Abstract
We investigate the effects of inequality aversion on equilibrium labor supply, tax revenue, income inequality, and median voter outcomes in a society where agents have heterogeneous skill levels. These outcomes are compared to those which result from the behavior of selfish agents. A variant of FehrSchmidt preferences is employed that allows the externality from agents who are “ahead” to differ in magnitude from the externality from those who are “behind” in the income distribution. We find first, that inequalityaverse preferences yield distributional outcomes that are analogous to taxtransfer schemes with selfish agents, and may either increase or decrease average consumption. Second, in a society of inequalityaverse agents, a linear income tax can be welfareenhancing. Third, inequalityaverse preferences can lead to less redistribution at any given tax, with lowwage agents receiving smaller net subsidies and/or highwage individuals paying less in net taxes. Finally, an inequalityaverse median voter may prefer higher redistribution even if it means less utility from own consumption and leisure.
This is a preview of subscription content, log in to check access.
References
Ackert, L.F., MartinezValdez, J., Rider, M.: Social preferences and tax policy: Some experimental evidence. Econ. Inq. 45, 487–501 (2007)
Algood, S.: The marginal costs and benefits of redistributing income and the willingness to pay for status. J. Public. Econ. Theory. 8, 357–77 (2006)
Alesina, A., Angeletos, G.: Fairness and redistribution. Am. Econ. Rev., pp. 960–980 (2005)
Alm, J., McClelland, G.H., Schulze, W.: Changing the norm of tax compliance by voting. Kyklos 52, 141–71 (1999)
Atkinson, A.B.: On the measurement of inequality. J. Econ. Theory. 2, 244–263 (1970)
Beckman, S.R., Formby, J., Smith, J.S., Zheng, B.: Envy, malice and pareto efficiency: an experimental examination. Soc. Choice. Welfare. 19, 349–367 (2002)
Bolton, G., Ockenfels, A.: ERC: A theory of equity, reciprocity, and competition. Am. Econ. Rev. 90, 166–193 (2000)
Clark, A.E., Frijters, P., Shields, M.A.: Relative income, happiness, and utility: an explanation for the easterlin paradox and other puzzles. J. Econ. Lit. 46, 95–144 (2008)
Dhami, S., AlNowaihi, A.: Existence of a condorcet winner when voters have other regarding preferences. J. Public. Econ. Theory. 12, 897–922 (2010)
Dhami, S., AlNowaihi, A.: Redistributive policies with heterogeneous social preferences of voters. Eur. Econ. Rev. 54, 743–759 (2010)
Dorfman, R.: A formula for the gini coefficient. Rev. Econ. Stat. 61, 146–149 (1979)
Easterlin, R.A.: Will raising the incomes of all increase the happiness of all. J. Econ. Behav. Organ. 27, 35–48 (1995)
Fehr, E., Schmidt, K.M.: A theory of fairness, competition and cooperation. Q. J. Econ. 114, 817–868 (1999)
Fehr, E., Fischbacher, U.: Why social preferences matter—the impact of nonselfish motives on competition, cooperation and incentives. Econ. J. 112, C1–C33 (2002)
Forsythe, R, Horowitz, J., Savin, N.E., Sefton, M.: Fairness in simple bargaining experiments. Game. Econ. Behav 6, 347–369 (1994)
Frank, R.H.: Should public policy respond to positional externalities. J. Public. Econ. 92, 1777–86 (2008)
Frohlich, N, Oppenheimer, J., Kurki, A.: Modeling otherregarding preferences and an experimental test. Publ. Choice 119, 91–117 (2004)
Galasso, V: Redistribution and fairness: a note. Eur. J. Polit. Econ. 19, 885–892 (2003)
Hochman, H.M., Rodgers, J.D.: Pareto optimal redistribution. Am. Econ. Rev. 59, 542–557 (2012)
Höchtl, W., Sausgruber, R., Tyran, J.: Inequality aversion and voting on redistribution. Eur. Econ. Rev. 56, 1406–1421 (2012)
Hopkins, E.: Inequality, happiness and relative concerns: What actually is their relationship. J. Econ. Inequal. 6, 351–72 (2008)
Hwang, S., Lee, J.: Conspicuous consumption and income inequality. Oxford. Econ. Pap. 69, 279–292 (2017)
Ireland, N.J.: Status seeking, income taxation and efficiency. J. Public. Econ. 70, 99–113 (1998)
Ireland, N.J.: Optimal income tax in the presence of status effects. J. Public. Econ. 81, 193–212 (2001)
Ledyard, J.O.: Public goods: A survey of experimental research. In: Kagel, J.H., Roth, A.E. (eds.) The Handbook of Experimental Economics, pp 111–194. Princeton University Press, Princeton (1995)
Lind, JT: Fractionalization and the size of government. J. Public. Econ. 91, 51–76 (2007)
Mankiw, N., Weinzierl, M., Yagan, D.: Optimal taxation in theory and practice. J. Econ. Perspect. 23, 147–74 (2009)
Meltzer, A.H., Richard, S.F.: A rational theory of the size of government. J. Polit. Econ. 89, 914–927 (1981)
Tyran, J., Sausgruber, R.: A little fairness may induce a lot of redistribution in democracy. Eur. Econ. Rev. 50, 469–485 (2006)
Wendner, R., Goulder, L.H.: Status effects, public goods provision and excess burden. J. Public. Econ. 92, 1968–85 (2008)
Author information
Affiliations
Corresponding author
Electronic supplementary material
Below is the link to the electronic supplementary material.
Appendix
Appendix
Claim: Wage income, wL(w,τ), is increasing in w if and only if
σ(1 − αH(w) + β[1 − H(w)]) > w(α + β)h(w) for all \(w\in [\underline {w},\overline {w} ]\).
Proof
Using (2) we have
Now differentiate the above with respect to w to get a necessary and sufficient condition for labor income to be increasing in the wage:
The parametric condition for \(\frac {\partial (wL(w,\tau ))}{\partial w}>0\) is thus
Finally, rewriting the above yields the necessary and sufficient condition (given in (3)) that must be satisfied at all w in order for labor income to be monotonically increasing in the wage: σ(1 − αH(w) + β[1 − H(w)]) > w(α + β)h(w). □
Proof of Proposition 1
An inequalityaverse individual i with an hourly wage w_{i} provides weakly greater labor than a selfinterested individual with the same hourly wage if and only if:
Rearranging the above yields the condition
Recall that \(\tilde {w}\) is defined as the w_{i} such that (9) holds with equality. Since H is a strictly increasing function, (9) is satisfied if and only if \(w_{i}\le \tilde {w}\). □
Before stating the proofs of Proposition 2 and 3, define average pretax income as
with I(0,0) corresponding to selfish agents. It is clear that I(α,β) is increasing in β and decreasing in α. For a given τ, both average tax revenue, S = τ I(α,β), and average consumption, (1 − τ)I(α,β), and are increasing in I(α,β), so the following proofs focus on I(α,β).
Proof of Proposition 2
 (i).:

We know from above that I(0,0) < I(0,β). Suppose β ≤ 1. If I(β,β) ≥I(0,0), the result holds for α^{′} = β. If I(β,β) < I(0,0) < I(0,β), the result follows from the observation that I(α,β) is a continuous function. Next, suppose β > 1. If I(α,β) ≥I(0,0), the result holds for α^{′} = 1. If I(1,β) < I(0,0) < I(0,β), the result follows from the observation that I(α,β) is a continuous function.
 (ii).:

Follows from 2(i) and Proposition 1.
Proof of Proposition 3
 (i).:

We first establish that I(β,β) < I(0,0) for a symmetric distribution with σ > 2. The result then follows from the fact that I(α,β) is a continuous decreasing function of α. Take the derivative of ρ(β) ≡I(β) to yield
Let the median wage be w_{M}. The above is negative if and only if
Using symmetry, which implies g(x) ≡ h(w_{M} − x) = h(w_{M} + x), and reversing the limits of integration we arrive at (12) which is equivalent to (11):
To show that (12) holds it is sufficient to show that (13) holds weakly for x = 0 and strictly for all \(x\in \left (0 \right .\frac {\overline {w} \underline {w}}{2}]\).
Clearly, (13) holds weakly for x = 0 since H(w_{M}) = 1/2. We now show that (13) holds strictly for \(x\in \left (0 \right .\frac {\overline {w} \underline {w}}{2}]\), which implies \(\frac {\overline {w} \underline {w}}{2}\le w_{M}\). So we have 2H(w_{M} − x) < 1 and, given that \(\frac {1}{\sigma 1}1<0\) for σ > 2, it follows that
Finally, (14) and (w_{M} − x) < (w_{M} + x) implies that (12) holds strictly for
(ii). Follows from part (i) and Proposition 1. □
Proof of the Lemma
Observe that γ(w_{M},α,β) can be written as
Average income of those above the median is given by \({\int }_{w_{M}}^{\overline {w}} {zL\left (z,\tau \right )} 2h(z)dz\) and average income of those below the median is given by \({\int }_{\underline {w}}^{w_{M}} {zL(z,\tau )} 2h(z)dz\). For all β > 0 and α ∈ [0,β] the sum in the first bracketed term is positive since average income of those above the median is greater than average income of those below the median. The sum in the second bracketed term is positive because average income of those above the median is greater than the median income. The sum in the third bracketed term is positive because median income is greater than the average income of those below the median. □
Proof of Proposition 5
Let τ_{M} denote the most preferred tax for an otherregarding median agent and let τ^{S} denote the most preferred tax for a selfish median agent. The condition α = β implies that labor income for the selfish median voter equals that of the inequality averse median voter; namely, w_{M}L(w_{M},τ). Thus, τ^{S} must satisfy
Now if we evaluate the expression in (7) at τ = τ^{S} we get
Given that τ_{M} must satisfy (6) it follows that τ_{M} > τ^{S}. □
Rights and permissions
About this article
Cite this article
Murray, M.N., Peng, L. & Santore, R. How does inequality aversion affect inequality and redistribution?. J Econ Inequal 16, 507–525 (2018). https://doi.org/10.1007/s1088801893897
Received:
Accepted:
Published:
Issue Date:
Keywords
 Income distribution
 Inequality aversion
 Redistribution