Smokers smoke. Gamblers gamble. Drinkers drink. Why should anyone else care?
Some non-economists believe that economics assumes selfishness. Each person is only concerned about themselves, and their material consumption. Selfishness can be represented formally like this:
A person's "utility", their well-being or happiness, is a function, u, of their consumption of goods and services, represented by the vector x.
An entirely selfish person doesn't care if others smoke or gamble or drink. Her well-being depends only on her own consumption. Live and let live (or, as the song goes...).
Yet people's choices affect others. Smokers exhale, filling the air with tobacco smoke. External effects of smoking upon other people's consumption, or "externalities", can be incorporated into a selfish non-smoker's utility function like this:
The non-smoker's well-being now depends upon the number of cigarettes, c, the smoker consumes. If a smoker creates second-hand smoke, and it causes a non-smoker discomfort, then ∂u/∂c<0 - smoking makes non-smokers worse off.
Externalities explain why cigarettes are regulated and taxed: why Canadians have to go outside if they want to smoke, even if it's -30 degrees Celsius with the windchill, or +45 with the humidex.
But externalities are not the only reason why people beg friends or family to stop drinking or gambling. People care when those whom they love drink or gamble, even if it happens when the drinker or gambler is alone in the middle of the night.
One way economists model the ties of kinship or friendship is through "caring preferences." An altruist, A, is someone who cares about another person, who we'll call B. In this example, the non-smoker is the altruist, and she cares about the smoker. Hence her overall well-being, UA, depends upon the pleasure, uA, she gets from her own consumption, xA, and the utility of the person she cares for, uB, as follows:
or, to make things simple, like this:
UA=uA(xA) + suB(xB,cB) (3')
Here cB represents B's consumption of cigarettes, x represents consumption of other goods, and s represents the strength of A's feelings or "sympathy" for B. If s=1 then A cares as much about B as she cares about herself.
Caring preferences are non-paternalistic. A only cares about B's smoking in as much as it causes B pain or gives B pleasure. She gets no direct utility one way or the other from B's smoking: she completely respects his or her preferences.
Equation (3) describes the circumstances of a friend of a friend of mine - let's call her "B". As I write this, B is dying. Cigarettes are one thing she can still enjoy. So her husband, "A" buys her cigarettes, wheels her outside in her wheelchair, and lights up her smokes for her. He doesn't ask her to stop. He loves her too much to deprive her of any pleasure.
But equation (3) does not explain why friends ask friends to stop smoking. If smoking gives B pleasure, shouldn't A be happy? Why should A try to deprive B of pleasure?
Smoking, I've been told, is a lousy addiction. Cigarettes stop being a source of pleasure; they are only a way of temporarily easing the body's cravings for nicotine. Behavioural economics recognizes that what people do isn't necessarily what people want - a smoker might wish he could stop, but be unable to do so. Suppose c* is B's desired level of cigarette consumption - the number of cigarettes he would plan, or choose, to consume, if he could resist the urgings of his impulsive inner Homer Simpson. Then we can represent B's utility function by:
where ∂u/∂|c*-cB|<0. Smoking more or less than his desired level of cigarettes makes B unhappy. If the altruist knows what B's true desires are, then her caring preferences become
UA=uA(xA) + suB(xB,|c*-cB|) (4)
She tells B to stop smoking, but only because this is what B really wants. This kind of caring is implicit in the interventions staged by reality TV shows such as Hoarders: forcing people to change, to give up their bad behaviours and addictions, will make them happy, and that makes everyone around them happy.
But life isn't reality TV.
I have a friend who smokes. I wish he didn't. Why? Because he's quite a bit older than me. Smoking could kill him in the next ten or fifteen years, and I hate that idea.
The caring preferences in (3') have no time dimension. But it wouldn't matter if they did - A respects B's preferences. If B smokes, presumably that's 'cause he's hoping for an early death. I went to the effort of writing down a beautiful function representing intertemporal caring preferences, and then realized: it makes no difference at all (but here's the utility function anyways. dA and dB represent the death of A and B respectively. t indexes time, and i is the (time invariant) interest rate.).
A libertarian altruist wants others to be happy, and if smoking is what it takes, that's fine.
But I'm not a libertarian altruist. I want "B" to stop smoking, because I enjoy having him around. Borrowing notation from the household production literature, B's existence produces a good, Z(B) - laughter, friendship, understanding - for A. The non-smoker's utility function is now:
If smoking decreases B's life expectancy, and A can expect to outlive B, then by smoking B is depriving A of his or her company. Individual A is utterly selfish - but also non-paternalistic - in wanting B to stop.
If A was older than B, and expected B to outlive her even if he did smoke, then with the preferences described by equation 6, she would have no reason to be concerned about his smoking.
Incidentally, equation (6), combined with caring preferences as in (3'), explains why some people quit smoking when they become parents. Suppose B is a middle-aged parent with a young child. Continuing with the notation above, B is the smoker (the parent) and A is the non-smoker (the child). The child's well-being depends upon parenting that only B can provide, Z(B), as in equation (6) above. If B cares for A, then B's preferences are, by analogy with (3'):
UB=uB(xB,c) + suA(xA,Z(B)) (7)
It comes down to: which does B value more - the momentary thrill of a cigarette, or being around to guide his child through university? Or perhaps B, as in 4 above, doesn't want to smoke, doesn't plan to smoke, but in the moment is unable to resist temptation?
I've been talking mostly about smoking, but anyone who has known a drinker will recognize many of the same dynamics I describe. Gambling a bit different. Whether gambling is a "problem behaviour" or not depends to a large extent on the skill of the gambler. The professionally successful stock trader or poker player may have just as much of a chemical addiction to gambling as the losers on the slot machines, but as long as they're making money, what's the problem?
It's fun to do fancy stuff with preferences, but there's a lot of insights to be gained by looking at budget constraints. If A and B have a common budget constraint, A is going to object to B spending money on alcohol and cigarettes, or incurring large gambling losses, because it's money that can't be spent on other things. Rewriting (1):
As before, xB is B's consumption of other goods and services, and c is B's spending on cigarettes. The family's total income is represented by m. The amount available to spend on A's consumption is reduced by a dollar for every dollar B gambles or smokes or drinks away. There's lots of moralizing about smoking. But one person's smoking doesn't cause another person to lose their home or their life savings: one person's gambling can.
Is there a point to this? Other than that I derive pleasure from playing with utility functions and thinking things through?
There is a lot of discussion right now about libertarian paternalism. It may be helpful to think, systematically, about why one person ever has any reason to want to interfere with another person's consumption choices.