Consumption theory with reference dependent utility

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  • The Journal of Socio-Economics 38 (2009) 415420

    Contents lists available at ScienceDirect

    The Journal of Socio-Economics

    journa l homepage: www.e lsev ier .com/ locate /soceco

    Consum t u

    Fredrik WGteborg Unive

    a r t i c l

    Article history:Received 3 ApReceived in revAccepted 7 Feb

    JEL classicatioD91E21

    Keywords:ConsumptionConsumptionHabit-formatioMarginal prop

    sumpumptan alt. Thistiona

    1. Introduc

    Empirical evidence suggests that individuals evaluate own con-sumption (levels of othStenman etThis paperextended vmodel. In Atheir owntion that inamong reletion for analso dependuce the inMPC). Earl(PIH) (Hall,as Alessie aconsume th

    Is it reaconsumptioical perspethe consum48) arguesconsumptio

    Tel.: +46E-mail add

    ns thnotion has long been overlooked in economicsmodels, although hehas advocators within psychology. For example, Runciman (1966)

    1053-5357/$ doi:10.1016/j.sincome) by comparing it to the consumption (income)ers; see e.g. Solnick and Hemenway (1998), Johansson-al. (2002), Alpizar et al. (2005), and Andersson (2008).presents a general consumption model that is anersion of Alessie and Lusardis (1997) consumptionlessie and Lusardi (1997), individuals merely care aboutcurrent and previous consumption. I add the assump-dividuals also compare own consumptionwith that seenvant others, andderive a closed formconsumption func-arbitrary individual. Since an individuals consumptionds on the consumption by his relevant others, I intro-dividuals total marginal propensity to consume (totalier theories like Halls permanent income hypothesis1978), and a pure habit formation behavior model, suchnd Lusardi (1997), imply larger marginal propensities toan found in this model.listic that individuals only have their own previousn levels as reference? Probably not. From a psycholog-

    ctive, individuals compare own consumption also withption levels of relevant others. Duesenberry (1949, p.that Any particular consumer will be inuenced byn of people with whom he has social contacts. . .;

    31 773 2679.ress: fredrik.andersson@economics.gu.se.

    argues that individuals have both a space and time dimension ofcomparison. Frank (1985, p. 146) presents an explanation to whyeconomists are not keen on adopting the space dimension: Tomany economists, the notion of consumers being strongly inu-enced by demonstration effects must have seemed troublinglyinconsistent with the reasoned pursuit of self-interest, if not com-pletely irrational. It seems reasonable to extend Alessie andLusardis (1997) model by including Duesenberrys demonstrationeffect. For example Frank (1985, p. 150) supports this by arguing:. . . concerns about relative standing are perfectly compatible withthe economists view that people pursue their own interest in arational way. I believe this extended consumption model addsmore knowledge about individuals actual consumption decision.1

    This paper has the following structure: Section 2 describes anindividuals utility maximization problem. In Section 3, I derivethe individuals closed form consumption function in addition toa recursive consumption function. Section 4 discusses the deni-tion of the individuals MPC given different notions of what theindividual utility depends on, and nally, Section 5, presents someconcluding remarks.

    1 I use an additive comparison function since Wendner (2002, p. 16) argues thatthe multiplicative [i.e., ratio] specication is not in line with elementary propertiesof habit persistence. Ratio comparisons are used by, e.g. Abel (1990), Carroll et al.(1997), Carroll (2000), and Aronsson and Johansson-Stenman (2008).

    see front matter 2009 Elsevier Inc. All rights reserved.ocec.2009.02.006ption theory with reference dependen

    . Andersson

    rsity, Department of Economics, Vasagatan 1, P.O. Box 640, 405 30 Gteborg, Sweden

    e i n f o

    ril 2007ised form 13 December 2008ruary 2009

    n:

    decisionby relevant othersn behaviorensity to consume

    a b s t r a c t

    This paper presents a closed form conon his own current and previous consmodel, I argue that we can introducein addition to the traditional denitionwhich I show is smaller than the tradi

    tion he coitility

    tion function for an individual when his utility depends bothion and on the consumption by his relevant others. Given thisernative denition of marginal propensity to consume (MPC)alternative denition can be called the individuals total MPC,l MPC.

    2009 Elsevier Inc. All rights reserved.

    is concept the demonstration effect. Duesenberrys

  • 416 F.W. Andersson / The Journal of Socio-Economics 38 (2009) 415420

    2. The individuals utility

    2.1. The individuals utility function arguments

    In order to emphasize how important individuals social inter-actions with each other are, Aristotle referred to human beings associal animals. By lookingatpsychological and sociologicalmotives,e.g. Duesenberry (1949), Runciman (1966), Frank (1985), and Elsterand Loewenstein (1992) argue that individuals have both a spaceand a time down currention of botprevious comentioneduals utilitythat peoplelevel, sinceLusardis (1consumptiosumption aindividual,

    c = c c

    where [0consumptiomore the inhow muchtion, and behavior. This previoudown to th = 0, and wused by, e.g

    2.2. The ind

    By assumuous, and tcset, andmc , to alway

    In orderhe needs tothe presentand the currindividualhany debt, aindividualsin additionthat the indincome andthe informa

    Then thebe specied

    max{c }T=tU

    2 Relevant o3 This is sim

    use in apaper tothers is a souwhich is the p

    4 The intere

    subject to his intertemporal budget constraint

    T=t

    (1

    1 + r)

    c +(

    11 + r

    )T+1aT+1 = a +

    T( 11 + r

    )y, (3)

    and(1

    1 + r)T+1a adebe inptimencere b

    t

    (1

    theget cptio

    t disthermis nouslindihereut anot diindbymbudgm is:

    }T=tL

    (a

    isr an

    t

    his e1:

    = t

    = 0.

    olvinbini

    +1)/u(ct

    + + r .

    his pitiveindivimension of comparison. I.e., individuals compare theirt consumption with a reference level that is a func-h the consumption by relevant others and their ownnsumption. Compared to the two consumption modelsin Section 1 this adds more realism to what individ-depends on. Put differently, Scitovsky (1992) argueswish to keep their status in relation to their referencelosing status may be painful. Here I extend Alessie and997) model by assuming that people also care about thenamong relevantothers. Then, the psychological con-mount that utility depends on at time , for an arbitraryis:

    1 c, (1)

    ,1] controls how much the individual cares about then among his relevant others,2c .3 The higher the , thedividual cares. The other parameter, [0,1], controlsthe individual cares about his own previous consump-> 0 implies that the individual has a habit-formationhe higher the , the more the individual cares abouts consumption. The formulation in Eq. (1) will then boile one used by Alessie and Lusardi (1997) for > 0 andhen = = 0 it will reect the conventional model as

    . Hall (1978).

    ividuals utility maximization problem

    ption, the individuals utility, u(c), is concave, contin-wice differentiable over the interior of the individualsoreover I restrict the individuals consumption amount,s be non-negative.for the individual to optimize his consumption prole,predict at time his stock of human wealth, which isdiscounted value of his expected future labor incomeent value of his non-human wealth (a). I assume that theasanite life, givesnobequests atperiodT, dieswithoutnd lives in a world with a perfect capital market (i.e.,canborrowand lendat the sameconstant4 interest rate)he is not liquidity constrained. Furthermore, I assumeividual has perfect foresight about his own future laborthe future consumption among his relevant others; i.e.,tion is complete and there is no uncertainty.individuals intertemporal maximization problem canas

    =T

    =tu(c(c, c1, c)), (2)

    thers refers to, e.g. neighbors, co-workers, and friends.ilar to thepsychological consumption thatAlonso-Carrera et al. (2004)hat analyzes the circumstancesunderwhich consumptionby relevantrce of inefciency. They also included a third reference argument,

    revious consumption, ct1, of relevant others.st rate is independent of the capital stock in the economy.

    whereunpaidfrom this not odies, htherefo

    a +T

    =

    Whenral budconsumpresen

    Furothersexogen

    Thetime,wrules odoes n

    Thesolvedporalproble

    max{c

    +

    wheretion fo

    L()ct

    =

    Since tfor t +L()ct+1

    Then sby com

    (u(ct(

    = 11

    Up to tan addof the=t

    aT+1 0, (4)

    nd c1 are given. Since the individual cannot havets at period T, aT+1 cannot be less than zero. Moreover,dividual intertemporal utility maximization problem, ital for the individual to have unused resources when heaT+1 = 0 will always hold. Constraints (3) and (4) can

    e combined into:

    1+ r)

    y T

    =t

    (1

    1 + r)

    c = 0. (5)

    interest rate, r, is constant over time, the intertempo-onstraint implies that the present discounted value ofn is equal to the individuals initial wealth (a) plus hiscounted labor income (y).ore, I assume that the consumption among relevant

    ot affected by the individuals consumption; i.e., c isy given.viduals discount factor, = 1/(1 + ), is constant over > 0, and is the individuals pure timepreference. Thisy possibility of discontinuity of U (i.e., assures that Uverge to innity).ividuals intertemporal maximization problem is thenaximizing his lifetimeutility (2) subject to his intertem-et constraint (5). The Lagrangian function for this

    (c, c+1, . . . ;) =T

    =tu(c(c, c1, c))

    +T

    =t

    (1

    1 + r)

    y T

    =t

    (1

    1 + r)

    c

    ), (6)

    the constant Lagrange multiplier. The rst order condi-interior solution at an arbitrary period t is:

    u(ct )ct

    ctct

    + t+1u(ct+1)ct+1

    ct+1ct

    (

    11 + r

    )t= 0. (7)

    xpression holds for all t, it is obvious that it also holds

    +1 u(ct+1)

    ct+1

    ct+1ct+1

    + t+2u(ct+2)ct+2

    ct+2ct+1

    (

    11 + r

    )t+1(8)

    g for the individualsmarginal rate of substitution (MRS)ng (7) and (8), we have (after some manipulation):

    ct+1)(ct+1/ct+1)+(u(ct+2)/ct+2)(ct+2/ct+1)

    )/ct )(ct /ct) + (u(ct+1)/ct+1)(ct+1/ct)

    (9)

    oint, the individuals MRS is valid for both a ratio andcomparison function. Let us continue the derivationiduals MRS with the additive comparison function as

  • F.W. Andersson / The Journal of Socio-Economics 38 (2009) 415420 417

    in (1). Thus, Eq. (1) has the following properties for the additivecomparison function:

    ctct

    =ct+1ct+1

    = 1, (10)

    ct+1ct

    =ct+2ct+1

    = . (11)

    Assuming that the individuals pure value of time preference isequal to the interest rate ( = r), the individuals MRS (9) may berewritten with the additional properties in (10) and (11) as

    (u(ct+1)/(u(ct )/

    Eq. (12) is s

    u(ct )ct

    =u

    where ismarginal uover time ifcave utilitypsychologicconsumptio

    Lemma 1.tion {ct }Tt=0

    Hence,period t + 1increase insumption cderive the i

    ct+1 = where ctsumption cconsumptiohis relevantAlessie and = 0 and H

    3. The indi

    The Eulehere possibtions in the

    ct = (1 + g1

    I use the asstion changereceive a simA consumpequation. W

    5 My only inproblem.

    6 In order toviduals consuuse the inform

    7 This corredepends mereindividuals ut

    possible to derive his closed form consumption function. By plac-ing (15) in (5), it is possible to write the individuals rst periodconsumption as

    c0 =

    (1 + g)+

    at+ T

    t=0

    (1

    1 + r)t

    ytT2jt=2

    Tj=0

    jct

    ,(16)

    where

    = (1 + )(1 + r )r(1 + r)T , (17)+ g

    r((1

    ) togtiseint.rdermpts precon

    ulatio

    1+ r)

    Lemmn, wual:9

    (1 +1 + r

    (1(1 Eq.t timptio

    g-uptureptio

    esena haptio

    ion fu

    an eadinarys to Al

    know

    r)T )cnumbin thct+1) (u(ct+2)/ct+2)ct ) (u(ct+1)/ct+1)

    = 1. (12)

    atised if and only if:

    (ct+1)ct+1

    =u(ct+2)ct+2

    = , t, (13)

    a constant (see Appendix A for the proof), i.e., thetility of psychological consumption must be constantthe MRS between any two periods equals 1. Any con-function implies that when the marginal utility of

    al consumption is constant, the level of psychologicaln is also constant c = constant. (see Lemma 1).Eq. (13) implies that the path of psychological consump-

    is constant over time.

    if the consumption by relevant others increases in, the individuals consumption in period t + 1 must alsoorder to keep the marginal utility of psychological con-onstant. By utilizing this knowledge, it is possible tondividuals consumption change:

    ct + ct+1, (14)

    +1 = ct+1 ct . This shows that the individuals con-hange in period t + 1 depends on his own previousn change and the current consumption changes amongothers.5 This is a general Euler equation that boils downLusardis (1997) consumption model when > 0 andalls PIH (1978) when = = 0.

    viduals closed form consumption function

    r equation is a recursive consumption function,which isle to rewrite as a function of the individuals consump-rst period as follows:6

    ) gt c0 +

    T2j

    t=2

    Tj=0

    jct

    , t 2. (15)

    umption that c1 = (1 + g)c0 (the individuals consump-dwith rate g between period t = 0 and t = 1) in order tople expression for the consumption in therst period.7

    tion path derived from Eq. (15) will satisfy the Eulerhen I consider the individuals budget constraint it is

    terest here is the interior solution to the intertemporal maximization

    derive this equation I use the Euler equation. I rst dene the indi-mption in period t = 1. Then I lead the Euler equation one period andation from the consumption in period t = 1, and so forth.sponds to the case when the individuals utility in the rst periodly on past consumption. It is not until the second period that theility depends on the consumption by his relevant others.

    = (1 = gEq. (15that saconstra

    In oa consuvidualbudgetmanip

    T=t

    (1

    Usingfunctioindivid

    c =(

    +

    Fromlevel aconsumkeepinfear (fuconsumalso prual hasconsumsumpt

    8 We cto an orcollapse

    9 We

    1)/(r(1 +10 The

    included )(1 + r )r((1 + r)T 1), (18)+ r)T T ). (19)ether with Eq. (16) give a unique consumption paths both the Euler equation and the individuals budget

    to discuss one of the aims in this paper, I need to deriveion function for the individual that depends on the indi-vious consumption. Hence, I rewrite the intertemporalstraint (5) by substituting in c from (1), and after somen I solve for the present discounted value of c :8

    c = c1 T

    =t

    (1

    1 + r)

    c

    +[1

    1 + r](

    a +T

    =t

    (1

    1 + r)

    y

    ). (20)

    a 1, I can derive from (20) a recursive consumptionhich satises the individuals budget constraint, for the

    r)T 1)T+1 1

    c1 i

    + (1 + r)T 1

    (1 + r)T+1 1c

    ii

    r(1 + r)T+ r)T+1 1

    T=t+1

    (1

    1 + r)

    c

    iii

    1 + r)

    r(1 + r)T(1 + r)T+1 1

    [a +

    T=t

    (1

    1 + r)

    y

    ] iv

    . (21)

    (21) it follows that the individuals consumptione depends on four features: (i) a habit level ofnthe individuals own previous consumption, (ii) aeffect current consumption by relevant others, (iii) apotential disutility) of falling behind effect the futuren by relevant others, and (iv) the wealth effect, which ist in the PIH, although it is reduced when the individ-bit-formation behavior ( > 0).10 The general recursiven function in Eq. (21) boils down to two other con-nctions found in the literature: Halls (1978) PIH when

    sily verify that if = 0, the intertemporal budget constraint collapsestextbook intertemporal budget constraint, and hence, if = 0, it

    essie and Lusardis (1997) intertemporal budget constraint.

    that Lemma 1 impliesT

    =t(1/(1 + r))c = ((1 + r)T+1

    .er of lagged variables depends on how many lagged variables aree c measure.

  • 418 F.W. Andersson / The Journal of Socio-Economics 38 (2009) 415420

    = = 0, which shows that an individuals consumption at time is equal to the annuity value of his lifetime resources and is constantover time, and the one in Alessie and Lusardi (1997), when > 0and = 0. The individuals consumption at time then dependspartly on his previous consumption and partly on his permanentincome.

    3.1. The imp

    It is posindividualshis relevantis the annuiand h umanand whereis the annusumption. T

    c = c1

    where((1 + r)T+1 ((1 + r)T+1

    Wecan ssame effectcal consumbehavior; i.Thus, the inincome as

    c

    yp= 1

    1

    FromEq. (2about his prpermanent

    2c

    yp=

    When theincome, strosumption dThis smoothan individu

    3.2. The im

    How doedegree of cwith ?

    c

    = ci

    The individeffect stemsumption letherst termlevel adjustrelevant othtracks the cond effect a

    11 It would aothers as perm

    path of the relevant others as painfuli.e., it reduces the individ-uals utility. This is captured by the last term in (25), where we cansee how the individuals consumption is negatively affected by hisrelevant others future consumption. Hence, the higher the futurepermanent consumption among his relevant others, the more theindividuals consumption at time is reduced.

    temporary increase in the consumption by relevant otherssideat cra amt con

    >

    fectmaythan

    . in ewn fusinesum

    indies atsum

    A per

    len (tabliow wclaimhigpwaimilathatroupowneir rettere inc.e., aptio

    c

    cp+

    , the it con

    rgina

    review

    nes (. . .

    easeuchptio

    e risetiona

    effectthat hdiscouact of the individuals permanent income

    sible to rewrite Eq. (21) by using concepts such as thepermanent income and the permanent consumption byothers,11 where the individuals permanent income (yp)ty valueof the sumof the currentnon-humanwealth (a)wealth (present discounted value of future income),

    the permanent consumption by relevant others (cp+1)ity value of the present discounted value of future con-hus, the individuals consumption in period is:

    + c cp+1 +(1

    1 + r)

    yp, (22)

    = ((1 + r)T 1)/((1 + r)T+1 1), yp = r(1 + r)T/1)(a +

    T=t(1/(1 + r))

    y), and cp+1 = r(1 + r)

    T/

    1)T

    =t+1(1/(1 + r)) c .

    ee from (22) that a change in permanent incomehas theon the individuals consumption as if the psychologi-

    ption measure would merely include a habit formatione., the individuals utility depends on c = c c1.dividuals consumption changes with his permanent

    + r . (23)

    3)we can see that if the individual increases his concernevious consumption, i.e., his habits, then a change in hisincome changes his consumption to a lesser extent.

    11 + r < 0. (24)

    individual has a negative change in his permanentnger habits (higher) implies that the individuals con-ecreases by a smaller amount than with weaker habits.er reduction comes from the fact that it takes time for

    al to alter his consumption habits.

    pact of the consumption by relevant others

    s the consumption at time depend on a change in theoncern about the consumption by relevant others, i.e.,

    cp+1ii

    . (25)

    uals consumption is affected in two ways: (i) The rsts from the individuals wish to keep up with the con-vels of his relevant others at time ; this is captured byin (25). This implies that the individuals consumption

    s upward by a fraction of the current consumption byers, i.e., the individuals consumption to some degreeonsumption levels of his relevant others. (ii) The sec-rises if the individual perceives the future consumption

    lso be possible to rewrite the permanent consumption by relevantanent income if we assume a constant saving rate.

    3.2.1. ACon

    othersan extcurren

    cc

    =

    This efhencehigher

    . .groBCon

    Theincreashis con

    3.2.2.others

    Vebwho esple belp. 101)tion ofmake ulevel. Sarguesence gor herthan thwith b

    If thnent, iconsum

    cc

    +

    Hencemanen

    4. Ma

    4.1. A

    Keyical lawto incrby as mconsumincompropor

    12 Thisimpliespresentr a temporary increase in the consumption by relevanturrent time, . This may be for example a bonus, i.e.,ount of money. This increase boosts the individuals

    sumption, since he wishes to keep up with them:

    0. (26)

    may impact the individuals consumption growth, andprovide some insight into why consumption growsincome.

    ach of the past three years, real consumer outlays haveaster than real aftertax income.ss Week 17/4 2006 (U.S.: Its Way Too Early to Count

    ers Out)

    vidual knows that the consumption by relevant otherstime but not at time + 1. He will therefore increaseption at time to not lose status.

    manent increase in the consumption by relevant

    1934) states that it is the best-off members in a societysh the consumption standard for the rest, and then peo-ish to emulate their consumption. Duesenberry (1949,s that Low-income groups are affected by consump-

    h-income groups but not vice versa., i.e., individualsrd comparisons when they evaluate their consumptionr thoughts, i.e., are voiced by, e.g. Schor (1998, p. 4)whoindividuals make comparison with, or choose, a refer-, people whose income are three, four, or ve times his. She nds that individuals with lower nancial statuseference groups save signicantly less than individualsnancial status than their reference groups.rease in the consumption by relevant others is perma-lso cp+1 changes and not just ct , then the individualsn changes as

    1

    = = ( 1) < 0, since < 1. (27)

    ndividuals consumption is negatively affected by a per-sumption increase among relevant others.12

    l propensity to consume

    of marginal propensity to consume

    1936, p. 36) argues that The fundamental psycholog-is that men are disposed, as a rule and on the average,their consumption as their income increases, but notas the increases in their income. Hence, the Keynesiann function hypothesizes that if an individuals currents/falls by oneunit, thenhis consumption should rise/fallllywith theMPC,which is less than1. This is theabsolute

    is a result of the individuals intertemporal budget constraint, whichis present discounted value of consumption cannot be larger than thented value of his human and non-human wealth.

  • F.W. Andersson / The Journal of Socio-Economics 38 (2009) 415420 419

    income hypothesis. Another venue is Friedmans (1957) permanentincome hypothesis, where MPC is determined by the relative vari-ations in permanent and transitory incomes. When the variationin permanent income is much greater than the variation in transi-tory income, consumption rises almost one-for-one with currentincome. Intuitively, an individuals consumption increases whenhis permanent income increases. Hall (1978) derives his versionof the permintertempoa proportioincome, anindividualsone. Duesethat once cfor an indivincome hypotain consumabandonedconsumptiosive consumimplicationand previoumodel of PIthe MPC islabor incom

    We are nties to consLusardi (199

    4.2. The ind

    After deit is possibltional den

    MPC dehis perm

    This deallow the insumption apossible to

    4.2.1. An incThe indi

    Eq. (22):

    c = c1

    Differentiatsure of an iSection 3.1

    mpc = cyp

    Hence, if thincome, hisunits.We camuch he caindividualsmpc mpc

    The otheHalls (1978

    13 One unitincreases by o

    MPC is:

    mpcPIH = cyp

    = 1. (30)

    This implies that if the individuals permanent income is one unithigher, then

    the ceve

    s to eion oe thet (cion ot incforetakehers

    totangeshe saers in

    The cassut effenge it to ais he

    al =

    0 and 0 < < 1, it isformulate the following proposition:

    1. When an individuals utility depends on both his ownprevious consumption in addition to the current consump-elevant others, his MPC is lower than if he had merely hadation behavior, as in Alessie and Lusardi (1997), while theighest in Halls (1978) PIH model.

    The inequality 1 = mpcPIH > mpcA&L = 1 (/(1 + r))n (0,1], since we have that /(1 + r) > 0. Fur-when (0,1] and (0,1), we have that 1 +(/(1 + r)) = mpctotal < mpcA&L = 1 (/(1 + r)) holds1) < 0. Hence, it is obvious that mpcPIH > mpcA&L >

    hen < 1, > 0, and 0 < < 1, we can conclude thatC is smallest: mpcPIH > mpcA&L > mpctotal.

    the individual has both a habit-formation behavior ande degree about the consumption among his relevanthis consumption is less sensitive to an increase in hisincome and to the permanent consumption levels ofothers compared to if he merely has a habit-formationdobviously if onlyhis absolute consumptiondrives util-oothness depends on the fact that the individual doesfall behind the consumption among his relevant otherse, and therefore he adjusts his consumption level less.model may be better at explaining the excess smooth-omenon14 found in the consumption data compared tories, which opens up for further research.

    eaton (1992).

  • 420 F.W. Andersson / The Journal of Socio-Economics 38 (2009) 415420

    5. Concluding remarks

    By looking at psychological and sociological arguments of whatindividuals utility depends on, I extend Alessie and Lusardis(1997) consumptionmodel, inwhich individualsmerelyhavehabit-formation behaviors, by adding the notion that individuals also careabout the consumption among their relevant others. I also derivea general closed form consumption function that boils down tothe closed form consumption functions of Halls (1978) PIH, or ahabit-formation behavior such as in Alessie and Lusardis (1997)consumptio

    The extconsumptioconsumptiosumption inwhen the cthe futureFurthermordoes not afthat the toAlessie andthat the indlevel of hismay be betup for furth

    It shouldtion dependamonghis rthe individu(relaxing thThis is in a swhere empis affected bCarbonell (2

    Acknowled

    I apprecOlof JohansHassler, Maanonymousthis paper.

    Appendix A

    We knowequal to (th

    (u(ct+1)/(u(ct )/

    Propositionsumption, {cu(ct )ct

    =u

    and where

    Proof 2. Ifconstantov

    to calculate (u(ct+2)/ct+2). In order for Eq. (32) to be satised,

    u(ct+2)ct+2

    = 1 +

    u(ct+1)ct+1

    1

    u(ct )ct

    . (34)

    Eq. (34) is a second order difference equation whose general solu-tion is:

    u(ct+n)ct+n

    = A + B(

    1

    )n, (35)

    where A and B are arbitrary constants. When an individual has aormationbehavior, then0 < < 1, and thenEq. (35) showse indingenhimplhis i, Prop

    nces

    1990.ricanR., Lusrs 55arrer

    ion an251.F., Carlutevganizon, F.Wumptn, T., Jmal puomicC.D., 2ics LeC.D., Onal ofA.S., 1endonerry,Unive

    , Loewenste132Carbopariso.H., 19rd Unn, M.,s, Prin., 1978theorn-Ste prefe), 362J.M., 1London, W.ress,B., 199sumery, T., 1rd UnS.J., Herns.T., 193r, R., 2Univn models.ension of Alessie and Lusardis (1997) psychologicaln measures (that utility depends on) implies that then among relevant others affects an individuals con-two ways: The individuals consumption (i) increases

    urrent consumption increases and (ii) decreases whenpermanent consumption by relevant others increases.e, a change in the consumption among relevant othersfect the individuals traditional MPC. However, I showtal MPC is lower compared to both Halls (1978) andLusardis (1997) MPC. This is a consequence of the factividual does not wish to fall behind the consumptionrelevant others in the future. Furthermore, this modelter at explaining the excess smoothness which openser research.be possible to test whether an individuals consump-s on both his own previous consumption and that seenelevant others, andwhether new information regardingals own future income and that among relevant otherse assumption of perfect foresight) affects consumption.ense analogous with papers in the happiness literature,irical evidence suggests that happiness of individualsy the income level of relevant others; see, e.g. Ferrer-i005).

    gements

    iate the thoughtful comments of Katarina Nordblom,son-Stenman, Hkan Locking, Wlodek Bursztyn, Johnrkus Knell, Debbie Axlid for editorial advices, and tworeferees for valuable comments on an earlier version of

    that an individuals MRS under certain assumptions ise same as Eq. (12)):

    ct+1) (u(ct+2)/ct+2)ct ) (u(ct+1)/ct+1)

    = 1. (32)

    2. The only admissible time series of psychological con- }T=t , that satises Eq. (32) when T is:(ct+1)

    ct+1=

    u(ct+2)ct+2

    = , t, (33)

    is a constant.

    themarginal utility of psychological consumption is noter timeand (u(ct+1)/c

    t+1) /= (u(ct )/ct ), it is possible

    habit-fthat this growcave, thwhichtime. THence

    Refere

    Abel, A.,Ame

    Alessie,Lette

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    Carroll,Jour

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    Elster, J.Loewpp. 2

    Ferrer-icom

    Frank, ROxfo

    FriedmaPres

    Hall, R.Eesis:

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    Grazividuals marginal utility of psychological consumptionover time. When an individuals utility function is con-is psychological consumption, ct+n, decreases over time,ies that his absolute consumption also decreases overs not a utility maximization, i.e., (2) is not maximized.osition 2 is true, and we can formulate Lemma 1.

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    Consumption theory with reference dependent utilityIntroductionThe individual's utilityThe individual's utility function argumentsThe individual's utility maximization problem

    The individual's closed form consumption functionThe impact of the individual's permanent incomeThe impact of the consumption by relevant othersA temporary increase in the consumption by relevant othersA permanent increase in the consumption by relevant others

    Marginal propensity to consumeA review of marginal propensity to consumeThe individual's marginal propensity to consumeAn increased permanent income affects MPCThe consumption by relevant others affects MPC

    Concluding remarksAcknowledgementsAppendix AReferences