MODELS OF ADDICTION

Models of addiction come out of both psychology/medicine and economics. Chaloupka and Warner (1999) identify three types: imperfectly rational, myopic, and rational addiction.

Imperfectly Rational Addiction Models
Imperfect rational addiction models propose that the addict has stable but inconsistent preferences in the short run as opposed to the long run. As Schelling (1978) described this person: Everybody behaves like two people, one who wants clean lungs and long life and another who adores tobacco . . . The two are in a continual contest for control. (p. 290) Are people really like this? Regret, in fact, occurs frequently. In film, there is even the cliché of the hero in comedy who enters the tiger’s cage telling the bystanders to ignore him should he change his mind and even scream for help. Of course, he changes his mind. Is he two different people at those two moments?

Myopic Addiction Models
Nearsightedness about the future harmful effects of the ingested drug provides a variant of the imperfectly rational model. Here, the individuals don’t see the facts clearly; they are naïve about the nature of the drug and its side effects. One may imagine someone easily persuaded by cigarettesmoking friends who may denigrate the societal information about cigarettes. One may see the teenager who only dimly perceives the realities of distant future health events, including cancers, and perhaps fails to connect the experience of smokers in older generations with his or her own behaviors and prospects.

Rational Addiction
Can addiction in some cases be a rational choice? Becker and Murphy (1988) discarded myopic models and investigated addiction by assuming that people incorporate rationally all information, past, present, and future, into their utility calculations. They showed that rationally choosing to ingest an addictive drug was possible under restrictive yet plausible conditions. The discussion here follows work by Becker and Murphy (1988), Becker, Grossman, and Murphy (1991), and MacDonald (2004). Addiction researchers usually speak of “reinforcement” and “tolerance.” Reinforcement means that greater past consumption of addictive goods, such as drugs or cigarettes, increases the desire for present consumption. In short, smoking more now may make us smoke more later. Tolerance occurs if the utility from a given amount of consumption is lower when past consumption is greater. This suggests that the future impacts of smoking or drinking or ingesting drugs decrease, when we consume more now. A single glass of wine may make someone tipsy the first time he or she drinks. Over time, with more drinking experience, the first glass of the evening may have little or no impact. We will use smoking to illustrate important model relationships, although drinking, illicit drugs, or even common substances such as caffeine, can provide similar examples. Becker, Grossman, and Murphy introduce the construct of “addictive capital stock,” S. For example, with more smoking experience, the smoker’s attitude toward cigarette consumption is likely to change. We assume therefore that addictive stock “reinforces” cigarette consumption, C, meaning that the more stock, the more one will smoke, leading to curves A1 and A2 in Figure 24-3. Though not shown in the figure, the utility function shows the smoker as gaining utility from cigarette consumption, C, from the addictive stock, S, as well as from income, which allows the purchase of other goods in addition to cigarettes.

The important questions in the model deal with what happens over time. For example, current consumption increases the addictive stock. Listening to Mozart at age 21 will likely increase enjoyment of Mozart at age 22, thus increasing our musical “capital stock.” Most smokers will remember how bad the first cigarette tasted, but similarly smoking or drinking at age 21 may increase enjoyment of smoking or drinking in subsequent years. So, a larger addictive stock makes future consumption more pleasurable. A myopic, or nearsighted, addict looks solely at the reinforcement effect. A rational addict, however, also considers the future harmful consequences of current addictive behavior. The rationally addicted smoker weighs the present pleasure against both the future health consequences and the beneficial impact of current consumption on future consumption enjoyment. The rational addiction theorists have drawn several further implications from their analyses. • Addiction is more likely for people who discount the future heavily, because they pay less attention to the potential adverse consequences. • Addiction is more likely when the effects of past consumption depreciate less rapidly. • Expected rises in future prices will have a dampening effect on current consumption, much like increases in current prices. Models examining people’s behavior over time typically search for a “steady state,” an equilibrium where all “outflows” and “inflows” maintain the system, like the equilibrium of a well-run fish tank. In the steady state equilibrium proposed here, the system will be maintained over time, provided that current cigarette smoking adds exactly enough C to the addictive stock to replace the depreciation δS of that stock during the period. Mathematically, C = δS, where δ is the constant depreciation rate. The C = δS line in Figure 24-3 depicts all the combinations of C and S that yield a steady state equilibrium. Reviewing the elements of the model, we see: 1. Consumption of cigarettes as a function of addictive stock. Curve A1 relates smoking to addictive stock for a person with a given rate of time preference (relating future utility to present utility) and a given level of wealth, and who faces a set of prices for cigarettes and nonaddictive goods. We can think of curve A1 as a cigarette consumption curve, so the more stock S, the more consumption C. In other words, any given stock S is just sufficient to maintain consumption level C. 2. Cigarette consumption needed to maintain addictive stock. The stock of addictive capital depreciates at a rate of δ (between 0 and 1) per year. Depreciated stock is replaced with more smoking. The ray from the origin, C = δS is the steady state line where current cigarette consumption just offsets the depreciation of the stock of smoking capital. The model provides a convenient way to see what happens to the rational addict over time. Consider a smoker who is on consumption curve A1 (as an exercise, explain why a price increase from “low” to “high” would shift the consumption curve from A1 to A2 ) with addictive stock S1. This stock implies a cigarette consumption of C1, or point B. Notice, however, that consumption, C1, will more than replace the depreciation in S1 during the period (point B lies above the steady state line, C = δS). It follows that addictive stock will grow and exceed S1 in the next period; for example it may rise to S2 at point B. Continuing this logic, it follows that whenever consumption, C, lies above the steady state line, the addictive stock, S, will grow. Finally, stock S3 and consumption C3 give a steady state equilibrium for case A1 . We label this equilibrium point as D. Compare steady state equilibrium D with another place where the two curves cross, point E. Notice that D is like a magnet; any stock near S3 is pulled toward D. That is, any stock a bit to the left of S3 will bring growth in stock up to S3; any stock to the right will depreciate down to S3. Point D represents a “stable equilibrium.” Try the same experiment with the equilibrium at point E, and see that it is unstable. Any stock slightly to the left of E will be pulled farther to the left; any stock slightly to the right will eventually increase all the way to S3. 2 This model provides important policy implications about impacts of price changes, often induced through tax policies. Starting at point D consider a rise in price so that the cigarette consumption curve shifts from A1 to A2 . With the price rise, smoking decreases at first from C3 (at point D), to point D. It then falls farther over time since D is below the steady-state line. Equilibrium smoking level falls to C4 at point D. This shows the model to be consistent with our prior conceptions about price and quantity demanded. The higher the price, all else equal, the lower the quantity demanded. Moreover, the long-run responses to price changes exceed shortrun responses. Initial decreases in smoking cause a subsequent decrease in the stocks of addictive capital, which then stimulate further smoking decreases. Second, at some point, a rising price will cause all equilibria to disappear. Starting from point D and letting the price rise even more, a new A3 curve will be everywhere below the C = δS steady state line. This prediction is unique to the rational addiction model, the prediction that some cigarette smokers quit “cold turkey,” without gradually reducing consumption down to zero, landing at a point similar to F where consumption equals 0. It also follows that expectations about future prices of cigarettes will affect the addicts’ current decisions about smoking. In Figure 24-3, we would interpret this by saying that a permanent price increase shifts the consumption curve downward farther than a temporary price increase. Both the price effect and the probability of going cold turkey are enhanced by permanent price increases. Likewise permanent restrictions on the advertising of cigarettes would have more effect than temporary ones.