarities with the budget-neutral environmental tax reforms studied in the environmental economics literature that analyzes in a second-best framework the possibility of obtaining a double dividend by recycling the environmental tax revenues in order to reduce other distortionary taxes. The double dividend occurs if and only if the revenue recycling effect outweighs the tax interaction effect as demonstrated in the seminal papers of Bovenberg and de Mooij (1994), Bovenberg and Goulder (1996) (see also Goulder (1995) or Bovenberg (1999)). Positional externality as studied in this paper is similar to an environmental externality in the sense that a tax on the good, which is the source of externality, increases welfare. However, positional externality differs from standard environmental externality because the existence of positional good provides extra incentive to supply more labor.^[3]

The purpose of this paper is to explore the optimal tax structure in the presence of status effect. We develop a game-theoretic model in which each individual with a different labor productivity unknown to the others engages in a status-seeking game, where government has a revenue requirement. Then, we examine the welfare effect of a revenue-neutral shift in the tax mix away from nonlinear income taxes toward positional-good taxes. Finally, we focus on the distributional consequences of the tax reform.

The contribution of this work is to provide economic rationale for the practical use of differentiated taxes on positional goods, which could be corrective and even revenue-raising instruments in a tax system. The welfare implications of tax policies are of high interest for policy makers. When individuals consume positional goods to achieve higher status in a society, income and commodity taxation might have different welfare effects due to the externality that the positional good creates. To correct the externality from conspicuous consumption, Hopkins and Kornienko (2004) suggest per-unit taxes positively associated with income levels, since individuals with relatively higher incomes spend money more on positional goods and, thus, generate more externality. A corrective instrument that depends on income is too unrealistic to apply to the actual tax environment. In contrast, this paper employs differentiated commodity taxes which do not depend on the income levels so that a government can use it in the real world. It still has the function of correcting the externality, however. Ireland (1994) uses a signaling model and shows that a linear tax on positional good is Pareto improving. His analysis is based on some examples for specific utility functions. In both Hopkins and Kornienko (2004) and Ireland (1994) labor income is exogenous which means there is no preexisting labor supply distortion. When labor supply is endogenous, the existence of positional goods alleviates preexisting labor tax distortions because individuals will work more in equilibrium to obtain higher status. Hence, a tax on positional good will exacerbate preexisting labor supply distortion, while reducing positional externality by causing equilibrium positional good consumption to decrease. These two offsetting effects on welfare exist in our model as we allow for endogeneity of labor supply. Hence, in the existence of preexisting tax distortions the desirability of a tax on positional goods is at stake. Ireland (2001) finds only optimal income taxes on the assumption that a tax authority cannot directly observe how individuals consume positional goods, and thus, it cannot levy any taxes on conspicuous consumption. Thus, the optimal income tax by itself acts as an instrument for both corrective and revenue-raising policy. However, a government can know which types of commodities are visible and carry status effect in the real world.^[4] We present a government problem in which the tax authority chooses an alternative tax system when given a set of possible tax instruments (i.e. not only income taxes but also commodity taxes). Finally, the results of Saez (2002) cannot give any specific guidelines for practical use of differentiated taxes on certain types of goods because a government does not know enough about individual tastes of particular goods. However, we may know more about wealthy individuals’ tastes of certain kinds of commodities. This analysis is based on conspicuous consumption in which individuals engage to flaunt their wealth. Since the rich spend relatively more on positional goods to enhance their social positions, this paper can provide useful insights to set differentiated commodity taxes on certain types of goods. Optimal taxation literature has ignored the positional externality for the most part. Moreover, the studies that take into account the status effect assume that income is exogenous (i.e. constant labor supply). However, allowing labor supply to change in the model may have important implications for the desirability of a tax on a positional good as it creates two opposing effects on welfare. To our knowledge, this is the first study that analyzes differentiated taxation of positional good under the assumption of non-linear income tax and endogenous labor supply.

On the same separable-utility assumption as used in Atkinson and Stiglitz (1976), Christiansen (1984) and Saez (2002), we show that the revenue-neutral shift in the tax mix away from nonlinear income taxes toward positional-good taxes enhances welfare. Hence, an optimal tax structure should have differentiated taxes on positional goods together with nonlinear income taxes. On the other hand, Atkinson and Stiglitz (1976), Christiansen (1984) and Saez (2002) insist that the differentiated commodity taxes cannot supplement the nonlinear income taxes and, thus, are necessary for the optimal tax structure. Furthermore, we have found that differentiated taxes on positional goods are required to some extent, even if demands for positional goods are positively related to labor supply. In this case, Christiansen (1984) suggests negative commodity taxes or subsidies. Moreover, income tax structure is found to be less progressive after a revenue-neutral tax reform.

This paper is organized as follows. In the next section, we present a status-seeking game that can be used to examine an optimal tax system in the presence of status effect. Section 3 solves a two-stage optimization problem, explains individual behaviors in a symmetric Nash equilibrium and solves for the optimal income tax without commodity tax. In Section 4, we explore the total welfare effect of the marginal revision in positional-good taxes. Distributional consequences of tax reform are analyzed in Section 5. We offer concluding remarks in the final section.

2 Model Environment

Consider an economy that has a unit measure of individuals who are identical in all respects, except work ability. A level of ability θ in some interval Θ:=θ_,θˉ with θ_≥0 is given to each individual. The upper and lower bars stand for maximum and minimum levels, respectively. Each individual knows his or her own ability of work, whereas the others cannot observe it. That is, one’s work ability is unobservable and thus becomes private information. However, all of the individuals have common knowledge of the ability distribution in this economy, represented by a twice continuously differentiable distribution function G⋅ on the ability set Θ, and gθ:=dG/dθ is the probability density function. Work ability is assumed to be equal to wage rate, since it implies labor productivity.

An individual who devotes his or her work hours l to the labor market at a given wage rate θ earns a gross income i:=θl. The time endowment is normalized to one, so l+L=1 with L denoting leisure. When a tax authority in this society sets an income tax schedule Ti,s, disposable income becomes z:=i−Ti,s. The shift parameter s determines the shape of the income tax function. The individual takes this parameter as a given, since it is a choice variable of the tax authority. Now, the disposable income is divided into two kinds of consumable goods, x and y, each of which can be distinguished from the other by some characteristics, and the budget constraint is

where qx:=px+tx and qy:=py+ty. The tax rates and producer prices on goods are denoted by t and p, with each subscript indicating one of two goods. Hence, q refers to the after-tax commodity prices.

Using the terminology of Frank (1985), the above consumption goods are classified into two types, positional goods and nonpositional goods. The positional good x is so visible that it carries social status to certain individuals. The consumption of a positional good is referred to as conspicuous consumption. In contrast, the consumption of nonpositional good y does not affect one’s status because others cannot directly observe it. Adopting the formulations of Frank (1985), Robson (1992) and Hopkins and Kornienko (2004), we assume that an individual’s social status is determined not only by his or her consumption level of the positional good but also others’ as follows:

where F⋅ is the distribution function of positional goods in this economy and f⋅ is its probability density function. Each individual has an incentive to consume a higher amount of the positional good and in turn seek a higher status than others, since the value of Fx is increasing in his or her own consumption level of x but decreasing in others. The person with the lowest positional good level x_ earns the rank of r. Therefore, the parameter r, which is assumed to be positive or zero, becomes the lowest status in this society.

We assume that all individuals have the following identical utility function:

where the conventional utility index u⋅≥0 is a twice-differentiable function which is strictly increasing and quasiconcave in two goods x and y, but is strictly decreasing and quasiconvex in hours of work l. In eq. [3], the conventional utility function and the above status function enter multiplicatively into the utility function U⋅. Hence, each individual faces a trade-off between a higher status and a lower direct utility when raising budget share of positional goods but reducing that of nonpositional goods.

In this society the government has a revenue requirement. To maintain constituent welfare at a particular level, the government must finance a constant expenditure E by income taxation or commodity taxation. Then the government budget constraint becomes

where we normalize the population size to unity.^[5] Since the purpose of the present analysis is to investigate the welfare effect of a revenue-neutral shift in the tax mix away from income tax and toward tax on positional goods, we exploit the analytical method as presented in Christiansen (1984). When the government sets the optimal income taxes T∗i for each i without any commodity taxes, the shift parameter s and some arbitrary function ζ⋅ can generally rewrite the income tax function as Ti,s:=T∗i+s⋅ζi and easily define any shift from the optimal income taxes. The value of s should be zero at the optimum.

We define a social welfare function W⋅ that includes all possible redistributive tastes of the government as

in which the function ω⋅ on Θ is such that ∫Θωθdθ=1, and then ωθ is the social weight on individuals with a wage rate θ∈Θ. Given a certain redistributive object, the level of social welfare varies according to the alternative tax system because individuals alter their consumption and labor supply behaviors. Thus, the government will design a tax structure that minimizes tax distortions.

3 Status-Seeking Game and Income Taxation

Before proceeding, it could be helpful to explain the timing of decisions by both individuals and government. As in Christiansen (1984) and Saez (2002), we decompose the individual maximization problem into two stages.^[6] At the first stage, all individuals engage in the status-seeking game, and they noncooperatively decide their demands for positional and nonpositional goods – conditional on their hours of work. Then the individuals move on to the second stage and choose their hours of work – conditional on the income tax function that the government imposes. Embodying individual demands for two goods and labor supplies in its constraints, the government optimally chooses a tax function at the end of this stage.

4 The Welfare Effect of Conspicuous Consumption Taxes

To explore the total welfare effect of a revenue-neutral change in the tax mix away from income tax and toward a tax on conspicuous consumption, the economy is assumed to be in such a state that the government sets an income tax optimally and does not tax consumable goods. That is, this analysis starts at an initial equilibrium with an existing optimal income tax (s=0), but without any commodity taxes (tx=ty=0), and then introduces a small tax dtx on conspicuous consumption. Differentiating the social welfare function [5] totally and substituting the first-order condition [37] that characterizes the optimal income tax, we have

The left-hand side of eq. [38] is the dollar value of the change in social welfare (dW/λ). Since we explore a change in the tax mix, we assume that the government does not change the public expenditure (dE=0). Differentiating the government budget constraint eq. [4] totally and evaluating it when s, tx and ty are zero, in turn yield

Replacing eq. [39] into eq. [38] and subtracting eq. [37] from this gives

The left-hand side of eq. [40] is the total welfare change in terms of dollar value when the government imposes a small tax change dtx on conspicuous consumption. The first term implies the change in tax burden, and the second and third terms represent the change in total revenue on the right-hand side of eq. [40]. Hence, the total welfare change is divided into these two terms.

The next step is to evaluate the change in tax burden on the right-hand side of eq. [40]. From eq. [35], the social welfare function is given as

Differentiating the social welfare function [41] partially with respect to qx and s, we get:

which is applied with two equalities that Vqx=vqx=−xvz and Vs=−vzTs from eqs [24], [26] and [30]. Plugging eq. [42] into eq. [40] rewrites the total welfare change as

Following the analytical method that Christiansen (1984) uses, we define the marginal shift as Tsi,s=ζi=x. In a symmetric Nash equilibrium, each individual choice ultimately depends only on the wage rate θ. Therefore, the equilibrium demand for positional goods is described as x=xθ for each θ∈Θ. Since gross income i is strictly increasing in θ we can rewrite the wage rate as θ=θi for all i. Substituting this function of wage rate into xθ yields the equilibrium demand for positional goods as a function of income, that is, xθ=xθi. Hence, the income tax function Ti,s=T∗i+s⋅xθi is well defined for all levels of gross income i, since the equilibrium demand for positional goods x is expressed for all levels of gross income i. The first term vanishes out in eq. [43]. Then the total welfare change becomes

Since the per-hour income tax Tiθ is positive, the sign of the term (ltx−ls) determines the total welfare effect of marginal tax dtx on positional goods.

The final step is to assess the sign of the term (ltx−ls) in the total welfare change [44]. Differentiating the first-order condition for hours of work l in eq. [30] with respect to tx and s, we get

Subtracting eq. [46] from eq. [45], we have the difference between the changes in work hours, with respect to the tax on positional goods and the shift parameter in the income tax function, as follows:

The defined marginal shift Tsi,s=x, together with eqs [24] and [26], gives the following relationship:

Plugging the above equalities eq. [48] into eq. [47] and dividing this result by vz, we have:

Differentiating the demand for positional good x in eq. [48] partially with respect to the disposable income z and the hours of work l, we then have

Using eq. [50] and the fact that Tis=Tsi=∂x/∂i, we rewrite eq. [49] as

Since the wage rate θ can be expressed as a function of gross income i, disposable income z=zθ and hours of work l=lθ are also functions of gross income i. This fact yields the derivative of the equilibrium demand for positional goods with respect to gross income i as

Replacing eq. [52] into eq. [51] and using the relationship that 1−θ∂l/∂i=ldθ/di>0 from the definition of gross income i=θl, we arrive at:

Finally, using eq. [53], we rewrite the total welfare change [44] as

where T∗ is an optimal tax (i.e. Ti,s=T∗i for s=0). Note that all the terms T∗, −vzr+Gθd2v/dl2 and dθ/di are positive in eq. [54]. Moreover, the term xGθgθθ/l is also positive, since the marginal effect of an increase in original wage-rate rank on demand for positional goods is always positive (xGθ>0). Therefore, the total welfare change becomes positive, if the marginal effect of an increase in work hours on demand for positional goods is zero (xl=0). This case is true when the conventional utility function ux,y,l is weakly separable between hours of work l and demand for positional good x.^[10] If the demand for a positional good is unrelated to hours of work, then the shift in tax mix going away from the income tax and toward the tax on positional goods increases social welfare. This statement implies that the tax on a positional good is desirable even when the preexisting income tax is optimal. In other words, both a differentiated tax on conspicuous consumption goods and an income tax constitute the optimal tax system in the presence of a status effect. Saez (2002) finds that commodity taxation is desirable when consumption of the good increases with leisure (i.e. xl<0). Our results show that when xl<0 commodity (positional good) taxation increases welfare because the term (xGθgθθ/l−xl) is positive as well as all other terms in eq. [54]. This result is in line with Saez (2002). However, our result above also shows that even if xl>0, when demand for positional good is positively related with labor supply, commodity tax can supplement income tax to some extent. This result is obtained due to existence of the term (xGθgθθ/l) in eq. [54]. This term is positive because the good in concern here is positional unlike Saez (2002).

5 Progressivity of the Tax System

We have analyzed the welfare effect of the revenue-neutral change in the tax system toward tax on conspicuous consumption in previous section. Together with this assessment of welfare effect, one would also be interested in knowing how the change modifies the shape of the optimal income tax. Especially, policymakers would like to know how the tax burden changes for people with different income levels when tax authority introduces tax on conspicuous consumption. That is, they would be concerned with the change in the progressivity of the income tax. In this section, we assess the change in the progressivity of the tax system when the revenue-neutral shift is away from income tax toward tax on conspicuous consumption.

In order to do this analysis, we start with the income tax function, Ti,s=T∗(i)+s.xθi for each i and s, which was defined previously. Totally differentiate this income tax function with respect to the shift parameter s in the income tax function and the tax rate tx on positional good. Then we have the total change in income tax as

In eq. [55], if s=0 and tx=ty=0, then dT=dT∗ and Ti=Ti∗, which implies that the total change dT∗ is from the optimal income tax without any initial commodity taxes. Integrating eq. [55] with respect to θ, and since dtx doesn’t depend on θ, and thus, ds doesn’t depend on θ from eq. [39], the integrated equation becomes ∫ΘdTdG=∫ΘTiθls+TsdGds+∫ΘTiθltxdGdtx. Subtract eq. [39] from this equation and rearrange it. Then

Assume for the moment that the integrand is equal to zero in eq. [56], i.e.:

Then the total change in the income tax at the initial optimum becomes dT∗i=−xidtx. This implies that the reduction in income tax is exactly the same as the increase in conspicuous consumption tax and, thus, the change in total tax doesn’t happen for each individual. That is, government recycles additional tax revenue at an individual level as well as at an aggregate level. Furthermore, such a tax redistribution is actually the case in which the introduction of conspicuous consumption tax can generally lead to a positive welfare effect for any social weight function ω⋅ on Θ in the social welfare function [5]. We formally prove this point in Appendix. Meanwhile, if a social weight function ω⋅ is given as specific according to a particular redistributive object of government, then a tax redistribution other than the one in eq. [57] could exist. For example, the government can redistribute tax burden from the rich to the poor in order to subsidize the poor. However, the tax redistribution other than the one in eq. [57] is satisfied with a specific social weight function only. As we consider various social weight functions specifically, we may encounter a large number of tax redistributions so that it is impossible for us to analyze all the cases. Thus, we focus on the tax redistribution in eq. [57] that is satisfied with any social weight function in general. In addition, the tax redistribution can easily apply to practical use. Since each individual’s tax burden doesn’t change, the individuals can reach a consensus on the tax redistribution. For these reasons, the tax redistribution we consider here is meaningful for the analysis.

The fact that each individual’s income tax burden is reduced exactly by the exact amount of conspicuous consumption tax he or she pays, has important implications in terms of how the tax burden changes for people with different income levels. We know from previous sections that x=x(i) is strictly increasing in i. In another words, individuals with higher income levels consume more positional goods than lower income individuals. For example, let i_ and i‾ represent income level of the poorest and the richest individuals respectively. So, the amount of reduction in income tax liability of the poorest and the richest individual will be x(i_)dtx and x(i‾)dtx respectively. At the initial income tax T∗(i), the tax reform reduces income tax burden of the rich more than for the poor. Thus the income tax becomes less progressive after the tax reform. This can better be seen in Figure 1. While the reduction in marginal tax rate for the rich is significant, for the poor marginal tax rate is reduced only slightly. Although marginal income tax rate for all income levels decrease, the rich gets the biggest reduction in their marginal tax rate because they consume the positional good most.

Figure 1:

Income tax progressivity after reform.

We can also assess how the progressivity of commodity tax (i.e. conspicuous consumption tax) changes. We should keep in mind that the tax rate on conspicuous consumption before the reform is zero. A marginal increase in conspicuous consumption tax from zero to positive will make the tax less regressive. In Figure 2 we show how the reform shifts the conspicuous consumption tax. Before the reform it is simply a horizontal line with zero tax rate. After the reform it becomes an increasing function. That is why, we can say that a marginal increase in tx will be less regressive. Since x=x(i) is strictly increasing in i, the burden of the tax, in terms of the amount paid, is higher for the rich compared to the poor. Although in Figure 2 the function x(i)dtx seems to be concave, it can be linear or convex based on the distribution of income i. In general, commodity taxation is known to be regressive because usually the poor usually spend a higher share of their budget on taxed goods. In our case, if the demand for positional good is increasing at a faster rate than income then the conspicuous consumption tax can even be progressive. Hence, the overall progressivity of the tax system (i.e. income tax and conspicuous consumption tax together) will not change because the tax reform is revenue neutral at the individual level, as well as aggregate level. Individuals will experience no change in their overall tax payment before and after reform. However, as shown before, the reform will be welfare increasing for each individual.

Figure 2:

Consumption tax progressivity after reform.

In a society income inequality can change over time. Also, the income inequality can be different across societies as well. Hence, it would be interesting to compare tax progressivity changes between two societies different in income distribution. Hopkins and Kornienko (2004) predict that the more equally income is distributed, the more individuals with middle incomes consume conspicuous consumption goods. If people get closer together, then they have greater incentive to differentiate themselves, since the marginal return to conspicuous consumption becomes higher. Suppose both of two societies have an equal average income, but one society’s income distribution Gθ is more dispersed than the other society’s Hθ (i.e. Gθ is a mean-preserving spread of H(θ)). In this case, our model implies that the introduction of small tax dtx on conspicuous consumption should reduce more income tax for those with middle income, but less income tax for those with low and high income in the society with Hθ than in the society with Gθ. Thus, as the consequence from the introduction of dtx, the progressivity of the income tax becomes higher for middle to high incomes in the society with Hθ, compared to the society with Gθ. That is to say, the more equally income is distributed, the lower income tax should be for those with middle income, but the higher income tax should be for those with low and high incomes.

6 Conclusion

In this study we have developed a game-theoretic model wherein individuals with different labor productivity engage a status-seeking game. In this context, we examined the welfare effect of a revenue-neutral shift in the tax mix away from nonlinear income taxes toward positional-good taxes. With a conventional utility function separable between positional goods and hours of work, we inferred that the optimal tax system needs a supplementary tax on positional goods together with an income tax. The result is based on the assumption that the preexisting income tax is at an optimal level. Kaplow (2006) notes that the preexisting income tax may not be optimal in reality. Then, he shows that, even in this case, commodity taxation is undesirable. However, the commodity taxation would still be desirable even with the nonoptimal income tax in the presence of consumption externality. This analysis identifies that the optimal income tax cannot correct the distortion from status-seeking behaviors by itself. Hence, a suboptimal income tax could leave the distortion at a higher level than at an optimal one. In turn, the result of this paper would be consistent even when the preexisting income tax is not optimal. We also showed that income tax will become less progressive after a revenue-neutral shift from income tax toward commodity tax. As rich people consume more positional goods, a revenue-neutral reform (imposing a tax on conspicuous consumption and at the same time decreasing income tax) implies higher subsidies in terms of a reduction in tax. This in turn means bigger reduction in marginal tax for the rich compared to the poor.

Luxury tax has been used at different times by different countries. Especially, when the luxury good is being used by individuals to advertise their position, inefficient amount of resources will be spent on this kind of luxury good. This inefficiency caused by positional goods should be taken into account in welfare analysis of income and commodity taxation. The model developed here can help policymakers make a better decision in terms of optimal tax mix and its distributional consequences. Our analysis is based on the assumption that a government can differentiate positional and nonpositional goods. However, it may be practically impossible for a government to differentiate between positional and nonpositional goods. Furthermore, some goods may generate positional externalities and environmental externalities at the same time (i.e. big cars). Extending this model in these two directions can be the subject of future research.