‘irrationality’ and Measuring the Social Costs Of Substance Abuse

A note prepared for the International Working Party on Substance Abuse.

Keywords: Health;


While considerable progress has been made on measuring the social costs of substance abuse, the question of how to deal with the ‘irrationality’ of consumers has not yet been resolved.

The incorporation of irrationality into actual behaviour does not come easily to economic theory, which traditionally has assumed that consumers are always rational. In recent years however, there as been a characterisation of consumer behaviour which involves time- inconsistency in their decision making.

This paper explores the implications of this characterisation for the measurement of the social costs of substance abuse, and thereby suggests a resolution to the problem of the extent to which the costs incurred by the substance abuser to her or himself should be included in aggregate social costs. The proposed resolution involves an analytical framework, together with the use of an empirical parameter, the estimation of which is hardly discussed here.

Rationality in Consumption – the Standard Account

There is a standard account in economics of how consumers make decisions which involve effects through time. At a very simple level it goes like this.

Each consumer faces a choice between two streams of net benefits reflecting different two different options. In one option the stream might be
b0, b1, b2, b3, …. bi …,

Where bi is the net benefit (benefits less costs) in the ith period.
and the other might be
c0, c1, c2, c3, … ci ….

Note the some of the elements may be negative, that is in a particular time period the costs may exceed the benefits.

In order tho choose between the options the consumer calculates
(1) B = Σbi/d^i
(2) C = Σci/d^i
– in each case i is summed from 0 to infinity.
– d is a discount rate (often characterised by 1+r) which reduces the value of future costs and benefits in proportion to the time they are away from the present. Notice that 1/d<1, so the consumer is likely to give little weight to the effects in ten years time, and even less to those in twenty years time.

The rational consumer in the theory then choses the option (either b or c) based on which of B or C is the larger.

It would be foolish to assume that individuals are as calculating as this. However, the basic notion of their taking into considerations of all the costs and benefits to them, but giving less (in a systematic way) weight to costs further in the future seems to be a reasonable characterisation of most people’s behaviour most of the time.

This behaviour is usually called ‘economically rational’.

Irrationality and Time-Inconsistency

In order to give an intuition of the phenomenon being discussed, consider a three period situation where in the first period the individual plans their consumption of alcohol in the second period, and potentially suffers a consequence, say a hangover, in the third. Suppose in the first period, the individual decides that they will confine themselves to, say, three glasses in the second period, thus avoiding a hangover in the third period. However, very often the actual consumption is, say, six glasses and the individual suffers a roaring hangover, laced with the regret that if only they had kept to their first period drinking to plan.

Economists label this ‘time- inconsistency’ which can be defined as situations where, with the passing of time, policies that were determined to be optimal (yesterday) are no longer perceived to be optimal (today). That applies between the first and second period of our example.

Because such terms as ‘rationality’ and ‘irrationality’ and ‘addiction’ are used rather loosely, while there are technical terms like ‘rational addiction’, it is proposed to hereafter call this behaviour ‘time- inconsistency’ and leave others to decide whether it si rational or irrational, or addictive.

This time- inconsistency can be modelled with ‘hyperbolic discounting’ proposed by David Laibson (1997). A simpler algebraic presentation will do for our purposes.

Suppose the net benefit in one course of action, say the restrained drinking, in each of the three periods is b0, b1, b2 (as judged by the consumer), and the other course, the greater imbibing, is c0, c1, c2. Since in our example b0 and c0, incurred while they are planning ,are the same, they may be taken as zero. The second period net benefits (including the offset for the financing of the drinking) b1 and c1 are both positive with c1 the greater because consumption is higher. We assumed that b2 was also zero, there being no hangover or other subsequent costs from the restrained drinking of the earlier period. However c2 is negative.

So the decision-maker faces two streams: cautious drinking (0, b1, 0) and higher imbibing (0, c1, -c2). In the first period the decision-maker does the standard discounting. of the flows and calculates the net benefit of the first option is b1/d and c1/d-c2/d2. (Where, we use, for simplicity ‘d ‘as the discount factor). Since the individual plans the more restrained option we know

(3) b1/d > c1/d – c2/d2
(4)b1 > c1 – c2/d.

In the second period the decision-maker faces (b1, 0) and (c1, -c2) which gives exactly the same decision. If b1 > c1 – c2/d, then the choice will remain the restrained consumption. There is time- consistency: the policy chosen in period 1 remains the policy chosen in period 2.

However, sometimes the individual chooses the high consumption option.

So we have to modify the analysis. Perhaps the simplest form of the hyperbolic discounting involves an adaption of the standard discounting rule from
(5 – ie.e (1)) maximise Σbi/d
(6) maximise b0 + βΣbi/d.

where β <1. (Were β=1, it would be the time- consistent formula again.)

What is happening is that when making the decision the individual devalues future costs and benefits relative to those in the decision period (above that of standard time- discounting). The smaller the β the less notice is taken of the future consequences of a current decision.

Apply this to the simple example we looked at earlier.

From the first period perspective equation 1 becomes
(7) βb1/d > βc1/d – βc2/d2
which remains as for equation 4..
(8) b1 > c1 – c2/d.
So exactly the same decision is made as in the time- consistent case.

In the next period the sequence (b1, 0) is valued as b1, but the sequence (c1, -c2) is valued as c1 – βc2/d, which is larger than c1 – c2/d.

The decision inequality is no longer (8), but b1 against c1 – βc2/d so that now it is possible (say β = 0) that
(7*) b1 < c1 – βc2/d.
so the consumer would abandon the restrained drinking option, and imbibe more generously. Thus the consumer exhibits time- inconsistency.

This analysis is being applied in many areas of consumer behaviour, including the case for higher sales taxes where such behaviour occurs, demonstrating they may generate a gain in consumer welfare. (O’Donoghue & Rabin, 2003) However, as far as is known, nobody has yet considered its relevance to estimating the social costs of substance abuse.

The Social Costs of Substance Abuse When there is Time-Inconsistent Behaviour

When the social costs of substance abuse is being estimated, one of two options are typically preferred in regard to the costs imposed by the consumption on the consumer. The first is that any costs that a substance abuser causes to her or himself is included in their rational calculation during the consumption decision, and therefore should not be included in social costs since it is offset by the benefit the consumer gets from the consumption. The best known proponent of this view is Gary Becker. (His 1988 paper with K. Murphy defends this view based on rationality but introduces the notion of rational addiction).

The alternative approach has to be to include all the costs incurred by the substance abuser after the consumption (that is excluding the purchase price).

Which is the more correct?

Suppose there is the time- inconsistent behaviour and the consumer takes into consideration only β of the future costs to her or himself. They ignore (1-β) of those costs in their calculations.

This suggests that this (1-β) of the costs should be included in the social costs of substance abuse, because just like the costs to other people, to businesses and to the public sector they are ignored when the consumption decision is made and are not offset by any benefits that the consumer gains from the use.

We can see that those who are arguing that none of the costs which a consumer imposed upon themselves should be included in net social cost, are assuming that β = 1 and there is no time-inconsistency. Conversely, those who argue that all of the costs should be included are arguing that β=0, and there is total time-inconsistent behaviour.

Thus what appears to a be a theoretical dispute proves to be an empirical one, the size of β.

Applying the Consequences of Time-Inconsistent Behaviour to Social Cost Estimates

In the following I am going to assume that the economist’s description of addiction is acceptable to sufficient specialists in the addiction field. Behavioural economics is based on economists’ understanding of the psychological literature. Even so, I have not seen a lot of non-economics expertise supporting it.

In some respects the above resolves a theoretical dispute by showing it is an empirical dispute by proposing to bell the cat. The tough job still has to be done. What are the β?

Note that we are considering only the application of the β to the personal costs to the substance abuser (including sickness and death as well as financial layouts). The costs to others, to businesses and to the government are to be treated exactly as they are recommended in such guideline as Single et al (2000) and Collins et al (2005)

In the current state of knowledge, the best we might get to a guidelines. The following is intended to be indicative – a basis for discussion. Empirical evidence to support some conclusions needs to be scouted out. The last section discusses how to deal with development of addiction.


Perhaps it will be recommended that β = 1 for narcotics, that is the abuser completely discounts the costs incurred. This is an extreme assumption. One could imagine a mild abuser whom we would not call an addict, making calculated assessments of the effects of their consumption including subsequent harm. However since such harm is likely to be small, β is probably very close to unity.


Many people consume alcohol with their β equal to or near equal to unity. But they probably dont cause a lot of damage to themselves. (How much?) What we need is an estimate of the βs for those who consumption leads to significant damage to themselves. It would be easy to assume that for them β = 0, that is they completely ignore subsequent costs when they are drinking. That may be true for some, but is probably not true for everyone (as when one takes just one more than is ‘good’ for one). Note too the relevant β is not the average for addicted drinkers but the average weighted by the self-damage they cause which is likely to be nearer to zero. Probably the required β is very low, but how low?

We need a panel of experts to make an assessment. What empirical evidence might help them?


Unlike alcohol, all smoking of tobacco is self damaging, although because of the damage to the heart (and perhaps for other medical conditions) the damage on average depends upon the age of the smoker.

We also have got past the stage that smokers can claim ignorance of the consequences of their smoking. There may be some – perhaps the very young – and there may be some dangers of which we are not yet aware. But the anti-tobacco/public health campaigns have sufficient effect that the message that smoking is damaging to one’s health is broadly understood by the vast majority of smokers.

More problematic is that much of the damage is some distance in time off. An ordinary discount rate may reduce the significance of the damage to a rational addict so they continue to smoke. We probably need to think more carefully about how this impacts on the social cost measurement. It may differ between the two standard counterfactuals which lead to either avoidable costs or total cost calculations.

But even ignoring this time dimension, there remains the problem of assessing an appropriate β.

When surveyed many, but not all, smokers regret they smoke, saying they would like to give it up. Presumably those smokers have lower βs than unity (although not necessarily zero). But what about those who say they have no regrets? Are their βs unity or are they showing bravado?

And how do we deal with the young? If the costs are low (as on their hearts) or a long way away they might smoke with a β of unity, even though later they incur considerable costs (say cancers precipitated years earlier). The next section discusses a further complication.

It is not evident from this that the relevant aggregate β is close to zero. Again we need a panel of experts to make an assessment. What empirical evidence might help them?

Consuming which Generates Addiction

Currently most behavioural economics assumes the β is given for each individual.

But practically we know of people who start off as non-addicts (β=1) and become addicts (β<1, even 0). It is not hard to envisage that the value of β depends upon past consumption either in terms of aggregates of some nonlinear function where intensity (consumption per unit time) is important.

For instance young people who have never smoked are not addicted to tobacco. As they smoke (presumably discounting the low likelihood of heart disease and the distant likelihood of cancer) many become addicted, their β falling below unity. How do we incorporate that behaviour into the personal costs they generate? Obviously we need to model the phenomenon more precisely than these paragraphs (and the modelling may lead to insights of how to better deal with the young’s pre-addictive behaviour).

And then there will be the task of incorporating the insights into these models, no doubt with some empirical evidence to guide us on the parameters.


Science generally develops by incremental steps. This paper has clarified the dispute between those who want to incorporate all personal costs from substance abuse into social costs estimates and those who argue that none should be included. It has shown that the true response depends on a parameter β which lies between zero and unity which reflect the two extremes of the dispute (and perhaps on some other parameters). However despite the progress, there is much theortical and empirical work to be done.

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