(i)(ii)Increases in the wage rate and in unearned income raise the value of peerconsumption which induces additional work effort;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 thatc∂fnc n n∂f ∂f ∂f= − e. = ∂ω> 0(17)∂ω ∂ω ∂σ∂f1−ω∂ 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:⎡ uθ⎤uω ⎢1 . c ⎥l+ ≤ , e ≥0. (18)⎢ 2(1 −θ) uc ⎥ uc⎣⎦So, when labour supply is positive, then, in the traditional case where happiness does notθ = 0 the marginal rate of substitution between leisure andaffect well-being ( )consumption 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 a( )factor 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 work 7 .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:wherevnθ⎛1⎞ −θ= ⎜ ⎟ ⎡ ⎤2 ⎣%⎦(19)⎝ ⎠n( ωσθ , , ) v ( ωσθ , , ) 17 Indeed it follows from (15) and (18) that in the extreme case where 1θ = thennnω ( σ,1) = 0 and f ω, σ,1 ≡ 1, so everybody spends their entire time in work.( )5

( ωσθ , , ) ≡ ⎡σ+ ω ( ωσθ , , ),1 − ( ωσθ , , )% n n n(20)v u⎣f fis 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 andn n nn∂v% ∂v% ∂v%v u uc( ωσθ , , ) = ( σ,1) ⇒ = = 0; = ( σ,1)%∂ω ∂θ ∂σ(21)so Roy’s identity holds:nn∂v∂v= e.∂ω∂σ(22)nIf ω ω ( σ,θ)we get:> labour supply is positive, then, by differentiating (20) and using (18)nn u∂v%⎡∂f θ⎤= u ⎢ce−ω.c ⎥; ∂ω ⎢ ∂ω 2(1 −θ)uc⎥⎣⎦(23)nn u∂v%⎡∂f θ⎤= u ⎢c1 −ω. c ⎥; ∂σ ⎢ ∂σ 2(1 −θ) uc⎥⎣⎦(24)In the traditional case where individuals place no weight on happiness ( 0)⎦⎤θ = 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.Proposition 1 If θ > 0 well-being is a strictly decreasing function of the wage rate forω≈ω σ, θ ⇒e≈0i.e. for some of those who are beingthose individuals for whom ( )induced 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 fromn nc∂f∂fthe Slutsky-Hicks equation, (17), ≈ > 0so 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 wellbeingare no longer those with the lowest level of ability.6

4. ExampleIf the well-offness function is Cobb-Douglas,straightforward to check that1uc (,) c α −l = l α , 0< α < 1. It isn⎧0, ω ≤ ω ( σ, θ)⎪⎛ θ ⎞n (1 − ασ ) n ⎪ α + ω−(1 −α)σω ( σ, θ)= ; f ( ω, σ, θ) =⎨ ⎜2(1 −θ) ⎟nand ⎛ θ ⎞⎝ ⎠, ω ω ( σ, θ)α⎪≥⎜ + θ2(1 θ )⎟ ⎛ ⎞⎝ − ⎠ ⎪ 1+ω⎪⎜ 2(1 −θ)⎟αn⎧σ , ⎩ ⎝ ⎠ω ≤ ω ( σ, θ)⎪α⎪⎛ θ ⎞1−αn ⎪v% ( ωσθ , , ) =α + (1 −α)⎨⎜2(1 −θ)⎟(25)⎝ ⎠−(1 −α)n⎪.( ω+ σ). ω , ω ≥ω ( σ,θ)⎪ ⎛ θ ⎞1+⎪ ⎜ 2(1 −θ)⎟⎩ ⎝ ⎠n∂v%From (29) it follows that > 0∂σnand that, for ω > ω ( σ,θ)n∂v%n∂ ω ⎡ (1 −ασ) ⎤ ∂v%= α − ⇒ < 0 ∀ ω, ω σ, θ < ω < ω σ,0n∂v%⎢⎣ 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.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.7

AppendixFigure 1v%n%v( ωσ , ,0)ασn%v( ωσθ , , )0ωσθ ( , )ωσ,0 ( )ω8

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