Gary S. Becker; Kevin M. Murphy

Transcription

1 ATheoryofRationalAddiction JPE, 96 (Aug.,1988) Gary S. Becker; Kevin M. Murphy IGIER VSI Presentations Presented by Marco Stenborg Petterson and Christoph Schilling March 14, 2014

2 Outline Motivation and literature review Model: basic setup dynamics Implications Criticism

3 Motivation Interesting approach to the topic The theme is relevant in the everyday life of many people The paper has some interesting policy implications

4 Past papers The paper builds on two main other papers Stigler and Becker (1977) De Gustibus Non Est Disputandum Iannaccone (1986) Addiction and Satiation It relies also on the insights given by Ryder and Heal (1973) Optimum Growth with Intertemporally Dependent Preferences

5 Novelty This paper is the first to stress the existence and importance of unstable steady states It shows why some addictions are broken by going cold turkey Relates temporary stressful events to permanent addictions

6 Definitions Rationality: a rational agent has a consistent plan to maximize utility over time, and tries to anticipate the future consequences of their choices Addiction: a person is potentially addicted if an increase in his current consumption of a good increases his future consumption it.

7 Utility function The formula of the utility function is u(t) =u [y(t), c(t), S(t)] (1) Where past consumption c affects current utility through a process of learning by doing summarized by the stock of consumption capital S This relationship is governed by the law of motion Ṡ(t) =c(t) S(t) h[d(t)] (2) Where Ṡ is the rate of change over time in S, the exogenous instantaneous depreciation rate of past consumption of c and D(t) is the expenditures on endogenous depreciation or appreciation D(t) can be interpreted as going into a rehabilitation clinic if we consider drugs or attend a seminar on Bach if we consider music

8 Maximization problem We have that the lifetime utility function is U(0) = ˆ T 0 e t u [y(t), c(t), S(t)] dt (3) Which is a standard utility function which depends additively on consumption at various dates, in which is a parameter representing time preference We maximize it subject to a budget constraint ˆ T 0 ˆ T e rt [y(t)+p c (t)c(t)+p d (t)d(t)]dt apple A 0 + e rt w(s(t))dt 0 (4) Where we take the price of y as numeraire

9 First order conditions The optimal paths of c(t) and y(t) are determined by the first order conditions u y = µe ( r)t (5) Where a(t) is a(t) = ˆ T t h d (t)a(t) =µp d e ( r)t (6) u c (t) =µp c e ( r)t a(t) = c (t) (7) ˆ T e ( + )( t) u s d + µ e (r+ )( t) w s d (8) t And it represents the shadow price of an additional unit of stock

10 Dynamics The FOC determine the initial consumption level, c 0 as a function of S 0 (initial stock of consumption capital) p c (t) price of c the marginal utility of wealth µ (which is a parameter similar to the lambda of the Lagrangians)

11 Simplifying Assumptions To simplify the math the following assumptions are made T = 1 = r, the rate of time preference is equal to the rate of interest D(t) =0, there is no endogenous depreciation p c (t) =p c 8t With the right utility function, the model has three steady states, where consumption will not change over time Two steady states are stable, one is unstable

12 Tolerance & Reinforcement Tolerance is an important characteristic of addictions, it means that over time, the same amount of the drug becomes less satisfying. In our model this means that higher past consumption reduces current utility, i.e. = u s < 0 Reinforcement is closely linked to the definition of addiction, namely: past consumption increases the desire for current consumption. In our model we will call this effect adjacent complementarity

13 Reinforcement (adjacent complementarity) To analyze the behavior of c and S, aquadraticutility function is assumed near the steady states, and by maximizing yout,thefollowingfunction: F (t) = c c(t)+ s S(t)+ cc 2 [c(t)]2 + (9) + ss 2 [S(t)]2 + cs c(t)s(t) µp c c(t) Optimization yields the following optimal c(t): c(t) =( + )S(t) S (10)

14 Reinforcement (adjacent complementarity) c(t) =( + )S(t) S (11) In which is a parameter that results from the coefficients,, ss, cc, cs If we want there to be a positive relationship between c and S (addiction), we have that > This condition gives rise to a further condition: ( + 2 ) cs > ss > 0 (12) Increased impatience might not reduce future consumption (as is the case with non-addictive goods)

15 Graph c(t) c=δs p p S L S H S(t)

16 Permanent changes in price Apermanentincreaseinprice,thatiscompensatedtoholdµ constant, would raise c(t), as the value function is c = + dc c ds Therefore, the effect of a compensated change in p c on c grows over time when present and past consumption are adjacent complements However, effects on drug consumption might be a lot larger than this... (13)

17 Graph c(t) c=δs c' H p' p c H c L c' L p' p S' L S L S H S' H S(t)

18 Temporary changes in price If we analyze temporary changes in price we are interested in both past and future prices Changes in past price affect current consumption through the stock capital The complementarity between present and future consumption is larger for more addictive goods hence stronger effects Consumers respond more to permanent price changes than temporary ones, permanent changes combine changes in price during the current period with equal changes in price during all future periods

19 Life Cycle The beginning and resumption of harmful addictions are often traceable to anxiety, tension and insecurity which may be due to divorce or job loss If these events lower total utility while raising the marginal utility of addictive goods then changes in life cycle events will have the same effect on consumption as changes in prices These events directly affect the stock of consumption capital by a term Z(t), transforming the law of motion (eq.2) Ṡ(t) =c(t)+z(t) S(t) (14)

20 Graph c(t) c=δs p' p p' p S' L S L S H S' H S(t)

21 Graph c(t) c=δs p' p p' p S' L S L S H S' H S(t)

22 Cold turkey and other ways to stop An addict will stop consuming when events lower sufficiently either her demand or her stock of consumption capital or when short-term loss in utility is counteracted with a bigger gain in the long-term It is rational to stop an addiction by trial and error Going cold turkey is defined as the actions of a person who abruptly gives up a habit or addiction rather than gradually easing the process through gradual reduction or by using replacement medication.

23 What does Gary think? So, what do you think is the most addictive good on earth, according to Gary Becker?

24 What does Gary think? So, what do you think is the most addictive good on earth, according to Gary Becker? Once you start consuming it, you want to consume more and more of it.

25 What does Gary think? So, what do you think is the most addictive good on earth, according to Gary Becker? Once you start consuming it, you want to consume more and more of it. Over time you build up a tolerance to it, i.e. you get less enjoyment out of consuming a fixed amount of it.

26 What does Gary think? So, what do you think is the most addictive good on earth, according to Gary Becker? Once you start consuming it, you want to consume more and more of it. Over time you build up a tolerance to it, i.e. you get less enjoyment out of consuming a fixed amount of it. Pursuit of that good leads you to sacrifice everything else in your life to get it, potentially leading you to do ridiculous things to try to get the good.

27 What does Gary think? So, what do you think is the most addictive good on earth, according to Gary Becker? Once you start consuming it, you want to consume more and more of it. Over time you build up a tolerance to it, i.e. you get less enjoyment out of consuming a fixed amount of it. Pursuit of that good leads you to sacrifice everything else in your life to get it, potentially leading you to do ridiculous things to try to get the good. There is a period of withdrawal when you stop consuming the good.

28 Conclusions Unstable steady states are crucial to understanding addictive behavior Ceteris paribus, individuals who discount the future more heavily are more prone to addiction Price changes can have a strong impact on the likelihood of addiction Future prices are taking into account, hence permanent price increases have a larger effect than temporary ones Cold turkey withdrawal is consistent with rationality

29 Criticism & Limitations Hyperbolic discounting Human brain reward system developed in a long evolutionary process, only recently possible to activate it directly Biological evidence for permanent change of the brain s reward system due to drug use Recurring craving after many years of drug use

30 Sources Robinson, T. E., & Berridge, K. C. (1993). The neural basis of drug craving: an incentive-sensitization theory of addiction. Brain research reviews, 18(3), Kalivas, Peter W., and Nora D. Volkow. "The neural basis of addiction: a pathology of motivation and choice." American Journal of Psychiatry (2005):