Addiction and Cue-Triggered Decision Processeseconweb.ucsd.edu/~jandreon/Econ264/papers/Bernheim...

Addiction and Cue-Triggered Decision Processes

By B DOUGLAS BERNHEIM AND ANTONIO RANGEL

We propose a model of addiction based on three premises (i) use among addicts isfrequently a mistake (ii) experience sensitizes an individual to environmental cuesthat trigger mistaken usage (iii) addicts understand and manage their susceptibil-ities We argue that these premises find support in evidence from psychologyneuroscience and clinical practice The model is tractable and generates a plau-sible mapping between behavior and the characteristics of the user substance andenvironment It accounts for a number of important patterns associated withaddiction gives rise to a clear welfare standard and has novel implications forpolicy (JEL D01 D11 H20 H21 H23 H31 I12 I18 K32)

According to clinical definitions substanceaddiction occurs when after significant expo-sure users find themselves engaging in compul-sive repeated and unwanted use despite clearlyharmful consequences and often despite astrong desire to quit unconditionally (see egthe American Psychiatric Associationrsquos Diag-

nostic and Statistical Manual of Mental Disor-ders known as DSM-IV) There is widespreadagreement that certain substances have addic-tive properties1 and there is some debate as towhether formal definitions of addiction shouldbe expanded to include other substances (suchas fats and sugars) and activities (such as shop-ping shoplifting sex television viewing andinternet use)

The consumption of addictive substancesraises important social issues affecting mem-bers of all socioeconomic strata2 Tens of mil-lions of Americans use addictive substancesNearly 25 million adults have a history of alco-hol dependence and more than five millionqualify as ldquohard-corerdquo chronic drug users Esti-mates for 1999 place total US expenditures ontobacco products alcoholic beverages cocaineheroin marijuana and methamphetamines atmore than $150 billion with still more spent oncaffeine and addictive prescription drugs Esti-mated social costs (health care impaired pro-ductivity crime and so forth) total more than

Bernheim Department of Economics Stanford Uni-versity Stanford CA 94305-6072 and NBER (e-mailbernheimlelandstanfordedu) Rangel Department ofEconomics Stanford University Stanford CA 94305 andNBER (e-mail rangellelandstanfordedu) We thankGeorge Akerlof Gadi Barlevy Michele Boldrin Kim Bor-der Samuel Bowles Colin Camerer Luis Corchon DavidCutler Alan Durell Dorit Eliou Victor Fuchs Ed GlaeserSteven Grant Jonathan Gruber Justine Hastings Jim HinesMatthew Jackson Chad Jones Patrick Kehoe NarayanaKocherlakota Botond Koszegi David Laibson Darius Lak-dawalla Ricky Lam John Ledyard George LoewensteinRob Malenka Ted OrsquoDonahue David Pearce ChristopherPhelan Wolfgang Psendorfer Edward Prescott MatthewRabin Paul Romer Pablo Ruiz-Verdu Andrew SamwickIlya Segal Jonathan Skinner Stephano de la Vigna AndrewWeiss Bob Wilson Leeat Yariv Jeff Zwiebel seminarparticipants at UCndashBerkeley Caltech Carlos III DarmouthHarvard Hoover Institution Instituto the Analysis Eco-nomico LSE Michigan NBER Northwestern UCSDYale Wisconsin SITE Federal Reserve Bank of Minneap-olis and the McArthur Preferences Network for usefulcomments and discussions We also thank Luis RayoDaniel Quint and John Hatfiled for outstanding researchassistance Rangel gratefully acknowledges financial sup-port from the NSF (SES-0134618) and thanks the HooverInstitution for its financial support and stimulating researchenvironment This paper was prepared in part while BDouglas Bernheim was a Fellow at the Center for AdvancedStudy in the Behavioral Sciences (CASBS) where he wassupported in part by funds from the William and FloraHewlett Foundation (Grant No 2000-5633)

1 Eliot Gardner and James David (1999) provide thefollowing list of 11 addictive substances alcohol barbitu-rates amphetamines cocaine caffeine and related methyl-xanthine stimulants cannabis hallucinogenics nicotineopioids dissociative anasthetics and volatile solvents

2 The statistics in this paragraph were obtained from thefollowing sources Center for Disease Control (1993) Na-tional Institute on Drug Abuse (1998) National Institute onAlcohol Abuse and Alcoholism (2001) Office of NationalDrug Control Policy (2001a b) and US Census Bureau(2001) There is of course disagreement as to many of thereported figures

1558

$300 billion per year On average over 500000deaths each year are attributed directly to ciga-rettes and alcohol

Public policies regarding addictive sub-stances run the gamut from laissez-faire to tax-ation subsidization (eg of rehabilitationprograms) regulated dispensation criminaliza-tion product liability and public health cam-paigns Each alternative policy approach haspassionate advocates and detractors Economicanalysis can potentially inform this debate butit requires a sound theory of addiction

This paper presents a new theory of addictionbased on three central premises first useamong addicts is frequently a mistake secondexperience with an addictive substance sensi-tizes an individual to environmental cues thattrigger mistaken usage third addicts under-stand their susceptibility to cue-triggered mis-takes and attempt to manage the process withsome degree of sophistication We argue thatthese premises find strong support in evidencefrom psychology neuroscience and clinicalpractice In particular research has shown thataddictive substances systematically interferewith the proper operation of an important classof processes which the brain uses to forecastnear-term hedonic rewards (pleasure) and thisleads to strong misguided cue-conditioned im-pulses that often defeat higher cognitive control

We provide a parsimonious representation ofthis phenomenon in an otherwise standardmodel of intertemporal decision-making Spe-cifically we allow for the possibility that uponexposure to environmental cues the individualmay enter a ldquohotrdquo decision-making mode inwhich he always consumes the substance irre-spective of underlying preferences and we as-sume that sensitivity to cues is related to pastexperiences The individual may also operate ina ldquocoldrdquo mode wherein he considers all alter-natives and contemplates all consequences in-cluding the effects of current choices on thelikelihood of entering the hot mode in thefuture3

As a matter of formal mathematics ourmodel involves a small departure from the stan-dard framework Behavior corresponds to thesolution of a dynamic programming problemwith stochastic state-dependent mistakes Ourapproach therefore harmonizes economic the-ory with evidence on the biological foundationsof addiction without sacrificing analytic tracta-bility We underscore this point by providingresults that illuminate the relationships betweenbehavior and the characteristics of the usersubstance and environment For example wefind that when one substance is more addictivethan another then ceteris paribus the more ad-dictive substance is associated with less con-sumption among relatively new users but withmore consumption (both intentional and acci-dental) among highly experienced users

The theory can account for a number of im-portant patterns associated with addiction Italso gives rise to a clear welfare standard andhas novel implications for public policy Ourpolicy analysis focuses on consumer welfareand therefore ignores supply-side effects andexternalities It emphasizes the role of policy inaverting mistakes and in either ameliorating ormagnifying significant uninsurable monetaryrisks indirectly caused by exposure to stochasticenvironmental cues We show that a beneficialpolicy intervention potentially exists if and onlyif there are circumstances in which users unsuc-cessfully attempt to abstain In that case theoptimal policy depends on usage patterns In anatural benchmark case it is optimal to subsi-dize an addictive substance when the likelihoodof use rises with the level of past experience Incontrast provided the substance is sufficientlyinexpensive it is optimal to tax the substancewhen the likelihood of use declines with thelevel of past experience Under weak condi-tions a small subsidy for rehabilitation is ben-eficial and a small tax is harmful When substancetaxation is optimal under some conditions crimi-nalization can perform even better Programs thatmake addictive substances available on a prescrip-tion basis have potentially large benefits Restric-tions on advertising and public consumption and

3 Our analysis is related to work by George Loewenstein(1996 1999) who considers simple models in which anindividual can operate either in a hot or cold decision-making mode Notably Loewenstein assumes that behaviorin the hot mode reflects the application of a ldquofalserdquo utilityfunction rather than a breakdown of the processes by which

a utility function is maximized He also argues contrary tothe findings of this paper that imperfect self-understandingis necessary for addiction-like behaviors

1559VOL 94 NO 5 BERNHEIM AND RANGEL ADDICTION

statutes requiring counter-cues on packaging arealso potentially beneficial

The remainder of the paper is organized asfollows Section I describes some important be-havioral patterns associated with addiction thatrequire explanation Section II lays out and jus-tifies with particular reference to evidence frompsychology and neuroscience the central pre-mises of our theory Section III presents theformal model Section IV explores the modelrsquospositive implications including its ability togenerate observed behavioral patterns SectionV concerns policy analysis Section VI clarifiesthe relationships between our theory of addic-tion and others that appear in the literatureincluding the standard model of rational addic-tion (Gary Becker and Kevin Murphy 1988)various extensions of this model (AthanasiosOrphanides and David Zervos 1995 AngelaHung 2000 David Laibson 2001) and a num-ber of behavioral alternatives (Loewenstein1996 1999 Ted OrsquoDonoghue and MatthewRabin 1999 2000 Jonathan Gruber andBotond Koszegi 2001 Loewenstein et al Fa-ruk Gul and Wolfgang Pesendorfer 2001a b)Section VII concludes and discusses directionsfor future research The appendices provide ad-ditional technical details and proofs in somecases we sketch proofs to conserve space

I Patterns of Addictive Behavior

What makes addiction a distinctive phenom-enon From the extensive body of research onaddiction in neuroscience psychology andclinical practice we have distilled five impor-tant behavioral patterns requiring explanation

1 Unsuccessful Attempts to QuitmdashAddictsoften express a desire to stop using a substancepermanently and unconditionally but are unableto follow through Short-term abstention iscommon while long-term recidivism rates arehigh For example during 2000 70 percent ofcurrent smokers expressed a desire to quit com-pletely and 41 percent stopped smoking for atleast one day in an attempt to quit but only 47percent successfully abstained for more thanthree months (see J E Harris 1993 Y I Hseret al 1993 C OrsquoBrien 1997 A Goldstein2001 A Trosclair et al 2002) This pattern isparticularly striking because regular users ini-

tially experience painful withdrawal symptomswhen they attempt to quit and these symptomsdecline over time with successful abstentionThus recidivism often occurs after users haveborne the most significant costs of quittingsometimes following years of determinedabstention

2 Cue-Triggered RecidivismmdashRecidivismrates are especially high when addicts are ex-posed to cues related to past drug consumptionLong-term usage is considerably lower amongthose who experience significant changes ofenvironment (see OrsquoBrien 1975 1997 Gold-stein and H Kalant 1990 Hser et al 19932001 Goldstein 2001)4 Treatment programsoften advise recovering addicts to move to newlocations and to avoid the places where previousconsumption took place Stress and ldquoprimingrdquo(exposure to a small taste of the substance) havealso been shown to trigger recidivism (seeGoldstein 2001 Terry Robinson and Kent Ber-ridge 2003)

3 Self-Described MistakesmdashAddicts oftendescribe past use as a mistake in a very strongsense they think that they would have beenbetter off in the past as well as the present hadthey acted differently They recognize that theyare likely to make similar errors in the futureand that this will undermine their desire to ab-stain When they succumb to cravings theysometimes characterize choices as mistakeseven while in the act of consumption5 It isinstructive that the 12-step program of Alco-holic Anonymous begins ldquoWe admit we arepowerless over alcoholmdashthat our lives have be-come unmanageablerdquo

4 L Robins (1974) and Robins et al (1974) found thatVietnam veterans who were addicted to heroin andoropium at the end of the war experienced much lower relapserates than other young male addicts during the same periodA plausible explanation is that veterans encountered fewerenvironmental triggers (familiar circumstances associatedwith drug use) upon returning to the United States

5 Goldstein (2001 p 249) describes this phenomenon asfollows the addict had been ldquosuddenly overwhelmed by anirresistible craving and he had rushed out of his house tofind some heroin it was as though he were driven bysome external force he was powerless to resist even thoughhe knew while it was happening that it was a disastrouscourse of action for himrdquo (italics added)

1560 THE AMERICAN ECONOMIC REVIEW DECEMBER 2004

4 Self-Control through PrecommitmentmdashRecovering users often manage their tendencyto make mistakes by voluntarily removing ordegrading future options They voluntarily ad-mit themselves into ldquolock-uprdquo rehabilitationfacilities often not to avoid cravings but pre-cisely because they expect to experience crav-ings and wish to control their actions They alsoconsume medications that either generate un-pleasant side effects or reduce pleasurablesensations if the substance is subsequently con-sumed6 Severe addicts sometimes enlist othersto assist with physical confinement to assureabstinence through the withdrawal process

5 Self-Control through Behavioral and Cog-nitive TherapymdashRecovering addicts attempt tominimize the probability of relapse through be-havioral and cognitive therapies Successful be-havioral therapies teach cue-avoidance often byencouraging the adoption of new lifestyles andthe development of new interests Successfulcognitive therapies teach cue-managementwhich entails refocusing attention on alternativeconsequences and objectives often with the as-sistance of a mentor or trusted friend or througha meditative activity such as prayer Notablythese therapeutic strategies affect addictsrsquochoices without providing new information7

While consumption patterns for addictivesubstances are distinctive in some respects it isimportant to bear in mind that they are ordinaryin other respects A number of studies haveshown that aggregate drug use responds both to

prices and to information about the effects ofaddictive substances For example an aggres-sive US public health campaign is widely cred-ited with reduction in smoking rates There isalso evidence that users engage in sophisticatedforward-looking deliberation reducing currentconsumption in response to anticipated priceincreases8

It is important to remember that consumptionpatterns for the typical addictive substance varyconsiderably from person to person9 Some peo-ple never use it Some use it in a controlled wayeither periodically or for a short time periodSome experience occasional episodes wherethey appear to ldquolose controlrdquo (binge) but sufferno significant ongoing impairment and have nodesire to quit permanently Some fit theDSM-IV definition of addiction In the rest ofthe paper the term addict is reserved for thethird and fourth groups whereas the term useris applied to everyone

II Central Premises

The theory developed in this paper is basedon three premises (i) use among addicts isfrequently a mistakemdashthat is a pathologicaldivergence between choice and preference (ii)experience with an addictive substance sensi-tizes an individual to environmental cues thattrigger mistaken usage and (iii) addicts under-stand their susceptibility to cue-triggered mis-takes and attempt to manage the process withsome degree of sophistication The thirdpremise is consistent with observed behavioralpatterns involving cue-avoidance andor pre-commitments and should be relatively uncon-troversial In contrast the notion that choicesand preferences can diverge is contrary to thestandard doctrine of revealed preference andtherefore requires thorough justification

There are plainly circumstances in which itmakes no sense to infer preferences fromchoices For example American visitors to the

6 Disulfiram interferes with the liverrsquos ability to metab-olize alcohol as a result ingestion of alcohol produces ahighly unpleasant physical reaction for a period of timeMethadone an agonist activates the same opioid receptorsas heroin and thus produces a mild high but has a slowonset and a long-lasting effect and it reduces the highproduced by heroin Naltrexone an antagonist blocks spe-cific brain receptors and thereby diminishes the high pro-duced by opioids All of these treatments reduce thefrequency of relapse (see OrsquoBrien 1997 Goldstein 2001)

7 Goldstein (2001 p 149) reports that there is a sharedimpression among the professional community that 12-stepprograms such as AA ldquoare effective for many (if not most)alcohol addictsrdquo However given the nature of these pro-grams objective performance tests are not available TheAA treatment philosophy is based on ldquokeeping it simple byputting the focus on not drinking on attending meetingsand on reaching out to other alcoholicsrdquo

8 See F Chaloupka and K Warner (2001) Gruber andKoszegi (2001) and R MacCoun and P Reuter (2001) fora review of the evidence

9 Even for a substance such as cocaine which is consid-ered highly addictive only 15ndash16 percent of people becomeaddicted within 10 years of first use (F A Wagner and J CAnthony 2002)


United Kingdom suffer numerous injuries andfatalities because they often look only to the leftbefore stepping into streets even though theyknow traffic approaches from the right Onecannot reasonably attribute this to the pleasureof looking left or to masochistic preferences Thepedestrianrsquos objectivesmdashto cross the street safelymdashare clear and the decision is plainly a mistakeThe source of this systematic error is traceable tofeatures of the human brain Habituated semi-automatic responses beneficially increase thespeed of decision-making in some circumstancesbut lead to systematic mistakes in others

Recent research on the neuroscience of addic-tion has identified specific features of the brainthat appear to produce systematic errors with re-spect to decisions involving the consumption ofaddictive substances The key process involves amechanism (henceforth called the ldquohedonic fore-casting mechanismrdquo or HFM) that is responsiblefor associating environmental cues with forecastsof short-term hedonic (pleasurepain) responses10

Normally the HFM learns through feedbackfrom the hedonic system with experience itassociates a situation and action with an antic-ipatory biochemical response the magnitude ofwhich reflects the intensity of expected plea-sure Addictive substances interfere with thenormal operation of the HFM by acting directly(ie independent of the pleasure experienced)on the learning process that teaches the HFM togenerate the anticipatory response With re-peated use of a substance cues associated withpast consumption cause the HFM to forecastgrossly exaggerated pleasure responses creat-ing a powerful (and disproportionate) impulseto use When this happens a portion of theuserrsquos decision processes functions as if it hassystematically skewed information which leadsto mistakes in decision-making

Next we describe some of the key evidencethat leads to these conclusions We organize ourdiscussion around four points

1 Brain Processes Include a Hedonic Fore-casting Mechanism (HFM) Which with Experi-ence Produces a Biochemical Response to

Situations and Opportunities the Magnitude ofWhich Constitutes a Forecast of Near-TermPleasuremdashNeuroscientists have long recog-nized that the mesolimbic dopamine system(MDS) is a basic component of human deci-sion processes11 A large body of recent re-search indicates that the MDS functions atleast in part as an HFM In a series of exper-iments subjects (often monkeys) are pre-sented with a cue that is associated with areward delivered a few seconds later (seeWolfram Schultz et al 1997 Schultz 19982000) Initially the MDS fires in response tothe delivery of the reward and not in responseto the cue However as time passes the MDSfires with the presentation of the cue and notwith the delivery of the reward Moreover thelevel of cue-triggered MDS activity is propor-tional to the size of the eventual reward Ifafter a number of trials the experimenterincreases the magnitude of the reward theMDS fires twice with the presentation of thecue (at a level proportional to the originalanticipated reward) and with the delivery ofthe reward (at a level reflecting the differencebetween the anticipated and actual rewards)After repeated trials with the new reward theMDS fires more intensely upon presentationof the cue and once again does not respondto the delivery of the reward Thus withexperience the MDS generates a cue-condi-tioned dopamine response that anticipates themagnitude of the eventual reward

2 Activation of the HFM Does Not Neces-sarily Create Hedonic Sensation and HedonicSensation Can be Experienced without HFMActivationmdashSince the MDS produces a dopa-mine response prior to an anticipated experienceand no response during the experience it isnatural to conjecture that this mechanism isneither a source nor a manifestation of pleasure

10 The phrase ldquohedonic forecasting mechanismrdquo summarizesthe role of this process in economic terms this terminology is notused in the existing behavioral neuroscience literature

11 The MDS originates in the ventral tegmentalarea near the base of the brain and sends projectionsto multiple regions of the frontal lobe especially to the nu-cleus accumbens The MDS also connects with the amyg-dala basal forebrain and other areas of the prefrontal lobeThese connections are believed to serve as an interfacebetween the MDS and attentional learning and cognitiveprocesses (Robinson and Berridge 2003)


Indeed the human brain appears to contain aseparate hedonic system that is responsible forproducing sensations of ldquowell-beingrdquo12 In aseries of papers neuroscientists Kent Berridgeand Terry Robinson have argued that two sep-arate processes are at work in decision makinga ldquowantingrdquo process which encompasses theimpulse created by a positive MDS forecastand a ldquolikingrdquo process which refers to a hedo-nic response (see Robinson and Berridge 19932000 2003 Berridge 1996 1999 Berridgeand Robinson 1998 2003)13 Their hypothesisemerges from numerous experimental studiesincluding the following Using measures ofldquolikingrdquo based on ratsrsquo facial expressions whenresponding to sweet and sour tastes severalexperiments have shown that neither the directactivation of the MDS nor its suppression af-fects liking (S Pecina et al 1997 H J Kacz-marek and S W Kiefer 2000 C L Wyvell andBerridge 2000) Others have demonstrated thatthe ldquolikingrdquo system functions well even withmassive lesions to the MDS (see Berridge andRobinson 1998) Direct activation of the MDSthrough microinjections of amphetamine in thenucleus accumbens (NAc) increases wantingbut fails to increase liking (Wyvell and Ber-ridge 2000) Finally blocking the MDS withdopamine antagonists does not have an impacton the level of pleasure obtained from using adrug reported by amphetamine and nicotine us-ers (L H Brauer et al 1997 2001 S RWachtel et al 2002)

3 HFM-Generated Forecasts InfluenceChoicesmdashA series of classic experiments by JOlds and P Milner (1954) demonstrated thatrats learn to return to locations where they havereceived direct electrical stimulation to the

MDS When provided with opportunities toself-administer by pressing a lever the rats rap-idly became addicted giving themselves ap-proximately 5000ndash10000 ldquohitsrdquo during eachone-hour daily session ignoring food waterand opportunities to mate These rats are willingto endure painful electric shocks to reach thelever (see Gardner and David 1999 for a sum-mary of these experiments) Complementaryevidence shows that rats given drugs that blockdopamine receptors thereby impeding the ap-propriate operation of the MDS eventually stopfeeding (Berridge 1999)

Notably the MDS activates ldquoseeking be-haviorsrdquo as well as immediate consumptionchoices That is it learns to make associationsnot just between consumption opportunities andhedonic payoffs but also between environmen-tal cues and activities that tend to produce theseconsumption opportunities For example thesight of food may create a powerful impulse toeat while an odor may create a powerful im-pulse to seek food The size of the set of envi-ronmental cues that trigger an associatedseeking behavior increases with the strength ofthe hedonic forecast (see Robinson and Ber-ridge 1993 2000 2003 Berridge and Robin-son 1998 2003)

While the MDS plays a key role in determin-ing choices it is not the only process at work Inan organism with a sufficiently developed fron-tal cortex higher cognitive mechanisms canoverride HFM-generated impulses Though thespecific mechanisms are not yet fully under-stood structures in the frontal cortex appear toactivate competing ldquocognitive incentivesrdquo (Ber-ridge and Robinson 2003) for example byidentifying alternative courses of action or pro-jecting the future consequences of choices Theoutcome depends on the intensity of the HFMforecast and on the ability of the frontal cortexto engage the necessary cognitive operations14

Thus a more attractive HFM-generated forecastmakes cognitive override less likely In addi-tion the MDS seems to affect which stimuli thebrain attends to which cognitive operations it

12 The existing evidence suggests that the hedonic sys-tem is modulated by a distributed network separate fromthe structures involved in the HFM that includes GABAer-gic neurons in the shell of the NAc the ventral palladiumand the brainstem parachial nucleus (see Berridge and Rob-inson 2003)

13 For decades neuroscientists and psychologists haveused the term ldquorewardrdquo to describe both liking and wantingIn most experimental settings the distinction is immaterialsince outcomes that are liked are also wanted and viceversa However as we will see this distinction is critical tounderstanding why repeated exposure to drugs leads tomistaken usage

14 The activation of the cognitive operations required forcognitive control depends on neocortical structures such asthe insula and the orbitofrontal cortex (see eg J D Cohenand K I Blum 2002 D C Krawczyk 2002 E T Rolls2002 Masataka Watanabe et al 2002)


activates (what it thinks about) and whichmemories it preserves and this may make itmore difficult to engage the cognitive opera-tions required to override the HFM15

We emphasize that the HFM and higher cog-nitive processes are not two different sets ofldquopreferencesrdquo or ldquoselvesrdquo competing for controlof decisions Hedonic experiences are generatedseparately and an individual maximizes thequality of these experiences by appropriatelydeploying both forecasting processes to antici-pate outcomes The HFMrsquos main advantage isthat it can produce rapid decisions with gener-ally beneficial near-term outcomes providedthe environment is stable It cannot howeveranticipate sufficiently delayed consequencesand when the environment changes it canneither ignore irrelevant past experiences noradjust forecasts prior to acquiring further expe-rience The competing cognitive forecastingsystem addresses these shortcomings (albeit im-perfectly) but is comparatively slow Balancedcompetition between these two processes appar-ently emerged as evolutionrsquos best compromise

4 Addictive Substances Act Directly on theHFM Disrupting Its Ability to Construct Accu-rate Hedonic Forecasts and Exaggerating theAnticipated Hedonic Benefits of Consump-tionmdashAlthough addictive substances differconsiderably in their chemical and psychologi-cal properties there is a large and growingconsensus in neuroscience that they share anability to activate the firing of dopamine into theNAc with much greater intensity and persis-tence than other substances They do this eitherby activating the MDS directly or by activatingother networks that have a similar effect on theNAc (see Ingrid Wickelgren 1997 Steven Hy-man and Robert Malenka 2001 E J Nestler2001 Robinson and Berridge 2003 Nestlerand Robert Malenka 2004)16

For nonaddictive substances the MDS learnsto assign a hedonic forecast that bears somenormal relation to the subsequent hedonic ex-perience For addictive substances consump-tion activates dopamine firing directly so theMDS learns to assign a hedonic forecast that isout of proportion to the subsequent hedonicexperience This not only creates a strong (andmisleading) impulse to seek and use the sub-stance but also undermines the potential forcognitive override17 Cognitive override still oc-curs but in a limited range of circumstances1819

Our central premises have two implicationsthat are worth emphasizing because they are atodds with some of the alternative models ofaddiction discussed in Section VI First theprocesses that produce systematic mistakes aretriggered by stochastic environmental cues andare not always operative Second cue-triggered

15 Notably more educated individuals are far more likelyto quit smoking successfully even though education bearslittle relation either to the desire to quit or to the frequencywith which smokers attempt to quit (Trosclair et al 2002)

16 Of the addictive substances listed in footnote 1 onlyhallucinogenics (or psychedelics) do not appear to produceintense stimulation of the MDS Instead they act on aldquosubtype of serotonin receptor which is widely distributedin areas of the brain that process sensory inputsrdquo (Goldstein2001 p 231) There is some disagreement as to whether

hallucinogens are properly classified as addictive substances(see Goldstein 2001 Ch 14) Notably laboratory animalsand humans learn to self-administer the same set of sub-stances with the possible exception of hallucinogenics(Gardner and David 1999 pp 97ndash98)

17 A stronger MDS-generated impulse is more likely toovercome competing cognitive incentives of any givenmagnitude In addition the MDS-generated impulse maymake it more difficult to engage the cognitive operationsrequired to override the HFM For example recoveringaddicts may pay too much attention to drugs activate andmaintain thoughts about the drug too easily and retainparticularly vivid memories of the high Consistent withthis S Vorel et al (2001) have shown that the stimulationof memory centers can trigger strong cravings and recidi-vism among rats that have previously self-administeredcocaine (J P Berke et al 2001 and C Holden 2001a bprovide nontechnical discussions)

18 The importance of cognitive override is evident fromcomparisons of rats and humans When rats are allowed toself-administer cocaine after a short period of exposurethey begin to ignore hunger reproductive urges and allother drives consuming the substance until they die (RPickens and W C Harris 1968 E Gardner and David1999) In contrast even severely addicted humans some-times resist cravings and abstain for long periods of timeThe difference is that rats rely solely on the HFM

19 Several studies (see J I Bolla et al 1998 J DJentsch and J R Taylor 1999 T W Robbins and B JEveritt 1999 A Behara and H Damasio 2002 Behara SDolan and A Hindes 2002) have shown that addicts sharepsychological disorders with patients who have damagedfrontal lobes affecting functions related to cognitive controlIn addition some of these studies have argued that drug useis partly responsible for this impairment Thus use mayincrease the likelihood of subsequent use by crippling cog-nitive control mechanisms


mistakes are specific to narrow domains Thatis they adhere to particular activities in partic-ular circumstances and do not reflect a generalbias toward immediate gratification Since poorcognitive control increases the likelihood of be-coming addicted it should not be surprising thatthe typical addict exhibits other self-controlproblems However it does not follow that ageneral deficit in cognitive control is necessaryfor addiction

In emphasizing the effects of addictive sub-stances on decision process we do not mean todiscount the significance of their hedonic ef-fects The typical user is initially drawn to anaddictive substance because it produces a hedo-nic ldquohighrdquo Over time regular use leads to he-donic and physical tolerance That is the drugloses its ability to produce a high unless the userabstains for a while20 and any attempt to dis-continue the drug may have unpleasant sideeffects (withdrawal) Cue-conditioned ldquocrav-ingsrdquo may have hedonic implications as well asnon-hedonic causes (ie HFM-generated im-pulses) All of these effects are clearly impor-tant and with one exception discussed in thenext section our model subsumes them How-ever there is an emerging consensus in neuro-science and psychology that decision-processeffects rather than hedonic effects provide thekey to understanding addictive behavior (seeRoy Wise 1989 G Di Chiara 1999 A EKelley 1999 Robbins and Everitt 1999 Rob-inson and Berridge 2000 Hyman and Malenka2001 Berridge and Robinson 2003 Nestlerand Malenka 2004)

III The Model

We consider a decision-maker (DM) who canoperate in either of two modes a ldquocoldrdquo modein which he selects his most preferred alterna-tive (by imposing cognitive control) and a dys-functional ldquohotrdquo mode in which decisions and

preferences may diverge (because he respondsto distorted HFM-generated forecasts) He livesfor an infinite number of discrete periods Ineach period he makes two decisions in succes-sion First he selects a ldquolifestylerdquo activity (a)then he allocates resources between an addictivesubstance (x 0 1) and a nonaddictive sub-stance (e 0) He enters each period in the coldmode and chooses his lifestyle activity ratio-nally This choice along with his history of useand other environmental factors determines theprobability with which he encounters cues thattrigger the hot mode If triggered he alwaysuses the substance even if this is not his bestchoice If he is not triggered he rationally de-cides whether to indulge or abstain

The intensity (or volume) of substance-related cues encountered c(a ) depends onthe activity a and an exogenous state of nature drawn randomly from a state space ac-cording to some probability measure Thefunction M(c s a ) denotes the attractivenessassigned to the drug by the HFM-generatedforecast this depends on the intensity of cuesthe chosen activity the state of nature and avariable s summarizing the DMrsquos history of use(his addictive state) The impulse from thisforecast defeats cognitive control and places theindividual in the ldquohotrdquo mode when its strengthexceeds some threshold MT

There are S 1 addictive states labeled s 0 1 S Usage in state s leads to state minSs 1 in the next period No use leads to statemax1 s 1 from state s 1 and to state 0from state 0 Note that it is impossible to reachstate 0 from any state s 1 The state s 0represents a ldquovirgin staterdquo in which the DM hashad no contact with the substance Since peoplebecome sensitized to cues through repeated usewe assume M(c s a) M(c s a ) fors s with M(c 0 a ) MT

The lifestyle activity a is chosen from the setE A R Activity E (ldquoexposurerdquo) entails a highlikelihood that the DM will encounter a largenumber of substance-related cues Examples in-clude attending parties at which the substance isreadily available Activity A (ldquoavoidancerdquo) isless intrinsically enjoyable than E but exposesthe DM to fewer substance-related cues [c(E) c(A )] and potentially reduces sensitiv-ity to cues [M(c s A ) M(c s E )]Examples include staying at home to read or

20 According to one user-oriented Web site tolerance tomarijuana ldquobuilds up rapidly after a few doses and disap-pears rapidly after a couple of days of abstinence Heavyusers need as much as eight times higher doses to achievethe same psychoactive effects as regular users using smalleramounts They still get stoned but not as powerfullyrdquo (seehttpwwwthegooddrugsguidecomcannabisaddictionhtm)


attending AA meetings Activity R (ldquorehabilita-tionrdquo) entails a commitment to clinical treat-ment at a residential center during the currentperiod It is even less intrinsically enjoyablethan A it may further reduce exposure andsensitivity to substance-related cues [c(A ) c(R ) and M(c s R ) M(c s A )] andmost importantly it guarantees abstention (x 0) during the current period

Let T(s a) M(c(a ) s a ) MT The DM enters the hot state if and only if T(s a) Let ps

a (T(s a)) denote theprobability of entering the hot mode in addic-tive state s after selecting lifestyle activity aOur assumptions on the functions c and M im-ply the following

ASSUMPTION 1 ps1a ps

a p0a 0 and

psE ps

A psR

In state s the DM receives an immediatehedonic payoff ws(e x a) (recall that e denoteshis consumption of nonaddictive goods) Thedependence of the payoff function on the addic-tive state incorporates the effect of past usageon current well-being (tolerance deteriorationof health and so forth) When evaluating thedesirability of any possible set of current andfuture outcomes the DM discounts future he-donic payoffs at a constant rate

Notice that we do not allow the hedonic pay-off to depend on the state of nature This is incontrast to the more conventional assumptionthat cravings reflect cue-triggered taste shocks(Laibson 2001) As indicated in the previoussection we recognize that cravings have hedo-nic implications We abstract from this possi-bility to focus more narrowly on the novelaspects of our theory which involve cue-triggered mistakes Allowing for dependence ofws on is straightforward but our model canaccount for the key features of addictive behav-ior without this extension

With ws independent of rehabilitation servesonly as a precommitment to abstain21 Since the

DMrsquos hedonic payoff from abstention is the sameregardless of whether he is hot or cold he neverenters rehabilitation with the object of reducingthe likelihood of cravings22 As a result the prob-abilities ps

R are irrelevant parametersIn state s the DM has access to resources ys

(ldquoincomerdquo) In many cases it is natural to as-sume that ys declines with s due to deterioratinghealth reduced productivity (eg through ab-senteeism) and increased out-of-pocket medi-cal expenses The price of the addictivesubstance is q the cost of rehabilitation is rs(which potentially depends on the addictivestate) and the price of the nonaddictive sub-stance is normalized to unity For simplicity weassume that the DM cannot borrow or save

The following notation simplifies our discus-sion Let us

a ws(ys 0 a) and bsa ws(ys q

1 a) usa for a E A and let us

R ws(ys rs 0 R) Intuitively us

a represents the baselinepayoff associated with successful abstention instate s and activity a and bs

a represents themarginal instantaneous benefit from use the in-dividual receives in state s after taking activitya Thus us

a bsa is the payoff for usage Let

ps (psE ps

A psR) us (us

E usA us

R) bs (bsE

bsA) s (ps us bs) and (0 S) The

vector specifies all pertinent ldquoderivativerdquo pa-rameters It reflects the properties of the sub-stance the method of administration thecharacteristics of the individual user and thepublic policy environment We make the fol-lowing assumption (the latter part of which is inkeeping with our earlier discussion)

ASSUMPTION 2 The payoff function ws isincreasing unbounded strictly concave andtwice differentiable with bounded second deriv-ative in the variable e (consumption of the non-addictive good) Moreover us

E usA us

R andus

E bsE us

A bsA

For each state s the DM follows one of fivecontingent plans engage in activity E and then

21 Though we assume that the DM can commit to reha-bilitation only one period at a time this is without loss ofgenerality since he starts each period in the cold mode Inpractice rehabilitation programs may also teach self-management skills and desensitize addicts to cues One canmodel these possibilities by assuming that ps

a (for a given

state or states) declines subsequent to rehabilitation or ther-apy Since the evidence suggests that these treatments arenot completely effective (Goldstein 2001 p 188) the forcesdescribed here would still come into play after treatment

22 When ws depends on and psA ps

R rehabilitation canserve as a strategy for avoiding cues that trigger reductionsin hedonic payoffs (through cravings)


use the substance when in the cold mode [(ax) (E 1)] engage in E and refrain from usewhen in the cold mode [(a x) (E 0) hence-forth ldquohalf-hearted abstentionrdquo] engage in Aand use when in the cold mode [(a x) (A 1)]engage in A and refrain from use when in thecold mode [(a x) (A 0) henceforth ldquocon-certed abstentionrdquo] or enter rehabilitation [(ax) (R 0)] From Assumption 2 it follows that(E 1) always dominates (A 1) so there are inpractice only four pertinent choices

The cold-mode DM is sophisticated in thesense that he correctly anticipates his futurechoices in either decision mode and he under-stands the process triggering the hot mode Ac-cordingly his choices in the cold modecorrespond to the solution of a simple dynamicstochastic programming problem with a valuefunction Vs( ) (evaluated as of the beginning ofa period) satisfying

(1) Vs 13 maxax13E113E013A013R013

usa s

axbsa

1 sax13Vmax1s 1 13 s

axVminSs 1 13

for s 123 where sax represents the probabil-

ity of consuming the substance in state s withcontingent plan (a x) (so s

E1 1 sE0 ps

Es

A0 psA and s

R0 0) Existence unique-ness and continuity of Vs( ) in follow fromstandard arguments

We close this section with several remarksFirst though simple and stylized our modeladheres closely to the three key premises de-scribed in Section II Specifically use amongaddicts is potentially a mistake experience withan addictive substance sensitizes the user toenvironmental cues that subsequently triggermistaken use and the awareness of this possi-bility leads users to manage their susceptibilities

Second our model reduces to the standardldquorational addictionrdquo framework when ps

a 0 forall s and a Thus the novelty of our approachinvolves the introduction of stochastic shocks(occurring with probability ps

a 0) that poten-tially cause decisions to diverge from prefer-ences This possibility is a central feature of our

model since without it the DM would neverchoose to avoid cues or enter rehabilitation(with ps

E 0 (E 0) dominates both (A 0) and(R 0)) For the same reason a naive DM whoincorrectly believes he does not suffer froma self-control problem (that is who acts as ifps

a 0) will never choose cue-avoidance orrehabilitation

Third even though our model allows for thepossibility that choices and preferences maydiverge with careful use of appropriate data itshould still be possible to recover preferencesand other critical parameters (such as hot-modeprobabilities) empirically Since we assume thatpreferences and choices are sometimes alignedthe most obvious approach involves the selec-tive application of the revealed preference prin-ciple The empirical challenge is to identifyinstances of alignment One cannot make thisdetermination using only information on choicesWe contend however that other evidence suchas the research results summarized in Section IIjustifies treating the central assumptions of ourmodel as maintained hypotheses This meansthat we can use choice data involving precom-mitments and cue-avoidance to infer hot-modeprobabilities and the utility costs of unintendeduse (recall the discussion in the preceding para-graph) Furthermore measures of physiologi-cal arousal andor self-reported affective statescould be used to differentiate ldquocoldrdquo choicesfrom ldquohotrdquo choices in experimental settings Fora more general discussion of preference mea-surement when choices and preferences system-atically diverge see Bernheim and Rangel(2005)

Fourth unlike other economic theories of ad-diction ours does not necessarily assume thatpresent use increases the marginal benefit offuture use (bs1 bs) We show that contraryto some claims in the literature it is possible toexplain the central features of addiction withoutinvoking intertemporal preference complemen-tarities (provided the probability of cue-triggered mistakes increases with s) This isimportant because intertemporal complementa-rities do not appear to drive some distinctiveaddictive behaviors24 and these behaviors are

23 The associated expression for s 0 is virtually iden-tical except that V0() replaces Vmax1s1()

24 The phenomenon of withdrawal is often interpretedas the key manifestation of intertemporal comple-


observed in contexts where such complementa-rities are probably not present (eg compulsiveshopping and kleptomania)

Fifth though one could incorporate the re-alistic possibility that some individuals arepartially myopic with respect to the likelihoodand effects of becoming addicted we assumethat the DM is sophisticated in the cold modeIf as we argue counterproductive addictivebehaviors can arise even with sophisticateddecision-makers efforts to eradicate addic-tion solely through education and information aremisguided

IV Positive Analysis

A Comparative Dynamics

Our comparative dynamic results concern theintensity with which the DM voluntarily usesthe addictive substance We study two notionsof intensity We say that the disposition to use isgreatest for (E 1) followed in order by (E 0)(A 0) and (R 0) Thus for example the dis-position to use increases when the DMrsquos choiceshifts from (A 0) to (E 1) We judge theintensity of intentional use by asking whetherthe DM plans to consume the substance Thusintentional use is highest for (E 1) and equiv-alent for (E 0) (A 0) and (R 0)25 An increasein intentional use implies an increase in thedisposition to use but not vice versa Bothdefinitions permit us to compare the intensity ofvoluntary use both within states and acrossstates

We study comparative dynamics with re-

spect to the elements of the parameter vector Since some of these are simple functions ofprices and income (q rs and ys) comparativedynamics with respect to the latter variablesfollow immediately We are particularly in-terested in the effects of the parameters ps

E

and psA since these are directly tied to the

novel aspects of our framework (stochasticevents that create pathological discrepanciesbetween preferences and choice) We are alsointerested in the effects of us

A bsA and us

Rsince these parameters are relevant only if thenovel components of our model are opera-tional ( ps

E 0)

1 Changes in Individual ParametersmdashInpractice we are rarely interested in phenomenathat affect only one state-specific parameterHowever examining these effects in isolationlays the groundwork for subsequent results in-volving changes in groups of parameters

PROPOSITION 1 (i) The disposition to use instate j is

(i-a) weakly increasing in bka and uk

a andweakly decreasing in pk

a for k j(i-b) weakly decreasing in bk

a and uka and

weakly increasing in pka for k j

(i-c) weakly decreasing in pjE and uj

R andweakly increasing in bj

E

(ii) Intentional use in state j is invariant withrespect to pj

E pjA uj

A bjA and uj

R

Parts (i-a) and (i-b) establish the intuitiveproperty that beneficial changes in parametersfor more (less) advanced states of addictionincrease (decrease) the disposition to use in thecurrent state Thus an increase in the likelihoodor severity of a cue-triggered mistake in state sinduces the DM to make choices that reduce thelikelihood of reaching state s Part (i-c) is alsointuitive the disposition to use in the currentstate rises with the benefits to current use andfalls with both the desirability of rehabilitationand the likelihood that the exposure activitytriggers the hot mode (since this increases theattractiveness of concerted abstention and reha-bilitation relative to half-hearted abstention)Part (ii) is perhaps less transparent A change inparameters can affect intentional use only if it

mentarities Notably W E McAuliffe (1982) showedthat only 275 percent of heroin addicts experiencedcue-triggered withdrawal symptoms and only 5 percentof these felt these symptoms were responsible for recid-ivism

25 For some parameter values the DM may be indif-ferent between two (but never more than two) choices inany particular addictive state When this occurs the set ofoptimal choices is always (E 1) (E 0) (E 0) ( A0) (E 0) (R 0) or ( A 0) (R 0) We say thata change in parameters from to weakly increases thedisposition to use (intentional use) if it leads to a weakincrease in both the minimum and maximum dispositionto use (intentional use) among optimal choices andstrictly increases the disposition to use (intentional use) ifeither the minimum or the maximum strictly increasesand neither declines


tips the balance between (E 1) and (E 0)26

Clearly this comparison does not implicate pjA uj

Abj

A or ujR neither does it depend on pj

E27

The characterization of directional effects inProposition 1 is not quite complete This isbecause the effects of bj

A ujA and uj

E on thedisposition to use in state j can be positive ornegative depending on the parameter values

2 Changes in Groups of ParametersmdashToexamine the effects of policy and environmentalchanges and to make comparisons between op-timal decision rules for different substances wemust typically consider the effects of varyingmany parameters simultaneously For examplea general reduction in the cost of rehabilitation(due perhaps to the development of a new thera-peutic drug) raises us

R for all s Likewise whenone substance is more addictive than another it isnatural to assume that ps

a is higher at every state sFor any state-indexed variable zs we say that

a change from (zs)s0S to (zs)s0

S represents ageneral increase (decrease) if zs zs (zs zs)for all s with strict inequality for some s Prop-osition 1 suggests that compound parameterchanges of this type often have ambiguous ef-fects on use For example a general increase inus

R or a general decrease in psa can reduce the

disposition to use in state j by making lowerstates (weakly) more attractive but can alsoincrease this disposition by making higherstates (weakly) more attractive

It is nevertheless possible to reach a numberof conclusions without imposing additionalstructure Public policy discussions often em-phasize initial use choices among casual userswho are at risk of becoming addicted and pat-

terns of behavior among hard-core addicts Toshed light on initial use we study behavior instate 0 To shed light on the choices of casualusers we examine behavior in state 1 the lengthof the first intentional use interval (defined as1 s1 1 where s1 is the largest integersuch that (E 1) is chosen for all s 1 s1 1 but not for s1) and the length of the initialresistance interval (defined as 1 s2 1where s2 is the largest integer such that (R 0) ischosen for all s 1 s2 1 but not fors2)28 To shed light on the behavior of thosewith substantial cumulative exposure we focuson choices in state S as well as the length of thefinal resignation interval (defined as s3 1 S where s3 is the smallest integer suchthat (E 1) is chosen for all s s3 1 Sbut not for s3) While these aspects of behaviorrespond ambiguously to general changes in someparameters other effects are unambiguous29

PROPOSITION 2 (i) A general increase in psE

or psA or a general reduction in us

A or bsA weakly

decreases the disposition to use in state 0 (andstate 1 for ps

E) weakly shortens the first inten-tional use interval weakly lengthens the initialresistance interval and weakly lengthens thefinal resignation interval

(ii) A general increase in usR weakly increases

the disposition to use in all states (includingstate 0) up to (but not including) the first state inwhich rehabilitation is an optimal choice afterthe increase It also weakly lengthens the firstintentional use interval weakly reduces the dis-position to use in state S and weakly shortensthe final resignation interval

(iii) A general increase in usE or bs

E weaklyshortens the initial resistance interval In addi-tion a general increase in bs

E weakly increasesthe disposition to use in states 0 and 1

How do patterns of use compare for two sub-stances that are the same in all respects except

26 If (E 0) yields a higher expected discounted payoffthan (E 1) then (E 1) is obviously not the DMrsquos bestchoice Conversely if (E 1) yields a weakly higher ex-pected discounted payoff than (E 0) then (E 1) is neces-sarily preferred to both (A 0) and (R 0) To understandwhy note that (a) us

E bsE VminSs1() us

E Vmax1s1() us

a Vmax1s1() for a A R[where the first inequality follows because the DM weaklyprefers (E 1) to (E 0) and the second inequality followsfrom Assumption 2] and (b) us

E bsE VminSs1()

usA bs

A VminSs1() (by Assumption 2) For (R 0)the desired conclusion follows from (a) for (A 0) it fol-lows from (a) and (b)

27 The DM prefers (E 1) to (E 0) if and only if heprefers it to E with the certainty of abstention The proba-bility pj

E does not enter this comparison

28 At least one of these intervals is always empty Thelength of the initial resistance interval is relevant only if pa-rameters change after the DM starts using the substance (oth-erwise he would never advance beyond state 1) In that case itsheds light on the DMrsquos ability to achieve permanent recovery

29 To allow for multiple optima we say that a parameterchange weakly shortens (lengthens) an interval if it weaklyreduces (increases) both the minimum and maximum lengthof the interval


that one is more addictive than the other (highervalues of ps

E and psA for all s) Part (i) of the

proposition provides a partial answer Not surpris-ingly an increase in addictiveness discourages useamong new users (reducing the disposition to usein state 0 shortening the first intentional use in-terval and lengthening the initial resistance inter-val) Strikingly it always has the opposite effecton hard-core addicts producing longer resignationintervals One might think that an increase inaddictiveness might discourage a relatively ad-vanced user from taking actions likely to placehim in an even more highly addicted state but thiseffect never materializes in the final resignationinterval Instead the DM is influenced by theincreased futility of resisting use at lower statesHe resigns himself to severe addiction because herecognizes his powerlessness to control his subse-quent behavior adequately at lower states despiteintentions to abstain According to part (i) generalchanges in the parameters governing payoffs fromthe avoidance activity (us

A and bsA) have similar

effectsHow does an improvement in rehabilitation

technology (higher values of usR for all s) affect

patterns of use According to part (ii) of theproposition use among those with low cumula-tive exposure increases in a strong sense (thedisposition to use rising in all states up to thepoint where the DM enters rehabilitation) Sincerehabilitation cushions the negative effects ofaddiction this is not surprising As in part (i)this development has the opposite effect onhard-core addicts shortening the resignation in-terval Notably increasing us

R only for states inthe resignation interval would have no effect onbehavior Thus for a general increase in us

R theDM turns away from intentional use in theresignation interval because rehabilitation be-comes a more attractive option in lower states

Part (ii) of Proposition 2 also implies that animprovement in rehabilitation technology canhave the perverse effect of shifting the entirepopulation distribution to more addicted statesProvided that all members of the populationstart out at s 0 this occurs when a generalincrease in us

R raises the lowest state at whichthe DM selects rehabilitation30

Part (iii) of the proposition concerns usE and

bsE These parameters do not relate to the novel

features of our model but we have includedtheir effects for completeness

Proposition 2 underscores the fact thatchanges in the environment have complex ef-fects on use often driving consumption amongnew users and hard-core addicts in oppositedirections It is natural to wonder whether thereare any general parameter changes that alwayshave the same directional effect on the disposi-tion to use in every addictive state Our nextresult provides an example if baseline well-being deteriorates more rapidly as the addictivestate rises then the disposition to use is lower inevery state This property holds in the standardrational addiction framework (ps

a 0) and ispreserved in the presence of cue-triggeredmistakes

PROPOSITION 3 Consider and derivedrespectively from w s(e x a) and w s(e x a) w s(e x a) ds (with the same values of ys rsq and ps

a) If ds is weakly increasing in s thedisposition to use is weakly higher with thanwith for all s

Propositions 2 and 3 shed light on the rela-tionship between income and the consumptionof addictive substances While an increase inincome raises the inclination to experiment rec-reationally it can reduce the inclination to useat higher addictive states accordingly themodel can generate higher rates of addictionamong the poor To see why suppose the utilityfunction has the following separable form ws(ex a) u(e) vs(x a) What happens when weadd a fixed increment to income in all statesThe parameters us

E and usA all rise by u(ys

) u(ys) which is weakly increasing in s(assuming ys is weakly decreasing in s) Theparameters us

R increase by u(ys rs ) u(ys ) u(ys ) u(ys) and theparameters bs

a increase by [u(ys q ) u(ys )] [u(ys q) u(ys)] 0 Thus wecan decompose the effect into three pieces (a) afixed increase in us

a equal to u(ys ) u(ys)for each s and a E A R (b) a general

30 From simulations we know that a general increase inus

R increases the lowest state at which the DM selectsrehabilitation for some parameter values and decreases it forothers


increase in usR and (c) a general increase in bs

a

for a E A Proposition 3 tells us that theeffect of the first piece is to weakly increase thedisposition to use in every state Part (ii) ofProposition 2 tells us that the second pieceincreases the disposition to use in state 0 andparts (i) and (iii) tell us the same thing for thethird piece Thus the addictive substance isnormal in state 0 Note however that the sec-ond and third pieces have ambiguous effects onthe disposition to use in more advanced states ofaddiction which is why the income effect canchange signs

B Patterns of Consumption

According to our theory the particular pat-tern of consumption that emerges in anyinstance depends systematically on the charac-teristics of the individual (including aptitude forcognitive control) the substance and the envi-ronment For reasonable parameter values themodel generates a wide variety of observedconsumption patterns31

Consider a highly addictive substance (psa

large) If baseline well-being declines rapidlywith consumption the DM may choose never touse [(E 0) at s 0] For most people crackcocaine appears to be a good example of this(see Goldstein 2001) In contrast if the declinein baseline well-being is initially gradual butaccelerates from one state to the next the modelcan produce a pattern of progressive resistanceThat is the DM may begin using the substanceintentionally engage in half-hearted abstention(and therefore use intermittently) after reachingan intermediate addictive state and shift to con-certed abstention after a string of bad luck Ifbad luck continues precommitment to absten-tion through rehabilitation may follow with sub-sequent probabilistic recidivism If baselinewell-being flattens out for sufficiently advancedaddictive states (the DM ldquohits bottomrdquo) themodel can also produce resignation That is aDM may give up opting for (E 1) once hereaches a highly addicted state after an unsuc-cessful battle to abstain

Now consider an enjoyable substance forwhich baseline well-being declines slowly withconsumption Irrespective of whether the prob-ability of entering the hot mode is high or lowconstant use often emerges Caffeine potentiallyfits this description

Finally a sufficiently sharp drop in the plea-sure generated by the substance from one ad-dictive state to the next can produce intentionalrecidivism That is the DM may choose (E 1)in one state and (R 0) in the next in which casehe oscillates between the two He enters reha-bilitation in each instance without any desire tostay clean he knows that he will resume usingthe substance upon release from rehabilitationand fully expects to enter rehabilitation onceagain This pattern is in fact observed amongserious heroin users when repeated use dilutesthe ldquohighrdquo (see Michael Massing 2000) It isevidence of fairly sophisticated forward think-ing among junkies whose objective is to renewthe high by temporarily getting clean and whoknow that rehabilitation accomplishes this morereliably than abstention

C Explaining the Distinctive Features ofAddiction

In Section I we argued that addiction is as-sociated with five distinctive behavioral pat-terns Our theory generates each of thesepatterns

1 Unsuccessful Attempts to QuitmdashSupposelife circumstances change over time graduallyshifting the parameters of the DMrsquos problemfrom to Suppose the DMrsquos best choice forstate 0 is (E 1) if prevails forever but thatthe optimal decision rule prescribes either (E0) (A 0) or (R 0) for all s if prevailsforever If the shift from to is eitherunanticipated or anticipated and sufficientlyslow the DM starts using the substance butsubsequently decides to quit unconditionallyWith p1

a 0 the attempt is unsuccessful wheneither (E 0) or (A 0) is chosen in state 1

2 Cue-Triggered RecidivismmdashFor the set-ting described in the previous paragraph unsuc-cessful attempts to quit are associated with highrealizations of c(a ) (that is exposure to rel-atively intense cues)

31 We have generated each of the patterns described inthis section through numerical simulations which we omitto conserve space


3 Self-Described MistakesmdashIn our modelchoices and preferences diverge whenever theDM selects (E 0) or (A 0) and then enters the hotmode This constitutes a recognizable mistake32

4 Self-Control through PrecommitmentmdashThe choice (R 0) is a costly precommitmentunder our assumptions its only purpose is toremove the option of consuming the substance

5 Self-Control through Behavioral and Cog-nitive TherapymdashThe choice (A 0) involvescostly cue-avoidance Its only purpose is to re-duce the probability of encountering cues thattrigger mistaken usage Though not modeledexplicitly cognitive therapy would influencebehavior in our setting by increasing MT (that israising the threshold impulse required to defeatcognitive control)

Our three central premises play critical rolesin accounting for each pattern We can removecue-triggered mistakes by setting MT sothat the DM always exercises cognitive controlWith this change ps

a 0 for all a and s and theDM always choose either (E 1) or (E 0) Allattempts to quit are successful and there is norecidivism Preferences and choices never di-verge so there are no mistakes The DM neverexercises self-control through precommitmentby choosing (R 0) or through cue-managementby choosing (A 0) Some sophistication is alsoessential otherwise the DM would ignore hissusceptibility to cue-triggered errors and makechoices based on the mistaken assumption thatps

a 0 for all a and sWe also observed in Section I that aggregate

consumption of addictive substances respondsto prices and information in the usual way Thistoo is consistent with our theory as users some-times make decisions in the cold mode

V Demand-Side Policy Analysis

In this section we study the welfare effects ofvarious public policies concerning addictive

substances In keeping with the focus of thepreceding sections we restrict attention to ldquode-mand siderdquo welfare effects ignoring ldquosupplysiderdquo consequences associated with the devel-opment of black markets the spread of corrup-tion and enforcement costs33

A The Welfare Criterion

In formulating our model we retain thestandard assumption that each individual hasa single coherent set of preferences Our de-parture which is grounded in the evidencefrom neuroscience presented in Section II isto assume that there are imperfections in theprocess by which the brain makes choicesand that these imperfections give rise to mis-takes in identifiable circumstances Since theindividual has only one set of preferencesdiscounted experiential utility yent0

twst(et

xt at) accurately measures his well-beingand is unambiguously the appropriate welfarestandard34

It may be tempting to reinterpret our model asone with multiple selves ldquohotrdquo and ldquocoldrdquowhere the preferences of the hot self can beinferred from choices in the hot mode Underthat interpretation our use of cold preferencesas a welfare standard is arbitrary In our viewthis interpretation commits a fallacy By assum-ing that choices are always consistent with un-derlying preferences it assumes away thepossibility that individuals make systematicmistakes This possibility is a central premise ofour analysis and is justified based on the state ofknowledge concerning the neuroscience of ad-diction One can certainly dispute the validity ofthis premise However given the premise andour adherence to the standard formulation ofpreferences the correct welfare criterion isunambiguous

32 When the HFM-generated forecast is sufficiently posi-tive cognitive override may not occur even when higher cog-nition forecasts undesirable consequences Thus an individualmay use a substance while simultaneously recognizing (interms of higher cognitive judgment) that this is a mistake

33 Supply-side effects are discussed elsewhere (seeeg MacCoun and Reuter 2001 J Miron and JZwiebel 1995)

34 This is in contrast with a number of the behavioraltheories discussed in Section VI for which one must eitheruse a weak welfare standard such as the Pareto criterion(applied to multiple selves or multiple perspectives) orselect a particular method of resolving conflicting prefer-ences for example by respecting the tastes of only one selfor perspective


B Policy Objectives

What might society hope to accomplishthrough public policies regarding addictive sub-stances Possible objectives include protectingthird parties from externalities (eg second-hand smoke) combatting misinformation andignorance moderating the consequences of un-insurable risks and helping consumers avoidmistakes Both externalities and informationalproblems provide well-understood rationalesfor government intervention and neither is in-trinsically linked to the novel aspects of ourframework We therefore focus primarily on thelast two sets of objectives

1 Amelioration of Uninsurable RisksmdashRiskand uncertainty relating to the effects of envi-ronmental cues on decision processes are cen-tral to our model The DMrsquos lack of knowledgeconcerning future states of nature t preventshim from perfectly forecasting future decisionmodes and choices in states for which he plansto select either (E 0) or (A 0) and therebycreates uncertainty about subsequent addictivestates This translates into monetary risk be-cause his resources depend on his addictivestate and because variation in expenditures onthe addictive substance and rehabilitation implyvariation in consumption of the nonaddictivegood Since the financial consequences of ad-dictionmdashits effects on job retention productiv-ity out-of-pocket medical costs (includingrehabilitation) and for some substances (egcocaine heroin) direct expendituresmdashare oftensubstantial this risk is quantitatively significant35

From the perspective of risk (ignoring otherconsiderations) policies that create actuariallyfair redistributions over realizations of futurestates of nature are beneficial (harmful) whenthey distribute resources toward (away from)outcomes for which the marginal utility of non-addictive consumption is relatively high In sub-sequent sections we initially impose theassumption that ws(e x a) u(e) vs(x a)which implies that the marginal utility derivedfrom nonaddictive consumption depends only

(and inversely) on the level of nonaddictiveconsumption We focus on this case because weregard it as a natural benchmark but we alsodiscuss the implications of relaxing separability

We assume throughout that private insurancemarkets fail completely As is well known thewelfare effects of public policies that redistrib-ute resources across states of nature can dependon the specific factors that cause markets to fail(see eg Mark V Pauly 1974) It is thereforeimportant to specify the source of the marketfailure and to explain how it interacts with thepolicies considered

We assume that private insurance companiesare unable either to observe or to verify the stateof nature t cues the DMrsquos decision mode theaddictive state lifestyle activities or consump-tion of the addictive substance36 The govern-ment is similarly handicapped However unlikeprivate companies it can observe transactionsinvolving legal addictive substances (typicallywithout identifying purchasers) and it can ma-nipulate the prices of these commoditiesthrough taxation and subsidization

Private companies can observe aspects oftreatment (rehabilitation and medical costs) butwe assume that treatment insurance is unavail-able because (i) practical considerations pre-clude ex ante contracting at age zero when risksare homogeneous (eg before teen or even pre-teen exposure) and (ii) adverse selection arisingfrom ex post heterogeneity precludes ex postcontracting37 The government is similarlyhandicapped by the second problem but canavoid the first by imposing a universal policy onall consumers ex ante

2 Mistake AvoidancemdashPublic policy canpotentially improve welfare by creating con-ditions that reduce the frequency with whichindividuals experience decision process mal-functions or by forcing them to make alternative

35 Among chronic users average annual expenditures oncocaine and heroin exceeded $10000 in 1999 (Office ofNational Drug Control Policy 2001a)

36 With respect to the addictive state clinical diagnosisof addiction is both costly and imprecise Consumption ispotentially observable when the substance is dispensed as aprescription medicine but in that case the same problemsarise as for treatment (discussed in the next paragraph)

37 In practice private health insurance policies do pro-vide some coverage for the treatment of addiction Yetmany people are not insured and coverage is typicallyincomplete


choices when malfunctions occur In our modelthese possibilities correspond respectively toreducing the probability of entering the hot modeand to ensuring abstention when appropriate

In solving the DMrsquos optimization problemwe treated the probabilities of entering the hotmode ps

a as fixed parameters Many of thepolicies considered below potentially changethese parameters for example one can model aban on advertising as a reduction in the volumeof cues encountered For some portions of ouranalysis we also allow for the possibility that ps

a

depends on the price of the addictive good qandor the DMrsquos income y We reason that thefrontal cortex is more likely to generate strongercognitive incentives and override cues when theimmediate consequences of use are more se-vere38 Accordingly we assume that MT weaklydecreases with y weakly increases with q andweakly increases with an equal increase in y andq39 It is useful to state these assumptions morecompactly in terms of ps

a (with the added tech-nical requirement of differentiability)

ASSUMPTION 3 The probability of enteringthe hot mode ps

a is differentiable in q and ywith

qps

a

yps

a 0

C When Is Government InterventionJustified

When do the objectives discussed in Sec-tion V B potentially justify government inter-

vention The following result provides aninitial answer Here and elsewhere we saythat use is continual if the DM selects (E 1)in every state

PROPOSITION 4 (i) Continual use solves theDMrsquos choice problem if and only if it is first best(in the sense that it solves the maximizationproblem when ps

a 0 for all a and s) (ii)Suppose there is some state s with ps

E 0 suchthat (E 1) is not a best choice in s Then theDMrsquos choices are not first best (in the sense thatsetting ps

a 0 for all a and s and reoptimizingstrictly increases the value function for somestates)

Part (i) tells us that noncontinual use isnecessary for the existence of a beneficialpolicy intervention Laissez-faire is thereforethe best policy for substance users who makeno serious attempt to abstain (eg contentedsmokers or coffee drinkers) Notably thisconclusion follows even when the substancein question is highly addictive ( ps

a risessharply with s) and well-being declines sig-nificantly with long-term use The intuition isthe same as for the final portion of Proposi-tion 1

Part (ii) tells us that noncontinual use is suf-ficient for the existence of a theoretical policyintervention that benefits the DM provided thedeparture from continual use occurs in a statefor which the DM is susceptible to cue-triggeredmistakes Of course this intervention may beimpractical given the governmentrsquos informationconstraints

D A Framework for Tax Policy Analysis

The formal results below concern the de-sirability of various types of tax policies Fol-lowing standard practice we evaluate thesepolicies by embedding our decision-maker ina simple economy and studying effects onequilibrium allocations Here we outline thestructure of the economic environment Nota-tion and some additional formal details ap-pear in Appendix A

The economy consists of an infinite sequenceof generations In the absence of governmentintervention every member of every generationis identical and confronts the decision problem

38 Since cognitive control often must be asserted quicklyif at all and since extrapolation of future consequences istime consuming we implicitly assume that the deploymentof cognitive control responds to variation in immediatecircumstance-specific consequences but not to variation infuture circumstance-specific consequences

39 When q is higher or y is lower the immediate negativeconsequences of use are plainly greater and potentiallymore likely to occupy the DMrsquos awareness When q and yrise by equal amounts the immediate hedonic payoff fromabstention rises while the immediate hedonic payoff fromuse is unchanged so the immediate negative consequence ofuse is again more severe It would also be natural to assumethat cue exposure c(a ) weakly declines in q (since useamong social contacts declines) and this would reinforceAssumption 3 In principle c(a ) could rise or fall withincome


described in Section III We interpret the DMrsquosdiscount factor as the product of a pure rate oftime preference and a constant single-periodsurvival probability We assume that the size ofeach new generation is just sufficient to keep thetotal population constant The total populationis very large and realization of hot and coldstates are independent across DMs so there isessentially no aggregate uncertainty Income ar-rives in the form of the nonaddictive good andthe addictive good is produced under competi-tive conditions with constant-returns-to-scaletechnology as are rehabilitation services Thusq and rs are fixed and equal to unit productioncosts (where the costs of rehabilitation servicespotentially vary with the addictive state)

In each period the government can tax (orsubsidize) either the addictive substance or re-habilitation (we consider these instruments oneat a time) There is no revenue requirementtaxes are purely corrective By assumption thegovernment cannot condition the associated taxrates on either the DMrsquos age or his addictivestate This could reflect either the practical dif-ficulties associated with tailoring these taxesand subsidies to an individualrsquos conditions (in-cluding the need for clinical diagnosis) or pri-vacy concerns Imagine in particular that thetaxsubsidy for the addictive substance is eitherapplied to anonymous transactions (like a salestax) or imposed on producers (like a value-added tax) while the rehabilitation taxsubsidynominally falls on service providers (again likea value-added tax) The government can also useage-specific (equivalently generation-specific)lump-sum instruments An intertemporal policyspecifies values for all available taxsubsidy in-struments in every period

Since there is no borrowing or lending in ourmodel and since we do not wish to advantagethe government artificially we assume that pol-icies cannot redistribute resources across peri-ods We say that an intertemporal policy isfeasible if there is for each generation an op-timal decision rule such that the governmentrsquosbudget is balanced in every period Feasiblepolicies permit within-period transfers acrossgenerations which can mimic borrowing andlending thereby leaving the government in anartificially advantageous position One couldtherefore argue for a stronger restriction requir-ing government budget balance for each gener-

ation within each period While we impose theweaker requirement our results also hold forthe stronger requirement40

A steady-state policy prescribes a constanttax rate and constant age-specific lump-sumtaxes Notably each individualrsquos problem ispotentially nonstationary because steady-statelump-sum taxsubsidies may change with ageThe set of feasible steady-state policies includesthe zero-tax alternative henceforth denoted for which all taxsubsidy instruments are set tozero

In the next two sections we focus on thesteady-state welfare effects of steady-statepolicies (often dropping the modifier ldquosteady-staterdquo for brevity) For any steady-state pol-icy we use the lifetime expected discountedhedonic payoff for the representative individ-ual as our welfare measure An optimalsteady-state policy maximizes this payoffamong all feasible steady-state policies Thisobjective function respects each individualrsquostime preference over his own lifetime but isinfinitely patient with regard to intergenera-tional comparisons in effect placing equalweight on all generations Since the DMrsquoschoice set is discrete best choices are ofteninsensitive to small parameter changes so theoptimal policy is typically not unique

E Taxation and Subsidization of AddictiveSubstances

Addictive substances are often heavily taxed(eg nicotine and alcohol) and occasionallysubsidized (see eg the description of a Swissheroin prescription program in MacCoun andReuter 2001) Some policy analysts argue fortaxation of addictive substances on the groundsthat this discourages excessive use (eg Gruberand Koszegi 2001) Others suggest that in theabsence of externalities use is voluntary solaissez-faire is best (eg Becker and Murphy1988) Our theory of addiction suggests a morenuanced view

Proposition 5 below relates the sign of theoptimal tax rate on the addictive substance to

40 In fact the proof of Proposition 5 requires only minoradjustments when we impose the strong requirement Prop-osition 6 holds as stated under either restriction


observable patterns of consumption Notablythe consumption patterns that determine opti-mal tax rates are endogenous and the proposi-tion requires us to assess them at the optimal taxrates41 This feature is common to many well-known optimal-tax results For example theRamsey rule relates optimal commodity taxrates to compensated demand elasticities evalu-ated at the optimal tax rates (though the rule isfrequently stated in a way that disguises thisdependency)

The proposition refers to the following twopossible patterns involving the likelihood ofuse42

Condition A For every age t the likelihood ofuse is weakly increasing in s over states reachedwith positive probability at that age and theDM does not enter rehabilitation in the lowestsuch state43 Moreover at some age t at leasttwo addictive states are reached with positiveprobability

Condition B For every age t the likelihood ofuse is weakly decreasing in s over states reachedwith positive probability at that age44 More-over at some age t at least two addictive statesare reached with positive probability with nei-ther expected use nor ys constant over suchstates

For each condition the requirement ldquofor all trdquois less demanding than it might initially appearRemember that in the absence of taxes andsubsidies each DMrsquos problem is stationary andthe best choices at each state are independent ofage In a steady state for the economy agematters only because it affects the lump-sum tax(or subsidy) If the lump sums are relativelysmall the general pattern of use will tend to besimilar at different ages provided it is not toosensitive to small changes in income

PROPOSITION 5 Suppose that ws(e x a) u(e) vs(x a) that ys is weakly decreasing ins and that ps

a does not depend on prices orincome

(i) Consider an optimal steady-state policy forwhich all budget-balancing optimal deci-sion rules satisfy Condition A The taxrate on the addictive substance is strictlynegative

(ii) Consider an optimal steady-state policy forwhich all budget-balancing optimal deci-sion rules satisfy Condition B If q is suffi-ciently small the tax rate on the addictivesubstance is strictly positive

To develop intuition for this result note thattaxation (or subsidization) potentially affectswelfare through three channels First it canchange decisions in the cold mode Second itcan redistribute resources across uncertain out-comes Third it can alter the effects of environ-mental cues on operational decision modes(through the trigger mapping T) With ps

a inde-pendent of prices and income the third channelvanishes (we discuss the implications of rein-stating it below) Effects involving the secondchannel dominate welfare calculations for smalltaxes and subsidies because they are generallyfirst order while effects involving the first chan-nel are not45 Accordingly starting from a sit-uation with no taxes one can determine whethera small tax or subsidy improves welfare byfocusing on the correlation between the taxed

41 Alternatively one can make statements about welfare-improving changes assessing usage patterns at arbitrarystarting points For example from the proof of Proposition5 we also have the following results eliminating a positivetax is beneficial if initially Condition A holds eliminating apositive subsidy is beneficial if initially Condition B holdsand q is small if Condition A holds with the no-tax policy a small subsidy is welfare improving if Condition Bholds with and q is small a small tax is welfare improving

42 In Appendix A we define st(13) as the probability of

use in state s at age t given a decision rule 13 accounting forthe possibility of entering the hot mode Here the ldquolikeli-hood of userdquo refers to s

t(13) Note that the likelihood of useis necessarily weakly increasing in s when the disposition touse is weakly increasing in s

43 Since the DMrsquos decision problem is potentially non-stationary it is possible for him to find himself in a statebeyond the lowest one in which he would select rehabilita-tion during the same period

44 This occurs for example if best choices are uniquethe disposition to use is weakly decreasing in s the firstintentional use interval is nonempty and ps

a is constantoutside of this interval (ie the DM is fully addicted by thetime he attempts to refrain from consuming the substance)

45 With continuous decision variables and interior solu-tions the first channel would be second order for small taxesand subsidies With discrete decision variables (as in ourcurrent model) it is literally zero for sufficiently small taxesand subsidies


activity and the marginal utility of nonaddictiveconsumption46 This helps to build intuitionconcerning the signs of optimal tax rates Oneshould bear in mind however that the optimal-tax problem is more complex because at theoptimum welfare effects involving the firstchannel (incentive effects) are also first order

A policy provides de facto insurance if itredistributes age-t resources toward outcomesin which the marginal utility of nonaddictiveconsumption is relatively high which in thebenchmark case [ws(e x a) u(e) vs(x a)]means that the level of nonaddictive consump-tion is relatively low This occurs when otherexpenditures are high and when the state is itselfhigh (since ys weakly declines with s)47 Asubsidy necessarily redistributes resources to-ward outcomes with relatively high expendi-tures on addictive substances Moreover if thelikelihood of use increases with the addictivestate (Condition A) it also redistributes re-sources toward outcomes for which income isrelatively low Since both effects are beneficiala subsidy is desirable [part (i)] Conversely ifthe likelihood of use declines with the addictivestate (Condition B) a positive tax (with abudget-balancing lump-sum payout) redistrib-utes resources toward outcomes for which in-come is relatively low and rehabilitationexpenditures are relatively high It also redis-tributes resources away from outcomes withrelatively high expenditures on addictive sub-stances but this effect is secondary when q issmall rendering the tax beneficial [part (ii)]

Proposition 5 underscores the fact that differ-ent policies are appropriate for different addic-tive substances and that the characteristics ofgood policies are related to usage patterns As

we have seen in Section IV usage patterns arein turn systematically related to aspects of thesubstance the user and the environment

Part (i) suggests that a subsidy may be wel-fare improving in the case of a substance forwhich initial use tends to be ldquospur of the mo-mentrdquo but where an intention to use becomesincreasingly predominant as the individual be-comes more addicted The argument for subsi-dization is stronger when the substance inquestion is more expensive The apparent im-plication that the government might beneficiallysubsidize substances such as cocaine and heroinis provocative to say the least and it should betempered by several considerations includingthe likely existence of externalities the poten-tial effects of price and income on the triggermechanism (discussed below) and the fact thatCondition A apparently does not hold univer-sally as many addicts seek treatment Still ouranalysis adds a potentially important cautionarynote to existing discussions of the benefits of sintaxes (eg Gruber and Koszegi 2001 TedOrsquoDonoghue and Matthew Rabin 2004) whichcan violate social insurance principles by penal-izing those who have experienced bad luck Italso provides a framework for understandingthe potential benefits of somewhat more refinedapproaches such as the Swiss policy of provid-ing cheap heroin to users who cross some diag-nostic threshold of addiction and who are notinterested in rehabilitation

Part (ii) suggests that a tax may be welfareimproving in the case of an inexpensive sub-stance that people initially use regularly forwhich attempts to abstain begin only after cuetriggers are well established and stable (so thatthey change little with further use) Coffee cig-arettes and alcohol arguably fall into thiscategory

How robust are these findings Complemen-tarity between addictive and nonaddictive con-sumption would raise the marginal utility ofnonaddictive consumption whenever the DMuses the addictive good strengthening the ad-vantages of a subsidy thereby reinforcing part(i) but potentially reversing part (ii) Substitut-ability would reduce the marginal utility of non-addictive consumption whenever the DM usesthe addictive good strengthening the advan-tages of a tax thereby reinforcing part (ii) butpotentially reversing part (i)

46 There are some subtleties here A small tax or subsidythat changes cold-mode decisions can alter the correlationbetween a taxed activity and the marginal utility of nonad-dictive consumption thereby changing effects through thesecond channel With discrete choice sets the pertinentcorrelation can change dramatically even for tiny taxes andsubsidies

47 In principle the government could also redistributeresources through an income tax Implicitly we take theincome-tax system as exogenously given This is reasonableas long as addiction is not one of the primary factorsinfluencing income distribution and the equityndashefficiencytrade-offs that an optimal income tax system is intended toaddress


We can also relax the assumption that psa is

invariant with respect to taxation and subsidi-zation A tax of per unit increases price by and from individuals of age t raises less than in per capita revenues Suppose the governmentdistributes the revenue raised from each agegroup back to the same age group as a lumpsum Since the amount received by each indi-vidual is less than the price increase Assump-tion 3 implies that ps

a falls in every state Anypolicy that reduces ps

a weakly increases welfarethrough the third channel [strictly if the state isreached with positive probability and the DMselects (a 0)] This strengthens the advantagesof a tax reinforcing part (ii) of the propositionand potentially reversing part (i)48

F Harm-Reduction Policies

Subsidization of rehabilitation is relativelycommon Popular justifications appeal to thenotion that treatment should be affordable anduniversally available though sometimes posi-tive externalities are invoked

In the context of our model there are at leasttwo reasons to subsidize rehabilitation Firstthis provides de facto insurance for a largeuncertain expense Second under Assumption3 the DM is less prone to make cue-triggeredmistakes when he receives resources in kind(through a rehabilitation subsidy) rather than incash

There is however an additional consider-ation arising from the correlation between reha-bilitation and income If rehabilitation is morelikely at advanced stages of addiction then asubsidy beneficially redistributes resources to-ward low-income states Since this reinforcesthe considerations discussed in the previousparagraph subsidized rehabilitation is unambig-uously desirable If however rehabilitation isless likely at advanced stages of addiction thena subsidy detrimentally redistributes resourcestoward high-income states offsetting the con-siderations discussed in the previous paragraphFormally one can prove a result analogous toProposition 5 relating the optimal taxsubsidy

treatment of rehabilitation to rehabilitationpatterns

Our next result deals instead with the welfareeffects of small rehabilitation taxes and subsi-dies It shows that a small rehabilitation subsidyis beneficial and a small tax harmful underextremely general conditions at the no-tax al-ternative rehabilitation must be chosen insome state and there must be some random-ness49 Here we allow from the outset for thepossibility that ps

a depends on ys and q

PROPOSITION 6 Suppose that ws(e x a) u(e) vs(x a) that ys is weakly decreasing ins and that rs q for all s Suppose also that inthe absence of taxes and subsidies (that is withpolicy ) the following conditions hold firstthere is at least one state in which rehabilitationis a best choice second rehabilitation is theunique best choice in the earliest of these thirdfor some earlier state (other than 0) (E 1) isnot a best choice Then within the class ofpolicies that do not create net inter-cohorttransfers a small steady-state subsidy for reha-bilitation is beneficial and a small steady-statetax is harmful

Since Proposition 6 holds even when the costof rehabilitation is very small it is not primarilyabout the desirability of insuring a large uncer-tain expense For the correct intuition note thatwith the no-tax alternative each DMrsquos prob-lem is stationary so best choices for each stateare independent of age This implies that theDM can never advance beyond the first state inwhich (R 0) is the best choice Consequentlythe likelihood of rehabilitation is positively cor-related with the addictive state and negativelycorrelated with income so the three effects dis-cussed at the outset of this section work in thesame direction in favor of subsidization Thepractical lesson is simple if addiction is rela-tively unlikely to advance beyond the pointwhere people start to seek rehabilitation thensubsidies are unambiguously desirable

An appropriately modified version of ourmodel could address the effects of other harm-

48 The proof of Proposition 6 formally demonstrates aclosely related point in the context of a subsidy for rehabil-itation services

49 The assumption that (E 1) is not a best choice in everystate up to the first in which rehabilitation is selected en-sures some randomness


reduction policies such as needle exchangesWe leave this for future work

G Criminalization

Historically criminalization has been the cor-nerstone of US drug policy with more than600000 citizens incarcerated for drug-relatedoffenses in 1999 (Office of National Drug Con-trol Policy 2001b) It affects users through twodistinct channels a price effect and a rationingeffect The price effect refers to changes in themarginal cost of using the substance resultingfrom penalties and other costs imposed on usersand suppliers The rationing effect refers to in-terference with the process of matching buyersand sellers since criminalization forces buyersand sellers to carry out transactions secretivelybuyers sometimes have difficulty locatingsupply50

It is instructive to consider the price andrationing effects separately The price effect isequivalent to a tax policy in which the revenueraised by the tax is destroyed If criminalizationonly created a price effect taxation would dom-inate it

Now consider the rationing effect Disrupt-ing access to supply is potentially beneficialwhen the DM chooses (E 0) or ( A 0) andpotentially detrimental when he chooses (E1) However the impact of the rationing ef-fect on consumption may be smaller when theDM chooses (E 1) An individual who in-tends to consume an illegal substance can setabout locating supply deliberately and sys-tematically and can maintain stocks in antic-ipation of transitory difficulties In theextreme case where the rationing effect hasno impact on consumption when the DM se-lects (E 1) it is unambiguously beneficialThis conclusion is obviously weakened oreven reversed if unsuccessful search activityis costly (eg because it exposes the DM tophysical harm)51

It follows that in some circumstances crimi-nalization may be superior to taxation and tolaissez-faire This result deserves emphasissince it is difficult to justify a policy of crimi-nalization based on demand-side welfare con-siderations without adopting the nonstandardperspective that supply disruptions can avertmistakes52 Since it is better not to disruptplanned consumption the case for criminaliza-tion is ironically strongest when enforcementis imperfect

H Selective Legalization with ControlledDistribution

Some policies permit transactions involvingaddictive substances in certain circumstancesbut not in others Examples include a 1998Swiss law legalizing the prescription of heroinfor severe addicts and ldquoblue lawsrdquo prohibitingalcohol sales on Sundays

Policies of selective legalization with con-trolled distribution often make deliberateplanning a prerequisite for availability selec-tively disrupting impulsive use without dis-turbing planned use (assuming the hot modeonly activates behaviors that target immediateconsumption) This effect is potentially ben-eficial if unintended For example with bluelaws alcoholics can make themselves lessvulnerable to compulsive drinking on Sun-days by choosing not to stock up in advanceThese laws appear to reduce impulsive use inpractice (Peter T Kilborn 2003 T Norstromand O J Skog 2003)

A prescription requirement can play a similarrole provided prescriptions are filled with a lagTo represent this possibility formally we mod-ify our model as follows Imagine that in eachperiod m the DM must decide whether to ldquocallinrdquo a prescription for the substance Taking thisaction makes the substance available in periodm 1 otherwise it is unavailable and con-sumption is impossible

With this option the DM can alwaysachieve the first-best outcome Solving the

50 Probabilistic consumption following the choice (E 1)changes the value function somewhat but the results fromSection IV extend to this case See Goldstein and Kalant(1990) for evidence that drug usage declines as substancesbecome less available

51 The costs of a successful search are part of the priceeffect

52 Though the mechanisms considered in this paper in-volve stochastic mistakes the same conclusion would fol-low in a model with deterministic mistakes for exampleone in which the DM always errs by placing too muchweight on the immediate hedonic reward


dynamic programming problem with ps 0for all s yields a deterministic consumptionpath The DM can mimic this outcome bycalling in his prescription in period m if andonly if he consumes the substance in periodm 1 on the first-best path In this way heprecommits to the first-best choice by opti-mally rationing himself53

If the hot mode also activates behaviors thattarget future consumption the preceding policyis ineffective However a small modificationrestores the first-best outcome allow the DM tocancel irrevocably at any point in period m hisprescription for m 1 It is then optimal forhim to cancel during period m while in the coldmode if and only if he does not wish to consumethe substance in period m 154

In more realistic settings these policiesmight not permit consumers to achieve first-best outcomes If for example the desirabil-ity of using a substance in period m dependsupon conditions (eg mood) that are not re-solved until the period is underway the indi-vidual may sometimes regret failing to call ina prescription However the policy stillweakly benefits consumers because it pro-vides them with a tool for self-regulationwithout mandating its use

Heterogeneity across individuals makes se-lective legalization with controlled distributioneven more attractive relative to other policies Aprescription program accommodates heteroge-neity by providing consumers with discretionintentional users can continue to indulge with-out impediment while unintentional users nev-ertheless benefit from improved self-control Incontrast any feasible tax subsidy or criminalstatute may be inappropriatemdasheven harmfulmdashfor large subsets of consumers

The policies considered in this section wouldbe advantageous in any model where the DMmakes similar types of mistakes and where he

understands this proclivity The particular sto-chastic mechanism discussed in this paper is notessential Our conclusions do depend on theassumption that the government can limit resaleof the substance (eg by requiring on-site ad-ministration) and can suppress illicit supplyNotably selective legalization impairs blackmarkets by siphoning off demand

I Policies Affecting Cue-Triggered DecisionProcesses

In our model public policy can potentiallyhelp consumers by attenuating either exposureor sensitivity to cues (ie reducing c(a ) orM(c s a ) or raising MT) Arguably theproducers of addictive substances raise the like-lihood of triggering hot modes by exposingconsumers to ubiquitous cues through billboardstelevision advertisements product placement instores and so forth Advertising and marketingrestrictions of the type imposed on tobacco andalcohol may eliminate a cause of compulsive useRestrictions on public consumption may havesimilar effects

Other public policies may reduce cue-sensitivity by creating counter-cues Braziland Canada require every pack of cigarettes todisplay a prominent viscerally charged imagedepicting some deleterious consequence ofsmoking such as erectile dysfunction lung dis-ease or neonatal morbidity55 These counter-cues are designed to activate the cognitivecontrol process described in Section II

In our model policies that reduce the likeli-hood of cue-triggered mistakes by removingproblematic cues or establishing counter-cuesunambiguously increase welfare As with selec-tive legalization these policies are attractivebecause they are noncoercive because theyaccommodate individual heterogeneity andbecause they have the potential to reduce unin-tended use without distorting choice in the colddecision mode Though individuals may havesome ability to avoid problematic cues and cre-ate their own counter-cues the government isarguably better positioned to do this

53 In a related analysis Loewenstein et al (2000) em-phasize the role of ldquomandatory waiting periodsrdquo in a modelwhere agents systematically overconsume durable goods

54 Alternatively if the hot mode has a greater tendencyto activate behaviors targeting future consumption when theplanning horizon is short one could restore (or at leastenhance) the policyrsquos efficacy simply by lengthening the lagbetween prescription requests and availability (eg callingin a prescription in period m makes the substance availablein m k with k 1)

55 See httpwwwhc-scgccahecs-sesctobaccoresearcharchive for a description and some preliminaryevidence on the effectiveness of the Canadian program


VI Related Literature

Existing economic theories of addiction in-clude (i) variations on the standard model ofintertemporal decision making (Becker andMurphy 1988 Orphanides and Zervos 1995)including generalizations that allow for randomshocks and state-contingent utility (Hung 2000Laibson 2001) (ii) models with ldquoprojectionbiasrdquo wherein agents mistakenly assume thatfuture tastes will resemble current tastes butwhich otherwise conform to the standard model(Loewenstein 1996 1999 Loewenstein et al2001) (iii) models with present-biased prefer-ences and either naive or sophisticated expecta-tions (OrsquoDonoghue and Rabin 1999 2000Gruber and Koszegi 2001) and (iv) models ofldquotemptationrdquo wherein well-being depends notonly upon the chosen action but also on actionsnot chosen (Gul and Pesendorfer 2001a bLaibson 2001) While all of these theories con-tribute to our understanding of addiction andshare some important features with our modelnone adheres to all of the central premises setforth and justified in Section II In particularnone of these models depicts addiction as aprogressive susceptibility to stochastic environ-mental cues that can trigger mistaken usage

All models of rational addiction (beginningwith Becker and Murphy 1988) presupposecomplete alignment of choices and time-consistent preferences thereby denying the pos-sibility of mistakes Precommitments are neverstrictly beneficial and a user would never statea sincere unconditional intention to quit with-out following through Stochastic environmen-tal cues play a role in Laibsonrsquos (2001)extension but the mechanism involves hedoniceffects (cues trigger a change in taste for thesubstance) rather than mistakes Laibsonrsquosframework can account for voluntary admissionto rehabilitation clinics and related behaviorsprovided that these activities reduce the likeli-hood of experiencing cravings However itcannot account for the observation that manyaddicts seek in-patient treatment not becausethey expect to avoid cravings but rather pre-cisely because they anticipate cravings and wishto control their reactions Furthermore even ininstances where entering a rehabilitation facilitydoes reduce the likelihood of cravings (eg byremoving environmental cues) the standard

framework implies counterfactually that the ad-dict would find the facilityrsquos program more at-tractive if it made the substance available upondemand (in case of cravings)

Adding projection bias to the standard modelintroduces the possibility that users may regardpast actions as mistakes For example an addictmay blame his initial drug use on a failure toanticipate the escalating difficulty of abstentionCoupled with state-contingent utility shocks (asin Laibsonrsquos model) projection bias could ac-count both for the high frequency of attemptedquitting (when not triggered users underesti-mate the future difficulty of abstention) and thehigh frequency of failure (once triggered usersoverestimate the future difficulty of continuedabstention) However even with projectionbias an otherwise standard decision-makerwould never anticipate making mistakes in thefuture and sees no need for precommitments

In models with present-biased decision-makers choice is always aligned with the pref-erences prevailing at the moment when thechoice is made Even so one can interpretpresent-bias as shorthand for considerations thatlead to systematic mistakes in favor of imme-diate gratification contrary to true (long-run)preferences (see eg Gruber and Koszegi2001) As a model of addiction this frameworksuffers from two main shortcomings First thedecision-making bias is not domain-specific Apresent-biased decision-maker mistakenly con-sumes all pleasurable commodities excessivelyin this respect there is nothing special aboutaddictive substances Second the bias is alwaysoperativemdashit is not cue-conditioned

In principle one could formulate a modelwith a powerful narrow-domain cue-triggeredpresent-bias The resulting model (which doesnot appear in the literature) would conform toour premises indeed it would be nearly equiv-alent to our approach Our model is somewhatsimpler and more tractable than this alternativebecause we treat behavior in the hot mode asmechanical whereas this present-bias approachwould portray even triggered choices as optimalgiven well-behaved preferences Naturally forour model one can say that the triggered decision-maker acts as if he optimizes subject to well-behaved preferences that attach enormousimportance to consuming the addictive sub-stance but we think this ldquoas ifrdquo representation is


unenlightening Since the decision-maker is as-sumed always to consume the substance in thehot mode and since we regard this as a mistakewhenever he would behave differently in thecold mode the representation illuminates nei-ther choices nor welfare

Finally Gul and Pesendorfer (2001a b) modeladdictive behaviors by defining preferences overboth the chosen action and actions not chosenthereby providing a potential role for ldquotemptationrdquoand a rationale for precommitment Their axiom-atic approach embraces the doctrine of revealedpreference and therefore presupposes an align-ment of choices and preferences ruling out thepossibility of mistakes In addition their model asformulated does not examine the role of stochas-tic cues in stimulating use

VII Final Remarks

This paper develops an economic model ofaddiction based on three premises (i) useamong addicts is frequently a mistake (a patho-logical divergence between choice and pref-erence) (ii) experience with an addictive sub-stance sensitizes an individual to environmentalcues that trigger mistaken usage and (iii) ad-dicts understand their susceptibility to cue-trig-gered mistakes and act with some degree ofsophistication We argue that these premisesfind strong support in evidence from psychol-ogy neuroscience and clinical practice Re-search indicates that addictive substancessystematically interfere with the proper opera-tion of an important process which the brainuses to forecast near-term hedonic rewards(pleasure) and this leads to strong misguidedcue-triggered impulses that often defeat highercognitive control As a matter of formal math-ematics our model is tractable and involves asmall departure from the standard framework Itgenerates a plausible mapping from the charac-teristics of the user substance and environmentto dynamic behavior It accounts for a numberof important patterns associated with addictiongives rise to a clear welfare standard and hasnovel implications for public policy

Our theory also has potentially important im-plications for empirical studies of addiction Itsuggests that users of addictive substances mayrespond very differently to changes in priceswith dramatically different implications for

welfare depending on whether decisions reflectldquohotrdquo impulses or ldquocoldrdquo deliberation In con-trast existing studies treat data on consumptionas if it were generated by a single process

The model could be extended in a variety ofways to improve realism and predictive powerPossibilities include developing a more com-plete model of cognitive control in which futureconsequences may influence the likelihood ofoverriding HFM-generated impulses (throughthe threshold MT) adding stochastic taste shocksrealized at the outset of each period (to producevariation in the contingent plan chosen for eachstate) allowing payoffs (ws) to depend directlyon (to reflect the hedonic effects of cravings)allowing for imperfect information concerningan individualrsquos susceptibility to cue-triggeredmistakes introducing partial rather than fullself-understanding modeling life-cycle changes(either anticipated or unanticipated) in prefer-ences and susceptibilities resulting from agingand changes in circumstances and modeling thelong-term effects of early-life experiences

It is natural to wonder whether the modelapplies not just to addictive substances but alsoto other problematic behaviors such as overeat-ing or compulsive shopping These questionsare currently the subject of study among neuro-scientists and psychologists and it is too earlyto say whether similar brain processes are atwork56 Notably people who suffer from patho-logical gambling overeating compulsive shop-ping and kleptomania describe their experienceas involving strong and often overwhelmingcravings they respond to cues such as stress andadvertisements and they exhibit cycles ofbinges and abstention

APPENDIX A THE DYNAMIC ECONOMY

This appendix contains additional technicaldetails concerning the economy described in

56 Some preliminary evidence suggests that there may besome connection For example compulsive gamblers andkleptomaniacs respond to drugs such as naltrexone whichblock the brainrsquos ability to experience euphoric states com-pulsive gamblers and bulimics experience sudden relapse evenafter many years of abstinence See Holden (2001a) for adiscussion of recent research concerning the commonalitiesbetween various behavioral pathologies and substanceaddiction


Section V D and referenced in Propositions 5and 6

Let g denote generation t denote age and mdenote time Members of generation g are bornin period m g and reach age t in period m g t Let denote the pure rate of time pref-erence and let denote the constant single-period survival probability so that Thesize of each new generation at age t 0 is (1 )N where N is the constant size of the totalpopulation

Let m denote the taxessubsidies applied inperiod m including either a tax on the addictivesubstance m or a tax on rehabilitation m aswell as age-specific lump-sum instruments T tmThe period-m policy determines tax-inclusiveprices and incomes from which we can com-pute (as described in Section III) for each gen-eration g m a parameter vector gt (1

gt Sgt) with t m g applicable in

period m An intertemporal policy assigns apolicy m to each period m and induces foreach generation an infinite sequence of param-eter vectors g (g0 g1 ) Since gt canvary over t (in contrast to the case treated insections III and IV) we must allow choice tovary with age as well as the addictive state Adecision rule 13 maps age t and state s into aprobability distribution over (E 1) (E 0) (A0) (R 0) (note that we allow for randomiza-tions) and implies a probability s

t(13) of use instate s at age t We use 13g to denote the decisionrule of generation g The optimized value func-tion Vs

t(g) depends on the particular sequenceof parameters confronted by generation g andvaries with age t Since decisions are discretean optimal decision rule need not be unique andindeed is definitely not unique when it involvesrandomizations

The optimized usage probabilities generate astate-transition probability matrix t(13g) For alarge population of DMs starting in state 0 atage 0 and following decision rule 13g the pop-ulation distribution across addictive states atage t is zt(13g) [k0

t1 k(13g)] z0 where z0 isan S-dimensional vector with a 1 in the firstposition and zeros elsewhere

We say that an intertemporal policy isfeasible if there is for each generation g somedecision rule 13g solving the DMrsquos choice prob-lem given g induced by such that thegovernmentrsquos budget is balanced in every pe-

riod A steady-state policy prescribes aconstant tax rate either or and constantage-specific lump-sum taxes T t Each genera-tion faces the same sequence of parameters (0 1 ) and V0

0() is the lifetimediscounted expected hedonic payoff for the rep-resentative individual

APPENDIX B PROOFS

Here we prove Propositions 3 and 4 andsketch the proofs of Propositions 1 2 5 and 6to conserve space Complete proofs are avail-able on the AERrsquos web site

SKETCH OF PROOF FOR PROPOSITION 1Sketch for parts (i-a) and (i-b)mdashThe proof

involves three stepsStep 1 Consider and such that (1)

k k (2) i i for i k and (3) Vs() Vs() for all s Then (a) for all j k Vj() Vj() Vj1() Vj1() and (b) for allj k Vj() Vj() Vj1() Vj1()The argument omitted involves inductionstarting with j 1 for part (a) and with j Sfor part (b)

Step 2 Consider and such that (1)k k (2) i i for i k and (3) Vs() Vs() for all s Then (a) for j k the disposi-tion to use in state j is weakly higher with than with and (b) for j k the disposition touse in state j is weakly lower with than with These conclusions follow from step 1 whichimplies that for j k ( j k) the difference incontinuation values following abstention anduse and hence the disincentive to use is weaklygreater (smaller) with than with

Step 3 It is easy to verify that Vs() isweakly increasing in uk

a and bka and weakly

decreasing in pka Combining this with step 2

completes the proof of parts (i-a) and (i-b)

Sketch for part (i-c)mdashConsider two param-eter vectors and such that b j

E b jE with all

other components equal or p jE pj

E with allother components equal We argue in twosteps that the disposition to use in state j isweakly higher with than with

Step 1 (a) If (E 1) is optimal in state j with then it is optimal in state j with and (b) if(E 1) is the unique optimal choice in state j with then it is the unique optimal choice in state j


with When p jE pj

E and all other componentsof and are equal (a) and (b) follow frompart (ii) of the proposition When b j

E b jE and

all other components of and are equal onecan show that the difference in discounted con-tinuation values following abstention and use instate j and hence the disincentive to use isstrictly less than the increase in the immediatebenefits of use b j

E b jE If the DM weakly

prefers use to abstention with he must there-fore strictly prefer it with

Step 2 (a) If neither (E 1) nor (E 0) areoptimal choices in state j for then the sets ofoptimal state j choices are identical with and (b) if either (A 0) or (R 0) is optimal in statej with it is also optimal with In each casethe result follows from the easily verified factthat the same value function Vs( ) continues tosatisfy the valuation equation (1) when the pa-rameter vector is changed from to

From part (a) of step 1 and part (a) of step 2the maximum disposition to use in state j isweakly greater with than with From part (b)of step 1 and part (b) of step 2 the minimumdisposition to use in state j is weakly greaterwith than with

Now consider two parameter vectors and such that u j

R u jR with all other components

equal We claim that if something other than (R0) is optimal in state j with then it is alsooptimal in state j with (from which it followsthat the maximum disposition to use cannot behigher with ) moreover if (R 0) is not optimalin state j with then the sets of optimal state jchoices are identical with and (from whichit follows that the minimum disposition to usecannot be higher with ) Analogously to step 2these conclusions follow from the easily veri-fied fact that the same value function Vs( )continues to satisfy the valuation equation (1)when the parameter vector is changed from to

Sketch for part (ii)mdashSuppose coincideswith except for pj

E pjA uj

A ujR andor bj

A

(subject to the restrictions imposed by Assump-tions 1 and 2) We claim that if (E 1) is optimalin state j for it is also optimal in state j for moreover if (E 1) is the unique optimum in thefirst instance it is also the unique optimum inthe second instance Analogously to step 2 ofpart (i-c) these conclusions follow from the

easily verified fact that the same value functionVs( ) continues to satisfy the valuation equa-tion (1) when the parameter vector is changedfrom to Part (ii) follows directly

SKETCH OF PROOF FOR PROPOSITION 2The proposition is proved by breaking each

change into components where the effect ofeach component is either neutral or described byProposition 1

To illustrate we consider the effect of chang-ing ps

E on the length of the final resignationinterval Consider and with ps

E psE for all

s (and all other parameters fixed) With let s3

denote the first state (working backward from S)in which (E 1) is not an optimal choice thisdefines the longest possible resignation intervalLet s0

3 s3 denote the first state (working back-ward from S) in which something other than (E1) is an optimal choice this defines the shortestpossible resignation interval Remember that s3

and s03 may differ because the optimal choice in

each state is not necessarily unique Considermoving from to in two steps (1) Changefrom ps

E to psE for s s3 Since (E 1) is initially

optimal for all such states this leaves all opti-mal choices unchanged [Proposition 1 part (ii)coupled with the observation that when (E 1) isoptimal neither (A 0) nor (R 0) is ever opti-mal] (2) Change from ps

E to psE for s s3 This

weakly increases the disposition to use in statess3 1 through S [Proposition 1 part (i-b)]Thus the disposition to use in all states s s3

is weakly lower with than with It followsthat (E 1) continues to be an optimal choice instates s s3 with so the maximum finalresignation interval is weakly longer with thanwith Since nothing other than (E 1) is opti-mal in states s s0

3 with nothing other than(E 1) can be optimal in states s s0

3 with sothe minimum final resignation interval isweakly longer with than with

PROOF OF PROPOSITION 3Select any state s We can decompose the

change from to into two components (i) achange from to derived from ws(e x a) w s(e x a) ds and (ii) a change from to The first change reduces us

a by ds for all statess and actions a This is simply a renormaliza-tion and has no effect on choices The secondchange weakly increases us

a by ds ds for all


s s which weakly reduces the disposition touse in state s by Proposition 1 part (i-b) andweakly decreases us

a by ds ds for all s swhich also weakly reduces the disposition touse in state s by Proposition 1 part (i-a) Thusthe disposition to use in state s weaklydecreases

PROOF OF PROPOSITION 4Part (i)mdashConsider some parameter vector

and let denote the parameter vector obtained bysetting ps

a 0 for all a and s leaving all otherelements of unchanged By part (ii) of Proposi-tion 1 continual use solves the DMrsquos choice prob-lem for if and only if it does so for

Part (ii)mdashConsider some parameter vector and suppose there is some state s with ps

E 0 such that (E 1) is not a best choice in sApplying (1) for and using the fact that(E 1) is not a best choice in s we have

Vs 13 max1 p sE13u s

E Vmax1s 1 1313

p sEu s

E b sE VminSs 1 1313 1 p s

A13

u sA Vmax1s 1 1313

p sA u s

A b sA VminSs 1 1313 u j

R

Vmax1s 1 13

Since (E 1) is not a best choice in s the firstterm in braces is strictly less than us

E Vmax1s1( ) given Assumption 2 so arethe other two terms Thus Vs( ) us

E Vmax1s1( ) Let denote the parametervector obtained by setting ps

a 0 for all a ands leaving all other parameters unchanged Sincethe DM could select (E 0) in s we haveVs( ) us

E Vmax1s1( ) usE

Vmax1s1( ) so Vs( ) Vs( )

SKETCH OF PROOF FOR PROPOSITION 5Without loss of generality we can proceed as if

for the optimal policy the net transfer to eachcohort is zero in each period If this is not the casesimply redefine income in state s at age t as yst ys Lt where Lt is the net transfer received at aget the original policy remains optimal

Sketch for part (i)mdashWe prove this in two stepsStep 1 An optimal tax rate must be weakly

negative To prove this we assume that there isa strictly positive optimal tax rate and establisha contradiction by showing that this policy mustbe strictly inferior to (the no-tax policy)

Consider a decision rule 13 (where we dropthe generational superscript g because we areexamining steady states) that is optimal andsatisfies budget balance with the optimal policyand any age t at which neither use nor nonuseis a certainty from the perspective of period 0(under the stated assumptions there is always atleast one such age) Now suppose that policy prevails but that the DM nevertheless continuesto follow 13 Through a series of algebraic stepsone can show that E0[u(et)xt 1] E0[u(et)xt 0] That is the expectation as ofage zero of the marginal utility of nonaddictiveconsumption in t is greater when conditionedon use than when conditioned on nonuse Intu-itively use tends to occur when income islower and it also entails a cost

Suppose we switch from the optimal policyto Assume for the moment the DM continuesto follow 13 From the perspective of age 0 theresult is an actuarially fair redistribution acrossage-t realizations of (s ) from realizationsin which the DM does not use the substanceto realizations in which he does SinceE0[u(et)xt 1] E0[u(et)xt 0] for the lastdollar redistributed and since u is strictly con-cave the transfer makes him strictly better offThus his discounted expected hedonic payoffweakly increases for every age t and strictlyincreases for some Reoptimizing the decisionrule given reinforces this conclusion

Step 2 The no-tax policy is not optimalIntuitively for the same reasons as in step 1 asmall subsidy coupled with lump-sum transfersthat achieve budget balance within each cohortand period should generate a first-order welfareimprovement by creating an actuarially fair re-distribution from realizations in which the DMdoes not use the substance to realizations inwhich he does Formally this reasoning en-counters two technical issues First we mustestablish that policies with small tax rates andbudget balance within each cohort and periodare feasible Allowing for randomized choicesthis is accomplished through standard argu-ments and a routine application of the KakutaniFixed Point Theorem Second any such redis-


tribution must be actuarially fair relative toprobabilities associated with a decision rule thatis optimal with the new policy not with

To deal with this second issue we consider asequence of tax rates associated age-specificlump-sum taxes and optimal decision ruleswith budget balance within each cohort andperiod (j Tj 13j) with j Tj 3 0 and 13jconverging to some limit 13 By standard argu-ments 13 is optimal with Let b

t denote thelikelihood of use at age t with 13 Fixing thechoice rule at 13 a small tax generates percapita revenue b

t from a cohort of age Distributing this back to the same cohort as alump sum and taking the derivative of the ex-pected age-t payoff with respect to we obtain(1 b

t )bt (E0[u(et)xt 0] E0[u(et)xt

1]) This is zero when bt is 0 or 1 and by the

same arguments as in step 1 is strictly positivefor intermediate values For large j 13j is arbi-trarily close to 13 so holding the choice rulefixed at 13 a switch from to (j Tj) creates aredistribution that is almost actuarially fair forthe probabilities implicit in 13 We thereforeknow that redistribution is almost neutral for tsuch that b

t 0 1 and strictly beneficial fort such that b

t (0 1) Accordingly there existsj sufficiently large such that the expectedpresent value of the DMrsquos payoff is higher with(j Tj) than with assuming he chooses 13Reoptimizing for (j Tj) reinforces thisconclusion

Sketch for part (ii)mdashThe argument parallelsthat given for part (i) except we use the fact thatE0[u(et)xt 0] E0[u(et)xt 1] when q issufficiently small

SKETCH OF PROOF FOR PROPOSITION 6First consider small subsidies The argument

generally parallels step 2 of the sketch for Prop-osition 5 part (i) Take any sequence of reha-bilitation tax rates associated age-specificlump-sum taxes and optimal decision ruleswith budget balance within each cohort andperiod (j Tj 13j) with j 0 j 3 0 Tj 30 and 13j converging to some limit 13 Let B

t

denote the likelihood of rehabilitation at age twith 13 Fixing the choice rule at 13 a small tax generates per capita revenue B

t froma cohort of age t Distributing this back tothe same cohort as a lump sum and taking

the derivative of the expected age-t payoffwith respect to we obtain (1 B

t )Bt (E0[u(et)at R] E0[u(et)at R])

This equals zero when Bt 0 1 and it is

strictly negative for Bt (0 1) (under the

conditions stated in the proposition the DMchooses R only in the highest state reached withpositive probability in t rehabilitation thereforeoccurs when income is lower and it entails acost greater than q so the expected marginalutility of nonaddictive consumption must begreater when conditioned on rehabilitation thanwhen conditioned on no rehabilitation)

We evaluate the change from ( 13) to (jTj 13j) in three steps First change the hot-modeprobabilities to those prevailing under (j Tj)leaving everything else constant Secondchange the policy from to (j Tj) still hold-ing the choice rule fixed at 13 Third reopti-mize changing the choice rule to 13j The thirdchange is obviously weakly beneficial as is thefirst (with j 0 the lump-sum transfers arenegative so under Assumption 3 the hot-modeprobabilities fall) Now consider the secondstep For large j (j Tj 13j) is arbitrarily close to( 13) so the hot-mode probabilities are al-most unchanged and we compute expected util-ity using almost the same probabilities as with( 13) moreover holding the choice rule fixedat 13 a switch from to (j Tj) creates aredistribution that is almost actuarially fair forthe probabilities implicit in ( 13) Thusj(1 B

t ) Bt (E0[u(et)at 0] E0[u(et)at

R]) approximates the period-t welfare effect Fromthe concluding sentence of the previous para-graph we therefore know that the second stepimproves the DMrsquos expected discounted payofffor sufficiently large j

Now consider small taxes For policy lets denote the earliest state in which rehabilita-tion is an optimal choice (recall that it is theunique optimal choice in s) and let s 1 s 1 denote a state in which (E 1) isnot a best choice (both states are referenced inthe proposition) For sufficiently small 0one can show that for all t s is also the earlieststate in which rehabilitation is an optimal choice(and that it is the unique optimal choice in s)and (E 1) is not a best choice in s This meansthat for any budget-balancing optimal deci-sion rule 13 there is at least one t in whichboth rehabilitation and no rehabilitation occur


with strictly positive probability for any such tthe same considerations as above implyE0[u(et)at R] E0[u(et)at R] where wetake expectations assuming the policy is inplace but the hot-mode probabilities associatedwith prevail and the DM continues to fol-low 13

We evaluate the elimination of a small tax inthree steps First eliminate the tax (and associ-ated lump-sum transfers) without changing thehot-mode probabilities and keeping the choicerule fixed at 13 This is strictly beneficial (itcreates an actuarially fair redistribution fromrealizations with no rehabilitation to realiza-tions with rehabilitation from the precedingparagraph we know this is strictly beneficial forthe t at which both types of realizations occurwith positive probabilities and neutral other-wise) Second reoptimize the decision rule thisis weakly beneficial Third change the hot-mode probabilities to those prevailing with thepolicy and reoptimize the decision rule underAssumption 3 this is also weakly beneficial

REFERENCES

Becker Gary and Murphy Kevin ldquoA Theory ofRational Addictionrdquo Journal of PoliticalEconomy 1988 96(4) pp 675ndash700

Behara A and Damasio H ldquoDecision-makingand Addiction Part I Impaired Activation ofSomatic States in Substance Dependent Indi-viduals When Pondering Decisions withNegative Future Consequencesrdquo Neuropsy-chologia 2002 40(10) pp 1675ndash89

Behara A Dolan S and Hindes A ldquoDecision-making and Addiction Part II Myopia to theFuture or Hypersensitivity to Rewardrdquo Neu-ropsychologia 2002 40(10) pp 1690ndash1705

Berke J P et al ldquoDrug Addiction and theHippocampusrdquo Science 2001 294(9) p1235ndash39

Bernheim B Douglas and Rangel Antonio ldquoTo-ward Welfare Analysis with Fallible Decision-Makersrdquo in Peter Diamond and HannuVartiainen eds Economic institutions andbehavioral economics Princeton PrincetonUniversity Press 2005 (forthcoming)

Berridge K ldquoFood Reward Brain Substrates ofWanting and Likingrdquo Neuroscience andBiobehavioral Reviews 1996 20(1) pp1ndash25

Berridge K ldquoPleasure Pain Desire and DreadHidden Core Processes of Emotionrdquo in DKahneman E Diener and N Schwarz edsWell-being The foundations of hedonic psy-chology New York Russell Sage FoundationPublications 1999 pp 525ndash57

Berridge Kent and Robinson Terry ldquoWhat Isthe Role of Dopamine in Reward HedonicImpact Reward Learning or Incentive Sa-liencerdquo Brain Research Review 1998 28(3)pp 309ndash69

Berridge Kent and Robinson Terry ldquoParsingRewardrdquo Trends in Neurosciences 200326(9) pp 507ndash13

Bolla J I Cadet J L and London E D ldquoTheNeuropsychiatry of Chronic Cocaine AbuserdquoJournal of Neuropsychiatry and ClinicalNeuroscience 1998 10(3) pp 280ndash89

Brauer L H et al ldquoDopamine Ligands and theStimulus Effects of Amphetamine AnimalModels versus Human Laboratory DatardquoPsychopharmacology 1997 130(1) pp 2ndash13

Brauer L H et al ldquoHaloperidol ReducesSmoking of Both Nicotine-Containing andDenicotenized Cigarettesrdquo Psychopharma-cology 2001 159(1) pp 31ndash37

Center for Disease Control ldquoSmoking-AttributableMortality and Years of Potential Life LostmdashUnited States 1990rdquo Morbidity and Mortal-ity Weekly Report 1993 42(33) pp 645ndash48

Chaloupka F and Warner K ldquoThe Econom-ics of Smokingrdquo in J Newhouse and DCutler eds Handbook of health econom-ics Amsterdam North-Holland 2001 pp1539 ndash 67

Cohen J D and Blum K I ldquoReward and Deci-sionrdquo Neuron 2002 36(2) pp 193ndash98

Diagnostic and statistical manual of mental disor-ders Washington DC American PsychiatricAssociation 1994

Di Chiara G ldquoDrug Addiction as Dopamine-Dependent Associate Learning DisorderrdquoEuropean Journal of Pharmacology 1999375(1ndash3) pp 13ndash30

Gardner Eliot and David James ldquoThe Neuro-biology of Chemical Addictionrdquo in JonElster and Ole-Jorgen Skog eds Gettinghooked Rationality and addiction Cam-bridge Cambridge University Press 1999pp 93ndash136

Gawin F H ldquoCocaine Addiction Psychology


and Neurophysiologyrdquo Science 1991251(5001) pp 1580ndash86

Goldstein A Addiction From biology to drugpolicy 2nd Ed New York Oxford Univer-sity Press 2001

Goldstein A and Kalant H ldquoDrug Policy Strik-ing the Right Balancerdquo Science 1990249(4976) pp 1513ndash21

Grim J W et al ldquoNeuroadaptation Incubationof Cocaine Craving after Withdrawalrdquo Na-ture 2001 412(6843) pp 141ndash42

Gruber Jonathan and Koszegi Botond ldquoIs Ad-diction lsquoRationalrsquo Theory and EvidencerdquoQuarterly Journal of Economics 2001116(4) pp 1261ndash1303

Gul Faruk and Pesendorfer Wolfgang ldquoTemp-tation and Self-Controlrdquo Econometrica2001a 69(6) pp 1403ndash35

Gul Faruk and Pesendorfer Wolfgang ldquoA The-ory of Addictionrdquo Unpublished Paper2001b

Harris J E Deadly choices Coping with healthrisks in everyday life New York BasicBooks 1993

Holden C ldquolsquoBehavioralrsquo Addictions Do TheyExistrdquo Science 2001a 294(5544) pp 980ndash82

Holden C ldquoZapping Memory Centers TriggersDrug Cravingrdquo Science 2001b 292(5519)p 1039

Hser Y I Anglin D and Powers K ldquoA 24-YearFollow-up Study of California Narcotics Ad-dictsrdquo Archives of General Psychiatry 199350(7) pp 577ndash84

Hser Y I Hoffman V Grella C and AnglinM D ldquoA 33 Year Follow-up of NarcoticsAddictsrdquo Archives of General Psychiatry2001 58(7) pp 503ndash08

Hung Angela ldquoA Behavioral Theory of Addic-tionrdquo Unpublished Paper 2000

Hyman Steven and Malenka Robert ldquoAddictionand the Brain The Neurobiology of Compul-sion and Its Persistencerdquo Nature ReviewsNeuroscience 2001 2(10) pp 695ndash703

Jentsch J D and Taylor J R ldquoImpulsivity Re-sulting from Frontostriatal Dysfunction inDrug Abuse Implications for the Control ofBehavior by Reward-Related Stimulirdquo Psy-chopharmacology 1999 146(4) pp 373ndash90

Kaczmarek H J and Kiefer S W ldquoMicroinjec-tions of Dopaminergic Agents in the NucleusAccumbens Affect Ethanol Consumption but

not Palatabilityrdquo Pharmacology Biochemis-try and Behavior 2000 66(2) pp 307ndash12

Kelley A E ldquoNeural Integrative Activities ofNucleus Accumbens Subregions in Relationto Learning and Motivationrdquo Psychobiology1999 27 pp 198ndash213

Kilborn Peter T ldquoHard-Pressed States Try Sun-day Liquor Salesrdquo New York Times 19 May2003 Section A p 1

Krawczyk D C ldquoContributions of the PrefrontalCortex to the Neural Basis of Human Deci-sion Makingrdquo Neuroscience BiobehavioralReviews 2002 26(6) pp 631ndash64

Laibson David ldquoGolden Eggs and HyperbolicDiscountingrdquo Quarterly Journal of Econom-ics 1997 112(2) pp 443ndash77

Laibson David ldquoA Cue-Theory of Consump-tionrdquo Quarterly Journal of Economics 2001116(1) pp 81ndash119

Loewenstein George ldquoOut of Control VisceralInfluences on Behaviorrdquo Organizational Be-havior and Human Decision Processes1996 65(3) pp 272ndash92

Loewenstein George ldquoA Visceral Account ofAddictionrdquo in Jon Elster and Ole-JorgenSkog eds Getting hooked Rationality andaddiction Cambridge Cambridge UniversityPress 1999 pp 235ndash64

Loewenstein George OrsquoDonoghue Ted andRabin Matthew ldquoProjection Bias in Predict-ing Future Utilityrdquo Quarterly Journal ofEconomics 2003 118(4) pp 1209ndash48

MacCoun R and Reuter P Drug war heresiesLearning from other vices times and placesCambridge Cambridge University Press2001

Massing Michael The fix Los Angeles Univer-sity of California Press 2000

McAuliffe W E ldquoA Test of Wiklerrsquos Theory ofRelapse The Frequency of Relapse Due toConditioned Withdrawal Sicknessrdquo Interna-tional Journal of Addiction 1982 17(1) pp19ndash33

Miron J and Zwiebel J ldquoThe Economic Caseagainst Drug Prohibitionrdquo Journal of Eco-nomic Perspectives 1995 9(4) pp 175ndash92

National Institute on Alcohol Abuse and Alcohol-ism ldquoEconomic Perspectives in AlcoholismResearchrdquo Alcohol Alert National Institutesof Health No 51

National Institute on Drug Abuse The economiccosts of alcohol and drug abuse in the United


States 1992 NIH Publication No 98-4327Bethesda National Institutes of Health 1998

Nestler E J ldquoMolecular Basis of Long-TermPlasticity Underlying Addictionrdquo Nature Re-views Neuroscience 2001 2(2) pp 119ndash28

Nestler E and Malenka Robert ldquoThe AddictedBrainrdquo Scientific American 2004 290(3)pp 78ndash85

Norstrom T and Skog O J ldquoSaturday Openingof Alcohol Retail Shops in Sweden An Im-pact Analysisrdquo Journal of Studies on Alco-hol 2003 64(3) pp 393ndash401

OrsquoBrien C ldquoExperimental Analysis of Condi-tioning Factors in Human Narcotic Addic-tionrdquo Pharmacological Review 1975 27(4)pp 533ndash43

OrsquoBrien C ldquoA Range of Research-Based Phar-macotherapies for Addictionrdquo Science 1997278(5335) pp 66ndash70

OrsquoDonoghue Ted and Rabin Matthew ldquoDoing ItNow or Laterrdquo American Economic Review1999 89(1) pp 103ndash24

OrsquoDonoghue Ted and Rabin Matthew ldquoAd-diction and Present-Biased PreferencesrdquoUnpublished Paper 2000

OrsquoDonoghue Ted and Rabin Matthew ldquoOptimalSin Taxesrdquo Unpublished Paper 2004

Office of National Drug Control Policy WhatAmerican users spend on illegal drugsPublication No NCJ-192334 WashingtonDC Executive Office of the President2001a

Office of National Drug Control Policy The eco-nomic costs of drug abuse in the UnitedStates 1992ndash1998 Publication No NCJ-190636 Washington DC Executive Officeof the President 2001b

Olds J and Milner P ldquoPositive ReinforcementProduced by Electrical Stimulation of SeptalArea and Other Regions of Rat Brainrdquo Jour-nal of Comparative and PhysiologicalPsychology 1954 47(6) pp 419ndash27

Orphanides Athanasios and Zervos David ldquoRa-tional Addiction with Learning and RegretrdquoJournal of Political Economy 1995 103(4)pp 739ndash58

Pauly Mark V ldquoOverinsurance and Public Pro-vision of Insurance The Roles of MoralHazard and Adverse Selectionrdquo QuarterlyJournal of Economics 1974 88(1) pp 44ndash54

Pecina S et al ldquoPimozide Does Not Shift Pal-atability Separation of Anhedonia from Sen-

sorimotor Suppression by Taste ReactivityrdquoPharmacological Biobehavioral Reviews1997 58(3) pp 801ndash11

Pickens R and Harris W C ldquoSelf-Administra-tion of d-Amphetamine by Ratsrdquo Psycho-pharmacologia 1968 12(2) pp 158ndash63

Robbins T W and Everitt B J ldquoInteraction ofDepaminergic System with Mechanisms ofAssociative Learning and Cognition Impli-cations for Drug Abuserdquo Psychological Sci-ence 1999 10(3) pp 199ndash202

Robins L ldquoVietnam Veteransrsquo Rapid Recoveryfrom Heroin Addiction A Fluke or NormalExpectationrdquo Addiction 1994 88(8) pp1041ndash54

Robins L Davis D and Goodwin D ldquoDrug Useby US Army Enlisted Men in Vietnam AFollow-up on their Return Homerdquo AmericanJournal of Epidemiology 1974 99(4) pp235ndash49

Robinson T and Berridge K ldquoThe Neural Basisof Drug Craving An Incentive-SensitizationTheory of Addictionrdquo Brain Research Re-views 1993 18(3) pp 247ndash91

Robinson T and Berridge K ldquoThe Psychologyand Neurobiology of Addiction An IncentiveSensitization Viewrdquo Addiction Supplement2000 2 pp 91ndash117

Robinson Terry and Berridge Kent ldquoAddic-tionrdquo Annual Reviews of Psychology 200354 pp 25ndash53

Rolls E T ldquoThe Orbitofrontal Cortex and Re-wardrdquo Cerebral Cortex 2000 10(3) pp284ndash94

Schultz W ldquoPredictive Reward Signal of Dopa-mine Neuronsrdquo Journal of Neurophysiology1998 80(1) pp 1ndash27

Schultz W ldquoMultiple Reward Signals in theBrainrdquo Nature Reviews Neuroscience 20001(3) pp 199ndash207

Schultz W Dayan P and Montague P R ldquoANeural Substrate of Prediction and RewardrdquoScience 1997 275(5306) pp 1593ndash99

Shaham Y Erb S and Steward J ldquoStress-Induced Relapse to Heroin and CocaineSeeking in Rats A Reviewrdquo Brain Re-search Reviews 2000 33 pp 13ndash33

Shalev U Grimm J W and Shaham Y ldquoNeu-robiology of Relapse to Heroine and CocaineSeeking A Reviewrdquo Pharmacological Re-views 2002 54(1) pp 1ndash42

Shefrin H M and Thaler Richard ldquoAn Eco-


nomic Theory of Self-Controlrdquo Journal ofPolitical Economy 1981 89(2) pp 392ndash406

Stewart J and Wise Roy ldquoReinstatement ofHeroin Self-Administration Habits Mor-phine Prompts and Naltrexone DiscouragesRenewed Responding after Extinctionrdquo Psy-chopharmacology 1992 108(1ndash2) pp 79ndash84

Trosclair A Huston C Pederson L and DillonI ldquoCigarette Smoking Among AdultsmdashUnited States 2000rdquo Morbidity and Mortal-ity Weekly Report 2002 51(29) pp 642ndash45

Ungless M Whistler J Malenka R and BonciA ldquoSingle Cocaine Exposure In Vivo InducesLong-Term Potentiation in Dopamine Neu-ronsrdquo Nature 2001 411(6387) pp 583ndash87

US Census Bureau Statistical abstract of theUnited States Washington DC US Gov-ernment Printing Office 2001

Vorel S et al ldquoRelapse to Cocaine-Seekingafter Hippocampal Theta Burst StimulationrdquoScience 2001 292(5519) pp 1175ndash78

Wachtel S R ldquoThe Effects of Acute Haloperi-dol or Risperidone on Subjective Responsesto Methamphetamine by Healthy Volun-

teersrdquo Drug Alcohol Dependency 200268(1) pp 23ndash33

Wagner F A and Anthony J C ldquoFrom FirstDrug Use to Drug Dependence Develop-mental Periods of Risk for Dependence uponMarijuana Cocaine and Alcoholrdquo Neuro-psychopharmacology 2002 26(4) pp 479ndash88

Watanabe Masataka ldquoCoding and Monitoringof Motivational Context in the Primate Pre-frontal Cortexrdquo Journal of Neuroscience2000 22(6) pp 2391ndash2400

Wickelgren Ingrid ldquoGetting the Brainrsquos Atten-tionrdquo Science 1997 276(5335) pp 35ndash37

Wise Roy ldquoThe Brain and Rewardrdquo in J MLiebman and S J Cooper eds The neuro-pharmacological basis of reward New YorkOxford University Press 1989 pp 377ndash424

Wyvell C L and Berridge K C ldquoIntra-accum-bens Amphetamine Increases the Condi-tioned Incentive Salience of Sucrose RewardEnhancement of Reward Wanting withoutEnhancing Liking or Positive Reinforce-mentrdquo Journal of Neuroscience 200020(21) pp 8122ndash30


$300 billion per year On average over 500000deaths each year are attributed directly to ciga-rettes and alcohol

Public policies regarding addictive sub-stances run the gamut from laissez-faire to tax-ation subsidization (eg of rehabilitationprograms) regulated dispensation criminaliza-tion product liability and public health cam-paigns Each alternative policy approach haspassionate advocates and detractors Economicanalysis can potentially inform this debate butit requires a sound theory of addiction

This paper presents a new theory of addictionbased on three central premises first useamong addicts is frequently a mistake secondexperience with an addictive substance sensi-tizes an individual to environmental cues thattrigger mistaken usage third addicts under-stand their susceptibility to cue-triggered mis-takes and attempt to manage the process withsome degree of sophistication We argue thatthese premises find strong support in evidencefrom psychology neuroscience and clinicalpractice In particular research has shown thataddictive substances systematically interferewith the proper operation of an important classof processes which the brain uses to forecastnear-term hedonic rewards (pleasure) and thisleads to strong misguided cue-conditioned im-pulses that often defeat higher cognitive control

We provide a parsimonious representation ofthis phenomenon in an otherwise standardmodel of intertemporal decision-making Spe-cifically we allow for the possibility that uponexposure to environmental cues the individualmay enter a ldquohotrdquo decision-making mode inwhich he always consumes the substance irre-spective of underlying preferences and we as-sume that sensitivity to cues is related to pastexperiences The individual may also operate ina ldquocoldrdquo mode wherein he considers all alter-natives and contemplates all consequences in-cluding the effects of current choices on thelikelihood of entering the hot mode in thefuture3

As a matter of formal mathematics ourmodel involves a small departure from the stan-dard framework Behavior corresponds to thesolution of a dynamic programming problemwith stochastic state-dependent mistakes Ourapproach therefore harmonizes economic the-ory with evidence on the biological foundationsof addiction without sacrificing analytic tracta-bility We underscore this point by providingresults that illuminate the relationships betweenbehavior and the characteristics of the usersubstance and environment For example wefind that when one substance is more addictivethan another then ceteris paribus the more ad-dictive substance is associated with less con-sumption among relatively new users but withmore consumption (both intentional and acci-dental) among highly experienced users

The theory can account for a number of im-portant patterns associated with addiction Italso gives rise to a clear welfare standard andhas novel implications for public policy Ourpolicy analysis focuses on consumer welfareand therefore ignores supply-side effects andexternalities It emphasizes the role of policy inaverting mistakes and in either ameliorating ormagnifying significant uninsurable monetaryrisks indirectly caused by exposure to stochasticenvironmental cues We show that a beneficialpolicy intervention potentially exists if and onlyif there are circumstances in which users unsuc-cessfully attempt to abstain In that case theoptimal policy depends on usage patterns In anatural benchmark case it is optimal to subsi-dize an addictive substance when the likelihoodof use rises with the level of past experience Incontrast provided the substance is sufficientlyinexpensive it is optimal to tax the substancewhen the likelihood of use declines with thelevel of past experience Under weak condi-tions a small subsidy for rehabilitation is ben-eficial and a small tax is harmful When substancetaxation is optimal under some conditions crimi-nalization can perform even better Programs thatmake addictive substances available on a prescrip-tion basis have potentially large benefits Restric-tions on advertising and public consumption and

3 Our analysis is related to work by George Loewenstein(1996 1999) who considers simple models in which anindividual can operate either in a hot or cold decision-making mode Notably Loewenstein assumes that behaviorin the hot mode reflects the application of a ldquofalserdquo utilityfunction rather than a breakdown of the processes by which

a utility function is maximized He also argues contrary tothe findings of this paper that imperfect self-understandingis necessary for addiction-like behaviors


















II Central Premises










































III The Model












a p0a 0 and

psE ps

A psR














ps (psE ps

A psR) us (us

E usA us

R) bs (bsE




E usA us

R andus

E bsE us

A bsA



a (for a given







(1) Vs 13 maxax13E113E013A013R013

usa s

axbsa


axVminSs 1 13



E1 1 sE0 ps

Es

A0 psA and s





















E



A bsA and us


E 0)






a and uka and




E


E pjA uj

A bjA and uj

R







Abj


E27


A ujA and uj













A or bsA weakly










E bsE VminSs1() us

E Vmax1s1() us


E bsE VminSs1()

usA bs



































a



























twst(et







B Policy Objectives
















a





qps

a

yps

a 0












































































G Criminalization






































VII Final Remarks






















APPENDIX B PROOFS











E b jE with all





with When p jE pj


E b jE and










E pjA uj

A ujR andor bj

A







E psE for all
















a by ds ds for all










E Vmax1s 1 1313

p sEu s


A13

u sA Vmax1s 1 1313

p sA u s


R

Vmax1s 1 13





E Vmax1s1( ) usE






















t















REFERENCES


















































































































II Central Premises










































III The Model












a p0a 0 and

psE ps

A psR














ps (psE ps

A psR) us (us

E usA us

R) bs (bsE




E usA us

R andus

E bsE us

A bsA



a (for a given







(1) Vs 13 maxax13E113E013A013R013

usa s

axbsa


axVminSs 1 13



E1 1 sE0 ps

Es

A0 psA and s





















E



A bsA and us


E 0)






a and uka and




E


E pjA uj

A bjA and uj

R







Abj


E27


A ujA and uj













A or bsA weakly










E bsE VminSs1() us

E Vmax1s1() us


E bsE VminSs1()

usA bs



































a



























twst(et







B Policy Objectives
















a





qps

a

yps

a 0












































































G Criminalization






































VII Final Remarks






















APPENDIX B PROOFS











E b jE with all





with When p jE pj


E b jE and










E pjA uj

A ujR andor bj

A







E psE for all
















a by ds ds for all










E Vmax1s 1 1313

p sEu s


A13

u sA Vmax1s 1 1313

p sA u s


R

Vmax1s 1 13





E Vmax1s1( ) usE






















t















REFERENCES




































































































































III The Model












a p0a 0 and

psE ps

A psR














ps (psE ps

A psR) us (us

E usA us

R) bs (bsE




E usA us

R andus

E bsE us

A bsA



a (for a given







(1) Vs 13 maxax13E113E013A013R013

usa s

axbsa


axVminSs 1 13



E1 1 sE0 ps

Es

A0 psA and s





















E



A bsA and us


E 0)






a and uka and




E


E pjA uj

A bjA and uj

R







Abj


E27


A ujA and uj













A or bsA weakly










E bsE VminSs1() us

E Vmax1s1() us


E bsE VminSs1()

usA bs



































a



























twst(et







B Policy Objectives
















a





qps

a

yps

a 0












































































G Criminalization






































VII Final Remarks






















APPENDIX B PROOFS











E b jE with all





with When p jE pj


E b jE and










E pjA uj

A ujR andor bj

A







E psE for all
















a by ds ds for all










E Vmax1s 1 1313

p sEu s


A13

u sA Vmax1s 1 1313

p sA u s


R

Vmax1s 1 13





E Vmax1s1( ) usE






















t















REFERENCES






































































































a p0a 0 and

psE ps

A psR














ps (psE ps

A psR) us (us

E usA us

R) bs (bsE




E usA us

R andus

E bsE us

A bsA



a (for a given







(1) Vs 13 maxax13E113E013A013R013

usa s

axbsa


axVminSs 1 13



E1 1 sE0 ps

Es

A0 psA and s





















E



A bsA and us


E 0)






a and uka and




E


E pjA uj

A bjA and uj

R







Abj


E27


A ujA and uj













A or bsA weakly










E bsE VminSs1() us

E Vmax1s1() us


E bsE VminSs1()

usA bs



































a



























twst(et







B Policy Objectives
















a





qps

a

yps

a 0












































































G Criminalization






































VII Final Remarks






















APPENDIX B PROOFS











E b jE with all





with When p jE pj


E b jE and










E pjA uj

A ujR andor bj

A







E psE for all
















a by ds ds for all










E Vmax1s 1 1313

p sEu s


A13

u sA Vmax1s 1 1313

p sA u s


R

Vmax1s 1 13





E Vmax1s1( ) usE






















t















REFERENCES




































































































(1) Vs 13 maxax13E113E013A013R013

usa s

axbsa


axVminSs 1 13



E1 1 sE0 ps

Es

A0 psA and s





















E



A bsA and us


E 0)






a and uka and




E


E pjA uj

A bjA and uj

R







Abj


E27


A ujA and uj













A or bsA weakly










E bsE VminSs1() us

E Vmax1s1() us


E bsE VminSs1()

usA bs



































a



























twst(et







B Policy Objectives
















a





qps

a

yps

a 0












































































G Criminalization






































VII Final Remarks






















APPENDIX B PROOFS











E b jE with all





with When p jE pj


E b jE and










E pjA uj

A ujR andor bj

A







E psE for all
















a by ds ds for all










E Vmax1s 1 1313

p sEu s


A13

u sA Vmax1s 1 1313

p sA u s


R

Vmax1s 1 13





E Vmax1s1( ) usE






















t















REFERENCES









































































































E



A bsA and us


E 0)






a and uka and




E


E pjA uj

A bjA and uj

R







Abj


E27


A ujA and uj













A or bsA weakly










E bsE VminSs1() us

E Vmax1s1() us


E bsE VminSs1()

usA bs



































a



























twst(et







B Policy Objectives
















a





qps

a

yps

a 0












































































G Criminalization






































VII Final Remarks






















APPENDIX B PROOFS











E b jE with all





with When p jE pj


E b jE and










E pjA uj

A ujR andor bj

A







E psE for all
















a by ds ds for all










E Vmax1s 1 1313

p sEu s


A13

u sA Vmax1s 1 1313

p sA u s


R

Vmax1s 1 13





E Vmax1s1( ) usE






















t















REFERENCES




































































































Abj


E27


A ujA and uj













A or bsA weakly










E bsE VminSs1() us

E Vmax1s1() us


E bsE VminSs1()

usA bs



































a



























twst(et







B Policy Objectives
















a





qps

a

yps

a 0












































































G Criminalization






































VII Final Remarks






















APPENDIX B PROOFS











E b jE with all





with When p jE pj


E b jE and










E pjA uj

A ujR andor bj

A







E psE for all
















a by ds ds for all










E Vmax1s 1 1313

p sEu s


A13

u sA Vmax1s 1 1313

p sA u s


R

Vmax1s 1 13





E Vmax1s1( ) usE






















t















REFERENCES






























































































































a



























twst(et







B Policy Objectives
















a





qps

a

yps

a 0












































































G Criminalization






































VII Final Remarks






















APPENDIX B PROOFS











E b jE with all





with When p jE pj


E b jE and










E pjA uj

A ujR andor bj

A







E psE for all
















a by ds ds for all










E Vmax1s 1 1313

p sEu s


A13

u sA Vmax1s 1 1313

p sA u s


R

Vmax1s 1 13





E Vmax1s1( ) usE






















t















REFERENCES














































































































twst(et







B Policy Objectives
















a





qps

a

yps

a 0












































































G Criminalization






































VII Final Remarks






















APPENDIX B PROOFS











E b jE with all





with When p jE pj


E b jE and










E pjA uj

A ujR andor bj

A







E psE for all
















a by ds ds for all










E Vmax1s 1 1313

p sEu s


A13

u sA Vmax1s 1 1313

p sA u s


R

Vmax1s 1 13





E Vmax1s1( ) usE






















t















REFERENCES


































































































B Policy Objectives
















a





qps

a

yps

a 0












































































G Criminalization






































VII Final Remarks






















APPENDIX B PROOFS











E b jE with all





with When p jE pj


E b jE and










E pjA uj

A ujR andor bj

A







E psE for all
















a by ds ds for all










E Vmax1s 1 1313

p sEu s


A13

u sA Vmax1s 1 1313

p sA u s


R

Vmax1s 1 13





E Vmax1s1( ) usE






















t















REFERENCES





































































































a





qps

a

yps

a 0












































































G Criminalization






































VII Final Remarks






















APPENDIX B PROOFS











E b jE with all





with When p jE pj


E b jE and










E pjA uj

A ujR andor bj

A







E psE for all
















a by ds ds for all










E Vmax1s 1 1313

p sEu s


A13

u sA Vmax1s 1 1313

p sA u s


R

Vmax1s 1 13





E Vmax1s1( ) usE






















t















REFERENCES





























































































































































G Criminalization






































VII Final Remarks






















APPENDIX B PROOFS











E b jE with all





with When p jE pj


E b jE and










E pjA uj

A ujR andor bj

A







E psE for all
















a by ds ds for all










E Vmax1s 1 1313

p sEu s


A13

u sA Vmax1s 1 1313

p sA u s


R

Vmax1s 1 13





E Vmax1s1( ) usE






















t















REFERENCES


























































































































VII Final Remarks






















APPENDIX B PROOFS











E b jE with all





with When p jE pj


E b jE and










E pjA uj

A ujR andor bj

A







E psE for all
















a by ds ds for all










E Vmax1s 1 1313

p sEu s


A13

u sA Vmax1s 1 1313

p sA u s


R

Vmax1s 1 13





E Vmax1s1( ) usE






















t















REFERENCES














































































































APPENDIX B PROOFS











E b jE with all





with When p jE pj


E b jE and










E pjA uj

A ujR andor bj

A







E psE for all
















a by ds ds for all










E Vmax1s 1 1313

p sEu s


A13

u sA Vmax1s 1 1313

p sA u s


R

Vmax1s 1 13





E Vmax1s1( ) usE






















t















REFERENCES


































































































with When p jE pj


E b jE and










E pjA uj

A ujR andor bj

A







E psE for all
















a by ds ds for all










E Vmax1s 1 1313

p sEu s


A13

u sA Vmax1s 1 1313

p sA u s


R

Vmax1s 1 13





E Vmax1s1( ) usE






















t















REFERENCES










































































































E Vmax1s 1 1313

p sEu s


A13

u sA Vmax1s 1 1313

p sA u s


R

Vmax1s 1 13





E Vmax1s1( ) usE






















t















REFERENCES














































































































t















REFERENCES




































































































REFERENCES


































































































Addiction and Cue-Triggered Decision Processeseconweb.ucsd.edu/~jandreon/Econ264/papers/Bernheim...

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Transcript of Addiction and Cue-Triggered Decision Processeseconweb.ucsd.edu/~jandreon/Econ264/papers/Bernheim...