Saturday, May 15, 2010

Tobacco: Optimal Fines for Enabling Adults

The other day I was walking past a liquor store and saw a sign in the window, explaining that adults who buy cigarettes for minors will face a $200 fine. This made me think of the concept of the optimal punishment for a crime, which I was first introduced to by Donald Wittman's Economic Foundations of Law and Organization, ( a great book I highly recommend.)
To determine the optimal punishment for a crime, societies take into account both the harm caused by the crime and the probability of catching the criminal, which tends to conform to the following model:
with P being the probability of getting caught if you commit a crime, and H being the harm the crime causes to society. This leaves F, the appropriate fine to be levied out so that, in the aggregate, it will make criminals pay for their behavior, thus efficiently deterring crime.
So if smashing someone's window costs the victim $100 dollars in damage, and there is a one in ten chance of being caught for the crime (P=0.1), the appropriate fine for smashing a window would be $1000. If suddenly, (maybe due to new window smashing technology), it became twice as hard to catch a window smasher (P= 0.05), the punishment should double to $2000. The punishment should also double if the cost of window repair were to double, (H=$200). So with optimal punishments, crimes that cause more damage, as well as those that are harder to catch, are met with proportionally harsher fines.
So is the $200 fine for buying tobacco for minors an optimal punishment? My initial reaction is "heck no." But sound policy is not based on reactions, here I shall try to provide quantitative analysis to help answer this question. Though I do not have all the data needed to answer it, I will set up a framework into which data could be plugged, to lead us closer to the truth.
To begin with, lets try to get an idea of H (the cost to society of buying a pack of cigarettes for a kid).
To find H, we must isolate the smoking (both present and future) that would happen directly as a result of an adult buying a pack of cigarettes for a minor. It must be differentiated from smoking that would happen otherwise. Obviously when an adult buys a pack of cigarettes for a kid, this is increasing smoking by at least one pack, and possibly more than that because that one pack could lead to more smoking in the future. While some kids will get hooked for life because of that one pack, and possibly die of lung disease, others may give it up after a single puff. The probabilities involved in this game of slow motion Russian roulette are very hard to quantify. But to arrive at something close to H, one could start by taking a large sample of people who had been given cigarettes by adults when they were minors. The next (very challenging) step would be to use regression analysis to try to isolate the effect of each illicit tobacco purchase on the minor's cigarette consumption over a lifetime. Lets assume that an amazing statistical study determines that each purchase of a pack of cigarettes for a minor leads to 1.1 more packs to be smoked in total than would happen in absence of the crime, (the extra 0.1 being because of kids led to further smoking as a result of the one pack that was bought for them). The next step would be to find the cost to society (to the smoker and everyone else) incurred because of that one pack. Searching around the internet, I've found a group of scholars who say the total cost to society from one pack of cigarettes is $40. For our purposes, lets assume this is the cost. Under these assumptions, we have found H.
H = $40*1.1= $44
So the total cost to society from the crime is $44, the societal cost times the expected additional quantity of tobacco consumed.
Now let's try to think of a way to find P, the probability of getting caught. (As an editorial note, this seems to me to be a pretty easy crime to get away with. All an adult has to do is find a discreet way of passing the cigarettes to the youth, end of story.) It would be difficult, but one could find the probability of getting caught for the crime, by taking the total number of convictions for the crime, and dividing this into an estimate of the total number of times cigarettes were purchased for youths, which could be estimated through surveys of young smokers.
That is beyond my means, so lets just assume that one out of every hundred of these crimes is discovered and prosecuted (which I would guess to be a very generous assumption.) Now we have P.
P = 0.01
And with P and H, we can find the optimal punishment, F.
Plugging P and H into the formula gives us:
So using these assumptions, the appropriate fine for buying a pack of cigarettes for a minor should be $4400. This is 22 times the actual fine for my jurisdiction.
However, this is not a real study and largely based upon numbers I pulled out of my imagination, and from an academic paper that, to be honest I only read the abstract of. But I wouldn't be surprised if the probability of getting caught for this crime is a lot lower than 1 out of 100 (thereby increasing F), and that $40 is a good estimate of the total societal cost of a pack of cigarettes.
So for the sake of argument let's now assume that this estimate of F is close to reality. What could be a reason for the big difference between F and the actual $200 fine. Perhaps because of the legal and social acceptance of smoking as an adult, the law only considers the damages to society incurred while these smokers are minors, while the actual costs of smoking (e.g. addiction, lung disease) are heavily back-loaded to times long after the young smokers have grown up, and their habit has long been accepted by the society it damages.
So who would be harmed by increased fines for this crime? Just the enabling adults and the tobacco industry.


Donald Wittman, Economic Foundations of Law and Organization, Cambridge University Press, 2006

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