Keeping Up With The Joneses: Who Loses Out?
S c h o o l o f E c o n o m i c s & Fi n a n c e D i s c u s s i o n Pa p e r sSchool of Economics & FinanceOnline Discussion Paper Seriesissn nfo: econ@st-andrews.ac.ukKeeping Up with the Joneses: WhoLoses Out?David UlphSchool of Economics and Finance Discussion Paper No. 141220 Sep 2014JEL Classification: D110; I31; J22Keywords: Veblen Effects; consumer behaviour; Nash equilibrium; wages and well- being
Keeping Up with the Joneses: Who Loses Out?David Ulph1AbstractThis paper investigates how well-being varies with individual wage rates whenindividuals care about relative consumption and so there are Veblen effects – Keeping upwith the Joneses – leading individuals to over-work. In the case where individualscompare themselves with their peers – those with the same wage-rate - it is shown thatKeeping up with the Joneses leads some individuals to work who otherwise would havechosen not to. Moreover for these individuals well-being is a decreasing function of thewage rate - contrary to standard theory. So those who are worst-off in society are nolonger those on the lowest wage.Keywords: Veblen Effects; consumer behaviour; Nash equilibrium; wages and wellbeingJEL Codes: D110; I31; J22October 20141Professor of Economics, University of St Andrews and Director, Scottish Institute for Research inEconomics (SIRE). School of Economic & Finance, University of St Andrews, St Andrews KY16 9AL,Scotland.E-mail du1@st-andrews.ac.uk. Tel: 44 (0) 1334 462440
Keeping Up with the Joneses: Who Loses?IntroductionDating back to Veblen (1924), there is an extensive literature on conspicuousconsumption whereby individuals lose esteem if their consumption of some good(s)which signal their status is below the average of the reference/peer group and gain esteemif their consumption exceeds the average. It is recognised that this can lead to a ‘rat race”in which individuals over-consume, with a consequent need to fund this extraconsumption by either working harder or saving less ( Frank (1985), Schor (1998)). Thisover-consumption is referred to as the Veblen Effect2 or the Keeping up with the JonesesEffect3.This paper develops some further implications for behaviour and well-being when peopleare concerned about their consumption relative to their peers – taken to be those with asimilar wage rate4. It is shown that the Keeping up with the Joneses Effect can leadpeople to work who would otherwise have chosen not to, and that, for such individualswell-being will be a strictly decreasing function of their wage rate. Thus those who areleast well off in society are not those with the lowest wage.1.The ModelIndividuals are endowed solely with 1 unit of time that can be spent on work or leisure.There is a tax/benefit system whereby everyone receives a tax-free universal benefit,σ 0 and all earned income is taxed at the rate τ , 0 τ 1 . Individuals differ in theirproductivity which is reflected in their net wage rate ω 0 . An individual with net wageω who spends a fraction l , 0 l 1 of time on leisure will end up with consumptionc ω (1 l ) σ .Individual well-being is a combination of well-offness, y, and happiness, h, as given bythe function:(1)w hθ y1 θ , 0 θ 1.Here:(i) Well-offness, y, is captured by a utility function(2)y u ( c, l )satisfying the standard assumptions – e.g. concavity.(ii) Happiness measures individuals’ perceptions of how well their life is going incomparison to their peers – those with the same net wage-rate, ω. It is assumed2The Veblen effect has also been invoked to help explain the Easterlin Paradox - Easterlin (2001).This has led to arguments for either taxing such conspicuous consumption or increasing the rate of income tax – seeBoskin and Sheshinski (1978) - to correct the consumption externality.4Beath and Fitzroy (2009) also consider a model in which individuals compare their consumption to that of others withthe same productivity/wage-rate. They also show that Keeping up with the Joneses can lead individuals to over-work.However their model and analysis differs in other respects from that considered here, and they do not obtain the crucialresult set out in Proposition 1 below.31
that this depends on an individual’s consumption relative to the averageconsumption c 0 of their peers, and that happiness is given by:cc c(3)c c1 ccThe two reasons for adopting this functional form for happiness are:a) Happiness is thereby bounded between 0 and 1, reflecting the way happinessis traditionally measured on some finite scale.b) Labour supply decisions depend on the average consumption of others. If,instead, happiness depends solely on c then, given (1) , the averagecconsumption of others would exert a negative externality on individual wellbeing but would not affect behaviour – thereby missing a crucial feature of theKeeping up with the Joneses effect5.h The parameter θ determines how much individual well-being depends on relativeconsumption6. So if θ 0 we have the conventional economists’ story about wellbeing, and there will be no Keeping up with the Joneses Effect. If 0 θ 1 then theKeeping up with the Joneses Effect is present, and is increasing in θ. Combining (1) – (3)well-being can be written as:θ1 θ c w c, l , c;θ u ( c, l ) , c c (2.)(4)Individual Labour Supply and Well-BeingConsider an individual with net wage rate ω. The individual takes as givenc 0 - the average consumption of those with the same net wage rate - and chooseslabour supply (effort) e 1 l to maximise well-being,θ1 θ σ ωe w σ ω e,1 e, c,θ u (σ ω e,1 e ) σ ωe c ()(5)Let()(e f ω, σ , c;θ arg max w σ ωe,1 e, c;θ0 e 1)(6)be the well-being-maximising labour supply decision, and()(v ω, σ , c;θ MAX w σ ωe,1 e, c;θ0 e 1)the associated indirect well-being function.The f.o.c. for maximisation is56This is true of the formulation adopted by Boskin and Sheshinski (1978).This formulation is consistent with that adopted by Boskin and Sheshinski (1978).2(7)
θ1 θ1 1 [ωuc ul ] 0, e 0 ,u σ ωe σ ωe c ω (8)where the inequalities hold with complementary slackness. From (8) there is areservation net wage rateul (σ ,1)(9)ω σ , c, θ c u (σ ,1)θ.uc (σ ,1) 1 θ σ cσat or below which labour supply is zero and above which it is positive. This reservationwage rate is: a strictly increasing function of unearned income, σ; a strictly decreasing function of average consumption, c ; a strictly decreasing function of the weight, θ, given to happiness.()When θ 0 , the reservation wage is just the conventional marginal rate of substitutionbetween consumption and leisure at zero hours of work. The fact that it is decreasing inboth c and θ means that the Keeping up with the Joneses Effect is inducing people towork who would not otherwise have done so.Since, conditioning on c and θ , the labour supply decision is a conventional utilitymaximising decision, it follows that, when individual labour supply is positive, it is astrictly decreasing function of unearned income, while the effect of an increase in the(net) wage rate is ambiguous, though the compensated labour supply response is positive.From (8) it follows that when labour-supply is positive it is a strictly increasing functionof c - the Keeping up with the Joneses Effect – and, consistent with this, is also anincreasing function of θ . In summary we have the following comparative static laboursupply predictions in the case where labour supply is positive: i.e. ω ω σ , c, θ( f f f c f f f f 0; e. 0; 0; 0 7.0; σ ω ω ω σ θ c)(10)Turning to the indirect well-being function, this again will satisfy the standard conditions,including Roy’s identity, so: v v v v 0; e. f ω , σ , c,θ . 0, σ ω σ σ()(11)So, conditioning on average consumption, c , for individuals who work, well-being is astrictly increasing function of the net wage rate. From (5) and (7) the envelope theoremimplies that7The superscript c denotes the compensated labour supply function.3
v 0 . cThus individuals are worse off the greater is the average consumption of others.3.(12)Nash Equilibrium Labour Supply and Well-beingSo far we have examined labour supply and well-being for any arbitrary level of averageconsumption of the peer group - those with the same net wage rate. To complete theanalysis we need to determine this average level of consumption. Since everyonemaximises well-being taking as given the decisions of everyone else as reflected in theaverage consumption of the group, the relevant equilibrium concept is non-cooperativeNash. Since everyone in the comparator group is identical, in the Nash equilibriumeveryone ends up with the same level of labour supply and consumption. This commonconsumption is therefore the average consumption of each group, which implies that foreveryone h 1/ 23.1 Labour SupplyFrom (6) the Nash equilibrium level of labour supply can be characterised as the implicitsolution to the equation:e f (ω, σ , σ ωe,θ ).(13)To ensure that there is a unique well-defined Nash equilibrium assume that: f 1. cDenote the Nash equilibrium labour supply function by f n (ω, σ ;θ ) . ω ω(14)Note that it follows from (8) that the reservation wage is now given by:ω n (σ ,θ ) ul (σ ,1)uc (σ ,1) θ2(1 θ ).u (σ ,1),(15)σwhich is a strictly increasing function of σ and a strictly decreasing function of θ withω n 0 as θ 1 . The fact that the reservation wage falls with θ is a manifestation ofthe Keeping up with the Joneses Effect since individuals are being induced to work whootherwise have chosen not to.From (13) it follows that, when Nash labour supply is positive:4
f f f f e. n f f ωσc c ,; f fσ ω 1 ω.1 ω. c cn(16)so Nash labour supply responses to increases in the wage rate and unearned income differfrom the individual labour supply response in two ways:(i)Increases in the wage rate and in unearned income raise the value of peerconsumption which induces additional work effort;(ii)There is a multiplier effect at work whereby changes in labour supply inducechanges in peer consumption which generates further changes in laboursupply.The sign of both of these terms is indeterminate. However, from (16) it follows that f cncnn f f f(17) e. ω 0 ω ω σ 1 ω f cso the Slutsky-Hicks decomposition still applies to the Nash labour supply function, andthe compensated Nash labour supply response is positive and is just the individualcompensated response scaled up by the multiplier effect.Now, from (8), the Nash labour supply can be characterised through the condition:u uθ (18)ω 1 . c l , e 0. 2(1 θ ) uc uc So, when labour supply is positive, then, in the traditional case where happiness does notaffect well-being (θ 0) the marginal rate of substitution between leisure andconsumption equals the (net) wage. However when happiness does affect well-being,(θ 0) , the marginal rate of substitution is greater than the wage rate multiplied by afactor that (a) depends on the ratio of average to marginal utility of consumption, and (b)is increasing in the weight individuals place on happiness. This additional term capturesthe distortion in Nash equilibrium labour supply induced by the Keeping up with theJoneses Effect. It is this distortion that leads individuals to supply too much labour sinceit increases the attractiveness of work8.8Indeed it follows from (15) and (18) that in the extreme case wherenω (σ ,1) 0 and fnθ 1 then(ω, σ ,1) 1, so everybody spends their entire time in work.5
3.2.Well-beingBy substituting the Nash equilibrium level of effort back into the well-being functiongiven in (4) we obtain the Nash indirect well-being function:θ1 θ 1 v (ω , σ , θ ) v%n (ω , σ , θ ) 2 (19)nv%(ω,σ ,θ ) u σ ω f n (ω,σ ,θ ) ,1 f n (ω,σ ,θ ) (20)nwhereis the Nash indirect well-offness function. To understand what happens to well-being allwe need to understand is what happens to well-offness.nIf ω ω (σ ,θ ) labour supply is zero andnv%(ω,σ ,θ ) u (σ ,1) nn v% v% v%n 0; uc (σ ,1) ω θ σ(21)so Roy’s identity holds:nn v% v%. e. ω σ(22)nIf ω ω (σ ,θ ) labour supply is positive, then, by differentiating (20) and using (18)we get:u n v% f n θc ; (23) uc e ω. ω ω 2(1 θ ) uc u n v% f nθc ; (24). uc 1 ω σ σ 2(1 θ ) uc In the traditional case where individuals place no weight on happiness (θ 0) then (24)and (23) just reduce to their conventional forms. In particular Roy’s identity (22) holds.However if θ 0 a marginal change in the wage or benefit induces an additional effecton well-being that is positive (resp. negative) if the change causes labour supply to fall(resp. rise) and so reduce (resp. increase) the distortion on labour supply.In certain circumstances an increase in the wage rate could actually make people worseoff as the distortion-intensifying effect dominates the direct benefit from a higher netwage.6
Proposition 1 If θ 0 well-being is a strictly decreasing function of the wage rate forthose individuals for whom ω ω (σ ,θ ) e 0 i.e. for some of those who are beinginduced to work only because of their desire to Keep up with the Joneses.Proof: If e 0 the first term on the RHS of (23) is approximately zero. Moreover from f n f ncthe Slutsky-Hicks equation, (17), 0 so the only effect of the higher wage is ω ωto intensify the distortion and so make people worse off.Corollary 1.1 The individuals with the lowest level of well-offness and hence wellbeing are no longer those with the lowest level of ability.4.ExampleIf the well-offness function is Cobb-Douglas, u (c, l ) cα l 1 α , 0 α 1. It isstraightforward to check thatω n (σ ,θ ) (1 α )σ 0,ω ω n (σ ,θ ) θ ω (1 α )σ α nf (ω , σ ,θ ) 2(1 θ ) ,ω ω n (σ ,θ ) θ 1 ω 2(1 θ ) ω ω n (σ ,θ ) ; θ α 2(1 θ ) σ α , α θ 1 α v%n (ω , σ , θ ) α 2(1 θ ) (1 α ).(ω σ ).ω (1 α ) , θ 1 2(1 θ ) andFrom (29) it follows thatω ω n (σ ,θ )(25) v%nn 0 and that, for ω ω (σ ,θ ) σ v%nn ω α (1 α )σ v% 0 ω , ω (σ ,θ ) ω ω (σ , 0 ) v%n ω ω σ(26)Thus well-offness and hence well-being are strictly decreasing in the wage rate forprecisely the group of individuals that are being induced to work purely because of thekeeping up with the Joneses effect.7
This is illustrated in Figure 1 in the Appendix.5.ConclusionWhen we situate consumers in a social context and their consumption may depend on thatof others, then many of the standard predictions of the conventional theory of consumerbehaviour may be overturned. Most strikingly those who are worst off in society are nolonger those on the lowest wage. The worst off will be people with a sufficiently highwage that they are induced into work because of the Keeping up with the Joneses Effect.This has implications for the understanding of poverty and inequality and the design oftax/benefit systems that warrant further investigation.8
AppendixFigure 1: Well-Offness and Wagesv%nv%(ω,σ ,0)σαnv%(ω,σ ,θ )0ω (σ ,θ )ω (σ ,0 )9ω
ReferencesBeath, J.A., FitzRoy, F.R. (2009). “Public economics of relative income and subjectivewell-being”, paper presented at the SIRE-Cornell Conference on Relativity, Inequality andPublic Policy, Edinburgh, 2009.Boskin, M., Sheshinski, E., 1978. Optimal Redistributive Taxation when IndividualWelfare Depends upon Relative Income. Quarterly Journal of Economics. 92, 589-602.Easterlin, R., 2001. “Income and Happiness: Toward a Unified Theory”, The EconomicJournal, 111, 465-484Frank, R., 1985. Choosing the Right Pond: Human Behavior and the Quest for Status.Oxford University Press, New York.Schor, J., 1998. The Overspent American. Basic Books, New York.Veblen, T., 1924. The Theory of the Leisure Class: An Economic Study of Institutions.George, Allen and Unwin, London10
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