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Redistribution and Inequality in a Heterogeneous Society: How Economic Inequality Harms Societies

David Chapinski

Thursday, November 8, 2012 • 6:10am

Presidential aspirants since Ronald Regan have urged us to ask whether we’re better off now than we were four years ago.  At any time from 1945 to the early 1970s the answer for most Americans would have been a resounding yes.  Throughout that period, incomes grew at about 3 percent a year for families up and down the income ladder.  Today, however, this question is more difficult to answer.  During the past several decades, the distributions of income and wealth in the United States have changed in such a way that the economic environment for most upper-middle-class people has become much more lie that of World A than that of World B in our earlier experiences.  For example although the top 1 percent of earners waved more than three times as much purchasing power as in the 1979, the real earnings of families in the middle have risen only slightly since then. The meager income growth that these families have experienced has come not from just one place.

I find that more extensive redistribution tends to lower inequality by benefiting low ability individuals at the expense of high-ability individuals, but to increase inequality by benefiting leisure-loving individuals at the expense of consumption-loving individuals with similar abilities.  More redistribution tends to decrease inequality if redistribution is limited, but to increase inequality if redistribution preferences is not innocent when discussing the effects of redistribution on social inequality.  When redistribution is limited, regenerous redistribution lowers inequality[i] because an individual’s equivalent wage depends primarily on his/her abilities, and because redistribution benefits individuals with low abilities at the expense of individuals with high abilities.  Extensive redistribution, however, makes it impossible for an individual to achieve much higher consumption levels than their average; all individuals thus choose similar bundles consisting of high leisure and relatively low consumption.  Consumption-loving individuals therefore have low equivalent wages while leisure-living individuals have relatively high equivalent wages.  Making a relatively extensive redistribution scheme more extensive then raise inequality, because it harms most the consumption-loving individuals who already have the lowest equivalent wages.

A non-monotonic relationship between redistribution and social welfare is a standard result in literature more and more because measures of social welfare come equity and efficiency considerations.  Social welfare normally decreases in the extent of redistribution if redistribution is so extensive that the economy is on the Laffer curve’s decreasing branch, while equity gains often outweigh efficiency losses when there is little redistribution.  This finding of a non-monotonic relationship between redistribution and social inequality, however, does not directly follow from the efficiency losses associated with extensive redistribution, it is this a stronger and more striking result than a non-monotonic relationship between redistribution and social welfare, and suggests that pure inequality considerations put an upper bound on redistribution when taking the heterogeneity in the individuals’ preferences into account.

One only has to focus on the lowest equivalent wage if one wants to study social welfare and accept its fairness requirements.  Indeed, their axioms single out particular social preferences like priority of the worst off and a particular measure of individual situations like the equivalent wage.  To focus on social inequality means to change the former but keep the latter.  Even when concerned primarily about social welfare, one might want to know how redistribution affects inequality in equivalent wages.  One reason is that there are possibly multiple redistribution schemes that maximize social welfare, and one might in this want to know how they affect social inequality.  Another reason is that social welfare might depend on inequality in equivalent wages more generally if one of the particular fairness requirements or axioms were modified or dropped even though these requirements seem reasonable to many of us.  The economics of traditional infrastructure is quite complex, as reflected perhaps in the fact that economists sometimes refer to infrastructure opaquely” as social overhead capital.  There are ongoing, hotly contested debates in economic especially about how the costs and benefits of infrastructures, for example, about the degree to which particular infrastructure investments contribute to social welfare or economic growth, and about how to prioritize infrastructure investments in developing countries.  Regardless, most economies recognize that infrastructure resources are important to society precisely because infrastructure resources give rise to large social gains.  The nature of some the gains as spillovers may explain why we take infrastructure for granted.  The externalities are sufficiently difficult to observe or measure quantitatively; much less capture in economic transactions and the benefits may be diffuse and sufficiently small in magnitude to excite the attention of individual beneficiaries.  We should be exploring the relationships these three generalizations.  The accepted role for government associated who infrastructure market failure be related to society’s need for nondiscriminatory community access or to the generation of substantial spillover or to both?  I cannot stress how the society’s need for nondiscriminatory community scaled or generation of substantial spillover or to both becomes the first interest? The societal need for nondiscriminatory community access to infrastructure and the generation of substantial spillovers each appears to independently constitute grounds from identifying a potential market failure and for supporting some role for government.  But the confluence of the two factors suggests that something more complex may be involved.  Might society’s need for nondiscriminatory community access to infrastructure be related to the generation of substantial spillovers?

When individuals differ in their earning abilities and their preferences for consumption and leisure, it is unclear how social inequality should be measured.  Since redistribution bends to benefit low ability and leisure loving individuals at the expense of high ability and consumption loving individuals, it is also unclear how redistribution affects inequality in such a heterogeneous society at least if one is not willing to assume that redistribution from consumption loving to leisure loving individuals with similar abilities reduces inequality.  Approaches based on inequality in consumption, and leisure are achieved in utility levels and unsuitable for measuring inequality in a heterogeneous society, and hence also for analyzing how redistribution effects social inequality. 

In principle then, social inequality measures could be based n the inequality in achieved utilities levels; however, any such measure requires interpersonal utility comparisons.  Such comparisons are fine if all individuals have identical preferences such that they all reach the same conclusions when comparing utilities interpersonally, However, they are not fine if preferences are heterogeneous, different individuals do in general reach different conclusion.  The inequality in such a heterogeneous society therefore cannot be meaningfully evaluated with measures of the inequality in achieved utilities levels.


[i] As an example, the popular public finance textbooks of Rosen (2005) and Stiglitz (2000) assume that individuals differ in their incomes only when discussing inequality.  Following Mirrlees (1971). The assumption that individuals differ only in their earning abilities has become standard in the economic literature on taxation and redistribution.

 

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