ࡱ> y` bjbj 8%b&1:,&&^ j~b(b(b(8(f)\~K),"-LR-j-E.E.E.IIIIIII$KhgNnI X7E.E.X7X7I  R-j-J@@@X7 R- j-I@X7I@@:E,  NLzFE.0@2|34%E.E.E.II^@dE.E.E.KX7X7X7X7~~~ b(~~~b(~~~        Public Economics of Subjective Well-Being and Relative Income John Beath Felix FitzRoy November 2008 Key words: subjective well-being, happiness, relative income, optimal taxes, unemployment benefits Abstract The importance of relative income comparison for subjective well-being has extensive empirical support, but the implications for taxation, unemployment and the public sector have hardly been explored. Here we develop a simple model where SWB depends on relative income, with a general distribution of ability, benefits for the lowest abilities who are voluntarily unemployed, and a public sector. This replicates the observed positive, concave cross-sectional relation between income, working time and SWB. We present simulations to show how optimal benefits, (flat) taxes and employment vary with the degree of concern for relative income, and differ in sometimes surprising ways under utilitarian and Rawlsian objectives. Aknowledgements We thank Tatiana Kornienko, David Ulph, Hans-Peter Weikard and audiences at St. Andrews, Stirling, the Scottish Economic Society, Aberdeen and at the Mansholt Lecture, Wageningen for useful comments and discussion. The authors retain responsibility. It remains a serious blot on modern economics, which prides itself as a science, that the relative income theory is rarely taken seriously, despite providing fruitful explanations for human behaviour and despite never having been empirically refuted (Green,F., Demanding Work, Princeton University Press, 2006, p.152) 1. Introduction In 1899 Veblen emphasized the importance for an individuals well-being of comparison and status. After half a century of neglect, this insight was taken up in Duesenberrys (1949) relative income hypothesis. But it was only after Easterlin (1974) discovered that economic growth in advanced economies did not always increase happiness or life satisfaction that research on subjective well-being (SWB) in several disciplines began to progress rapidly. This is now one of the fastest growing areas in economics (and other areas), attracting numerous recent surveys, including Frey (2008), (whose title, Happiness: A Revolution in Economics, aptly summarizes current developments), Clark et al (2008), Blanchflower (2007), Offer (2006), Layard (2005, 2006), Di Tella and MacCulloch (2006), and Lane (2001). Many models of SWB have been proposed, and a variety of explanatory variables have turned out to play an important role in empirical studies. These include employment and unemployment, divorce, family and friendship, inherited personality traits, and social capital including democracy and trust. In stark contrast to traditional theory, some form of relative income comparison seems to be a key economic variable, with data from rich countries. Thus Blanchflower (2007) uses education as a proxy for relative income which is highly significant in a large international panel of individual data with many controls. However he finds that per capita GDP has no additional effect in the richest countries, but is significant for poor countries. Several country-level studies with micro-data have found that the income of geographical neighbours or individuals in the same educational and occupational groups has a negative effect on SWB of similar magnitude to the positive effect of own income, while unemployment and divorce always have strong negative effects. Thus with US data, Luttmer (2005, p.990) reports that an increase in neighbors earnings and a similarly sized decrease in own income each have roughly the same negative effect on well-being. Ferrer-i-Carbonell (2005) has obtained similar results with German data (but using quite different reference groups in terms of similar education), as have Helliwell and Huang (2005) with Canadian data. The consistency of these findings in the presence of numerous controls and robustness checks is remarkable, and they are compatible with both the failure of average SWB to increase with average real income over time in the US and other countries, and with the generally observed positive cross-sectional relationship between income and SWB. Clark and Oswald (1996) related job-satisfaction to comparison income. Not withstanding these results, there has been little response to Layards (2005) plea for the incorporation of relative income effects into models of taxation and welfare. An early attempt by Boskin and Sheshinski (1978) did find taxes rising with concern for relative income, but in this model revenues were redistributed as a universal basic income, and there was no unemployment or public sector. Abel (2005) considers redistribution in an overlapping generations model without unemployment, and there have been applications to macroeconomics (Abel, 1990, 1999; Ljungquvist and Uhlig, 2002). Arrow and Dasgupta (2007) develop a dynamic model of relative consumption, but without taxation or a public sector. Here we develop a simple general equilibrium model with a distribution of ability, endogenous labour supply and unemployment, a flat tax and a public sector. Unemployment benefits compete with the latter for public funds, and utility or SWB depends on own income relative to the earnings of others in the same ability class. Although labour has negative marginal utility in the usual way, unemployment causes a discrete loss of utility, (following the survey evidence, but usually ignored in modelling labour supply). Since analytic results are difficult to obtain without drastic simplification, we present simulations based on a Beta distribution of ability, and utility that is quasi-linear in leisure. Thus we include both income effects, and the inevitable poverty trap effect when marginal workers lose benefits as they exit unemployment and face an income tax on their earnings. We compare the effects of varying the two policy instruments benefits and taxes under the two benchmark social welfare functions, utilitarian, and Rawlsian or maxi-min. We then show how optimal policies under the two polar opposite objectives vary with the degree of concern for relative income. As expected, optimal taxes increase rapidly with concern in both cases, and are much higher with Rawlsian policy when concern is low. Quite surprisingly, however, the respective optimal tax rates converge for (realistically) high levels of concern, in spite of radically different objectives, a result that could have considerable policy and political implications. Not surprisingly, there is almost full employment under the utilitarian policy, with only those essentially unable to work receiving minimal benefits. However, there is again a remarkable convergence of Rawlsian (under-) employment to fairly close to utilitarian full employment for the highest levels of concern for relative income. This holds in spite of Rawlsian benefits that are much higher than under utilitarian policy, and which do not decline with growing concern in the way the (already meagre) utilitarian benefits do. These results are rather counter- intuitive, and show how the complex interactions in even a basic general equilibrium model with a public sector can yield quite surprising outcomes. 2. A Model of Relative Income In this section, we explore the implications of a utility function to represent SWB or happiness that depends on both relative income, and on endogenous leisure, where work effort depends on ability. The empirical evidence reviewed above suggests that various measures can proxy for the complex psychology of aspirations and comparison with a reference group that will also vary across individuals. To keep the model simple, we just use equilibrium income of each individuals ability class as reference income, though we indicate how alternatives can generate similar results. This is very close to the empirical specification of Ferrer-i-Carbonell (2005), who uses the average income of those with similar educational qualifications as reference income. Our model thus generalises previous attempts to include relative income in representative agent models, as well as including unemployment and a public sector. We do not include the important issues of aspirations and adaptation to changing income, which would require a dynamic model (Stutzer, 2004). Finally it should be emphasized that the importance of relative income is likely to depend upon absolute income exceeding levels of poverty at which basic necessities are lacking. In other words our model implicitly requires that minimal income is high enough to maintain a basic standard of living. We shall assume that individuals differ in terms of their ability  EMBED Equation.DSMT4  and the density of the distribution is f(a), with F(1) = 1. If e is effort or working time, the effective labour supply of someone with ability a is ae and output will be  EMBED Equation.DSMT4  with a linear technology. If someone is employed, SWB or utility (we use the terms interchangeably) is assumed to be quasi-linear in leisure, and to depend on the ratio of own income to the (Nash)- equilibrium income of individuals with the same ability, with an exponent  EMBED Equation.DSMT4 , which represents concern with relative income. Thus 1.  EMBED Equation.DSMT4 . where utility, U, is concave and increasing, and y is the individuals net or after- tax income or consumption when the price of output is normalised to unity:  EMBED Equation.DSMT4 . Equilibrium income is  EMBED Equation.DSMT4 , where  EMBED Equation.DSMT4  is equilibrium effort for those with ability a, who face a proportional tax on their earned income at a rate t , and the tax revenue provides for the provision of public goods and unemployment benefits. The value of government expenditure, G, on public goods is represented by the concave, increasing function  EMBED Equation.DSMT4 . Concavity captures both decreasing returns in the technology of provision as well as diminishing marginal utility of the good or service. Marginal utility of the public good is assumed to be infinite when G =0, so optimal policy will always require a positive supply of the public good. The unemployed receive a benefit B. The reference income in the relative income term is just the benefit received by other unemployed people, with the same exponent as before. This simplifying assumption is no doubt unrealistic. It might be more appropriate to assume that the reference income is the lowest earnings, or the income of the marginal employed worker. However, this would complicate the determination of the marginal worker in equation (11) below, without yielding much additional insight. Since there is ample empirical evidence on the stigma of unemployment, we allow for this by letting the utility of consumption of the private good be subject to scale and level reductions. Thus the utility or SWB of someone who is unemployed is given by 2.  EMBED Equation.DSMT4 , where 0 < d d"1 and e > 0. Thus utility of the unemployed obviously increases with the level of benefits. These utility functions follow the tradition of using relative income/consumption discussed above. Similar results follow from using mean income in the whole economy as reference income, though this adds some unnecessary complication. Alternatively, with upward looking comparisons, using the income of the highest earners as the reference income for aspirations also preserves the essential results. Furthermore, we could define a sequence of ability subgroups, with the maximum income in each as the reference income for the subgroup. Then we obtain similar results for each subgroup, with equilibrium functions differing only by constants, and we avoid the extreme case of the poorest groups in society forming aspirations based on the highest incomes, in favour of more local comparisons. Those who are employed will choose equilibrium effort so as to maximise utility. As this is a large economy and agents are small, they will take the equilibrium level of income of those with the same ability as given in choosing their own optimal effort. This yields the first-order condition for optimal effort,  EMBED Equation.DSMT4 , and after- tax income, EMBED Equation.DSMT4 , from (1) as 3.  EMBED Equation.DSMT4 . Rearranging and writing  EMBED Equation.DSMT4 , so  EMBED Equation.DSMT4 , we obtain 4.  EMBED Equation.DSMT4  as the defining equation for equilibrium effort, which is now obviously a function of x.. The weighting of relative income by the exponent,  EMBED Equation.DSMT4 , is in principle subject to empirical testing, with some cross sectional results, as mentioned above, suggesting a value close to one. Simplifying (4), we write the defining equation for equilibrium earnings in terms of ability and taxes as 5.  EMBED Equation.DSMT4  By differentiating (5) we can obtain the response of earnings to change in ability or taxation: 6.  EMBED Equation.DSMT4   EMBED Equation.DSMT4  which is positive by concavity. Thus, as expected, earnings increase with ability, and fall as the tax rises. However, it turns out that the response of effort cannot be signed unambiguously, due essentially to conflicting income and substitution effects. From the positive earnings response it does follow that the elasticity of effort must exceed minus one, where the effort elasticity is  EMBED Equation.DSMT4 . To obtain monotonic responses and numerical simulations we shall continue with a constant elasticity utility which is quasi-linear in leisure, as follows: 7.  EMBED Equation.DSMT4  with  EMBED Equation.DSMT4 . From the FOC we obtain equilibrium effort as a simple, monotonic increasing function: 8.  EMBED Equation.DSMT4  Note that EMBED Equation.DSMT4 . The latter case must thus be excluded to obtain equilibrium effort that increases with ability and declines as the tax rate rises, as both casual observation and empirical results indicate. This implies that equilibrium effort increases with concern for relative income, a kind of keeping -up -with -the -Joneses effect. This is intuitively plausible, because individual earnings impose an externality on others in the same ability group, so they are encouraged to supply more effort in order to compensate for the externality. Equilibrium net earnings are  EMBED Equation.DSMT4 , and utility for x, (or an individual with ability a facing tax t ) , then follows by substituting (8) into (7), so 9.  EMBED Equation.DSMT4  Next we determine the lower bound to ability of the employed, say  EMBED Equation.DSMT4 . Individuals with this level of ability are indifferent between work and unemployment, but for consistency we assume they choose unemployment. Those with higher ability prefer to work, given the tax and benefit levels, while those with lower ability prefer unemployment. Thus it follows from (9), and equation (2) for unemployed utility, after substituting the constant-elasticity specification in (7) that 10.  EMBED Equation.DSMT4  Simplifying and using the definitions (8) we find that the marginal ability is given by: 11.  EMBED Equation.DSMT4  so unemployment,  EMBED Equation.DSMT4 , increases with both the tax and benefits as expected. From (8) we see that the effort elasticity becomes arbitrarily small as  EMBED Equation.DSMT4  approaches one, so the observed low labour supply elasticities of at least full time male workers with respect to taxes and wages suggests a high weighting (close to one) of the reference income in utility (1). By contrast, (11) shows a unit tax elasticity of the participation or marginal ability, in accordance with much higher responsiveness of the (particularly female) participation rate to wages and taxes found empirically. Note also that unemployment increases with the degree of concern for relative income. From (9) we see that there is a minimum or full-employment benefit, say  EMBED Equation.DSMT4 , for which the marginal ability is the minimum,  EMBED Equation.DSMT4 , at which no labour can be supplied. These individuals, with measure zero, are thus the only unemployed, while all others with positive ability prefer employment EQ . From (11) the minimum benefit is 12.  EMBED Equation.DSMT4  Notice that with a positive fixed cost of unemployment, the earnings of very low ability individuals who are working will be less than the benefit level (since earnings tend to zero with ability), though their utility or SWB is higher. This is not entirely unrealistic in a welfare state where some may choose to work part time or casually for very low earnings. On the other hand, arbitrarily low earnings without any other income is clearly infeasible, and greater benefits can indeed put a floor under earnings through a (positive) marginal ability (11), below which people do not work. In the normal case that marginal ability is positive, so there is a positive measure of unemployment, the lower bound on earnings is given by the potential earnings of those with marginal ability (though we are assuming that this group actually choose not to work). Write this, using (11), as: 13.  EMBED Equation.DSMT4  Then again we see that the lowest earnings, as ability tends to the marginal level, may be less than or greater than the benefit, depending on parameter values. Clearly our model of voluntary unemployment with no labour market frictions is highly stylized, but it does seem to capture some important features such as the inherent conflict between redistributive benefits and labour-market participation. These are issues that remain in more complex and realistic models of employment. The public sector Government revenue, R, from the tax on income is 14.  EMBED Equation.DSMT4  Clearly a rising tax will initially raise but ultimately reduce - revenue from existing employment, as well as raising the participation ability and hence unemployment, thus yielding a Laffer curve, as shown in a Figure 1 in Section 3 below. With a balanced budget, revenue has to meet unemployment benefit costs  EMBED Equation.DSMT4  and any other spending on public goods, so  EMBED Equation.DSMT4 . First order conditions for the optimal tax and benefits under the budget constraint are too complicated to yield much insight, so we turn to numerical simulations to explore our main objective how the degree of concern for relative income affects optimal taxation and redistribution under differing utilitarian and Rawlsian policy goals. 3. Numerical simulations In this section we explore the implications of concern for relativity for the design of tax and benefit policy. In our model this is captured by the parameter b (see equation 1). If we were to assume that ability was uniformly distributed on the [0,1] interval, we can certainly establish some analytical results. However, we wish to consider more realistic ability distributions than the uniform and analytical results arelimited in such cases. For this reason we have numerically simulated our model and explored the sensitivity of our results on public finance and the optimal tax rate to variations in the underlying parameters of the model, in particular, concern for relativity. Since in the longer term we wish to explore the implications of variations in the shape of the ability distribution we have used the Beta distribution. This is the obvious candidate as it is defined on [0,1] and, by varying its two parameters, a wide range of cases can be explored. In particular, we can explore the implications of non-symmetric distributions of ability. However, noting that the empirical evidence on ability distribution suggests broad symmetry, we shall restrict our attention to the symmetric case in this paper. Thus we have chosen a distribution that is symmetric about 0.5 and set  EMBED Equation.DSMT4 . For our stigma effect we let d = 0.7 and e = 0.3. In the theoretical section, we did not specify a specific functional form for the utility from public goods. Since we require this for numerical analysis, we need to do so now. We allow for diminishing marginal utility of the public good and let the sub-utility function be  EMBED Equation.DSMT4 , where 0 < r d" 1 is the elasticity of utility with respect to the level of public good consumption. In our base scenario we set r = 0.4. We are interested in how welfare and the optimal tax rate vary with b. We follow the approach of Atkinson and Stiglitz (1980) to this problem and define social welfare as 15.  EMBED Equation.DSMT4 , where  EMBED Equation.DSMT4 reflects the equilibrium choice made by someone of ability a facing the tax rate t. z is a parameter that allows us to control for inequality aversion: the Benthamite (strict utilitarian) case is z = 0 and the Rawlsian case is the limit as  EMBED Equation.DSMT4 . The latter is equivalent to maximising the utility of the unemployed. As we only wish to consider feasible public finance scenarios, we shall restrict our attention to rates in the interval [tmin, tmax] where these are the bounds set by the budget requirement that tax revenue (14) equals (non-negative) expenditure on the public good and benefits, and the bounds depend on the choice of all the other parameters in the simulations. Although our numerical model lets us vary the degree of inequality aversion in a continuous fashion, because we are interested in exploring relativity in this paper, we shall simply focus on the two polar cases of a Utilitarian and a Rawlsian social welfare function. As a preliminary, we note that in this model government revenue initially rises with the tax rate, and subsequently declines in a standard Laffer curve. In addition, the supply of the public good initially increases with the tax rate, which raises the welfare of all, but as taxes rise further, increasing expenditure on benefits for the growing number of unemployed reduces the residual revenue available for public goods. Tax Revenue and Benefit Expenditure as a function of the tax rate is illustrated in Figure 1.  Figure 1: The Laffer Curve, Benefit Expenditure and the Tax Rate The two panels of Figure 2 show how social welfare varies with the tax rate and the benefit level.   Figure 2: Social Welfare and the Tax and Benefit Rates While one cannot compare the welfare levels between the Rawlsian and Utilitarian cases, these results have three implications. The first is that, given the level of benefits being paid, a Rawlsian government prefers a much higher tax rate than a Utilitarian government. However, around the optima, welfare is flat, and insensitive to the precise choice. The second is that, for a given tax rate, the Utilitarian optimal benefit is much lower than the Rawlsian, as we further illustrate below. Finally and rather surprisingly, Utilitarian welfare is essentially flat over most of the benefit range, so very insensitive to the actual choice. This means that much greater benefits could be given to the unemployed, starting from a Utilitarian optimal level of tax and benefits, with hardly any reduction in the Utilitarian welfare. In other words, the cost of much less inequality would be tiny, even in terms of the least egalitarian objective. Notice also that this result does not depend on any particular value of the concern for relativity. The above case show the (partial) optimal tax and benefit results for the benchmark version of the model and so allow us to identify how optimal public finance depends on attitudes to inequality in a model in which relativity matters. However, we are equally interested to know how the (jointly) optimal tax and benefit rates vary, given the attitude to inequality, as the importance of relativity varies. To do this we allow the  parameter to vary between 0 and 1 and calculate optimal tax and benefits for the Utilitarian and Rawlsian versions of our model. The results are shown in Figure 3.  Figure 3: Optimal Tax and Benefit Rates Both cases show the same expected rising optimal tax with concern for relativity, in order to reduce the negative externality which household earnings impose on others in the same skill class. In the standard case with no (or little) concern for relativity, the optimal Utilitarian tax is much lower than the Rawlsian. Also not surprisingly, the benefit level is always very much lower under Utilitarian government. Less obviously, it declines to essentially zero for high concern with relativity, meaning starvation for the disabled who cannot supply much labour. By contrast, Rawlsian benefits remain almost flat for most of the range, though declining slightly before rising very steeply for the highest levels of concern, a non-monotonic behaviour that is hard to explain intuitively. Perhaps the most interesting finding, however, is that for high  the two tax rates converge, to almost equality. Even for  in the range [0.7, 0.8] which is consistent with some empirical evidence reviewed above, the optimal taxes are almost identical at 50%  60%. Thus, remarkably, optimality does not depend on the redistributive (or otherwise) objectives of government, which could have important political economy consequences. Another comparison we can make is to look at how the employment rate varies with the concern for relativity. This is shown in Figure 4  Figure 4: Employment Rates Here the Utilitarian objective attains essentially full employment, at the cost of very low benefits for the disabled, and very low earnings for the least able workers, irrespective of the concern for relativity. This result is of course at least partly an artefact of our assumption of frictionless labour markets. More surprising is the almost full employment (in terms of modern labour markets) attained under Rawlsian policy with high concern for relativity, in spite of much higher benefits and taxes. This contradicts much conventional economic wisdom, and might be very roughly compared with the success of the Nordic economies in combining redistribution and low inequality with high employment.  Figure 5- Public Good Expenditure Finally, we can see how expenditure on the public good varies as b varies. As one would expect, given the universal nature of the benefits from a public good, provision increases as with the concern about relative position. However, it is worth pointing out that there is very little difference throughout the range, and, as b approaches 1, the two levels converge. 4. Conclusions We have combined a simple model of utility or SWB depending on relative consumption with a continuum of ability types in a simple general equilibrium model. We include voluntary unemployment with a categorical benefit that is lost when any labour is supplied at least a rough approximation to most existing systems that impose high marginal tax rates on low earners as unemployment benefits are lost. While standard models of labour supply assume that unemployment increases utility at constant income due to the always positive marginal utility of leisure, much recent research shows unemployment to be a major cause of unhappiness, comparable to divorce or close bereavement. Thus we incorporate the welfare loss or stigma of unemployment in the model and simulations, which can override the marginal utility of leisure, depending on parameter values. In general equilibrium, effort increases with individual ability and wages, as universally observed in modern advanced economies. Taxes in equilibrium affect the participation decision, while the effect on welfare or labour supply of the employed declines as the weight on relative income in utility increases. Government revenue initially rises with the tax rate, and subsequently declines in a standard Laffer curve. The supply of the public good initially increases with the tax rate, which raises the welfare of all, but as taxes rise further, increasing expenditure on benefits for the growing number of unemployed reduces residual revenue for public goods. Since further comparative static results of parameter variation are difficult to derive analytically, we have explored some of the most salient with numerical simulations using the convenient beta distribution of ability. Budget feasibility or non negative expenditure on benefits and public goods, imposes restrictions on parameters, which are also chosen to yield reasonable tax and unemployment rates. Some of our results are intuitively plausible, such as generally higher optimal taxes and benefits under Rawlsian welfare than in the Utilitarian case, and an optimal tax that increases with concern for relativity in both cases. However, Utilitarian welfare turns out to be very insensitive to tax or benefit levels in their lower respective ranges. The Utilitarian objective attains almost full employment at the price of very low benefits and earnings for the lower tail of the ability distribution. When there is little concern for relativity, we also have the expected result of high unemployment, benefits and taxes under Rawlsian government. However, as concern rises we find that employment and the optimal tax also increase, while the optimal benefit level hardly changes. Only at the highest degree of concern for relativity do we observe a steep rise in benefits, while full employment is almost attained. With these individual preferences for relativity, then, we have best of both worlds, reminiscent, perhaps, of the Nordic economies. Rawlsian taxation alleviates poverty, giving much greater well being to the lowest abilities than under Utilitarian low- tax policy, but with relatively little unemployment. All this, it must be emphasized, has been achieved while including the empirically well-founded, stigma or negative effect of unemployment on subjective well-being which is usually neglected in theoretical models of labour markets. 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(2006) Well Being, Social Capital and Public Policy: Whats New? The Economic Journal,116, C34 C46 Helliwell, J. and Huang (2005) Hows the Job? Well Being and Social Capital in the Workplace. Working Paper 11759, NBER, November 2005 Helliwell, J. and Putnam, R. (2004) The Social Context of Well Being, Phil Trans R. Soc Lon. B, vol.359, pp.1435 46. Hirsch, F. (1976), The Social Limits to Growth (Cambridge, Mass.: Harvard University Press). Hopkins, E and Kornienko, T. (2004), Running to Keep in the Same Place: Consumer Choice as a Game of Status, American Economic Review, Vol. 94, September 2004, 1085-1107. Lane, R. E. (2001), TheLoss of Happiness in Market Economies. New Haven: Yale University Press Layard, R. (2005), Happiness: Lessons from a New Science (London: Allen Lane)  7Gz    - . 5 = U W _    G Q ^ r Ŀ h#\ hwY\ h;\ h \ hwYhwY hwYh' h'\ h 3\ hs\ h'5 h'\aJ h'5aJ h'5CJaJh 35CJaJh 5CJaJh5CJaJh5CJaJ8Gyz{|}~   $ 9r  a$$  a$$a$W     BCTUkl!!$dh 9r    $ . 0 ? 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Ljungquvist, L. and Uhlig, H. Tax Policy and Aggregate Demand Management Under Catching up with the Joneses. American Economic Review, June 2002, 90(3), pp. 356 366. Luttmer, R.F.P. (2005), Neighbors as Negatives: Relative Earnings and Well-Being, Quarterly Journal of Economics, Vol. xxx, August 2005, 963-1002. Moffitt, R. (1983), An Economic Model of Welfare Stigma, American Economic Review, Vol. 73, No. 5, 1023-35. Offer, A. (2006), The Challenge of Affluence, (Oxford, Oxford University Press). Stutzer, A. (2004) The Role of Income Aspirations in Individual Happiness. Journal of Economic Behavior and Organization 54(1), 2004, pp. 89-109. Veblen, T. (1899), The Theory of the Leisure Class (New York: Macmillan).  There is a literature that focuses on the social rank-ordering of conspicuous consumption of positional goods as a measure of status (Hirsch, 1976; Frank, 1985; Cooper et al, 2001; Hopkins and Kornienko, 2004).  Clearly, those with zero ability cannot supply labour, but we could introduce a positive lower bound on ability without fundamentally changing the results.  For tractability, we make the extreme assumption here that all benefits are withdrawn for any level of labour supply, but there are no constraints on the choice between receiving the given benefit (without working), or supplying individually optimal effort and income. In practice, most welfare systems do subject low skill workers to very high marginal rates of taxation as benefits are withdrawn after some minimal threshold. However, work related benefits for low wage workers have become common in the UK, US and other countries.  For example, R. Moffitt (1983) used scale and level effects to explain US data on low-income individuals entitled to benefit. A model incorporating these effects found them significant factors in explaining non-take-up. Stigma has also been amply demonstrated in the sociological literature on interviews with social welfare recipients. Layard (2005, 2006) summarises this and more recent research showing unemployment to be a major cause of unhappiness, comparable to divorce or bereavement.  It is a two-parameter distribution with the density given by  EMBED Equation.DSMT4 , usually denoted as  EMBED Equation.DSMT4 . Its mean is  EMBED Equation.DSMT4 , and its variance is  EMBED Equation.DSMT4 .  Thus B(1,1) is the uniform distribution. By varying the two parameters one can change the peakedness and the skewness of the distribution.  Setting e at 0.3 ensures that a range of the lowest ability people will not choose employment. Of course, people of zero ability cannot supply labour . It may help to think of these as disabled.  The relevant functions are given by equations 2 and 9.  A full set of tables showing the simulation results is available on request from the authors.     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