Friday, May 21, 2010

The Efficient Allocation of the Right of Way

This may not be representative of society in general, but lately when passing by crosswalks, I have noticed two things:
1. Cars being less willing to stop for waiting pedestrians.
2. Pedestrians being more willing to wait for a break in the traffic before starting to cross, instead of demanding that cars stop for them.
This got me thinking about the traffic rules for crosswalks (giving pedestrians the right to cross whenever they want to), and has led me to some interesting insights into why the rules are the way they are. I do not know, however, why I see so many drivers and pedestrians acting contrarily to the rules. What follows is a meditation on proper crosswalk behavior, and how economic efficiency dictates what customs we follow (or rather should follow).
To begin with, let's make some assumptions that will allow this thought experiment to take place.
Let's assume that drivers and pedestrians can all be categorized into four groups, and that people in these groups behave the same each time they approach a crosswalk. The four groups are as follows:
1. Pedestrians who wait for the cars to pass before they walk, denoted by Pw (pedestrians who wait)
2. Pedestrians who do not wait for the cars to pass before they start walking, denoted by Pnw (pedestrians not waiting)
3. Drivers who wait for pedestrians to cross, following the law as it currently stands, denoted by Dw (drivers who wait)
4. Drivers who do not wait for pedestrians to cross, just driving through and forcing the pedestrian to wait or get run-over, denoted by Dnw (Drivers not waiting)

Thus there are the following four scenarios that could happen at the crosswalk:
Pnw meets Dw (pedestrian crosses easily)
Pnw meets Dnw (pedestrian and driver both try to go, resulting in a dangerous face-off)
Pw meets Dw (pedestrian and driver both wait around like idiots, resulting in a delay until they sort out who should go)
Pw meets Dnw (Driver goes and pedestrian waits for break in traffic)

Now lets consider the costs involved in each scenario.
(denoting "meets at the crosswalk" with a /)
Pnw/Dw: the cost of the driver having to waste time and gas to stop.
Pnw/Dnw: the cost to both pedestrian and driver of a possible harmful or fatal accident.
Pw/Dw: the cost of the driver's time and gas, as well as the pedestrian's time.
Pw/Dnw: the cost of the pedestrian's time.

Clearly Pnw/Dnw entails the highest cost.
We'll return to this discussion of cost shortly, for now we have more assumptions to consider.
Let's assume that 80% of pedestrians don't wait for a break in traffic, and the remaining 20% wait for the cars to pass. This gives us probabilities that a random pedestrian will be of each group. Here are the probabilities:
("probability of an event" is here denoted by P(event))
Secondly, lets assume that 80% of drivers are those who stop for people at crosswalks, and the remaining 20% are the jerks who just plow through. This gives us probabilities that a random driver will be of each group. Here are the probabilities:
From these probabilities we can create a probability distribution for each of the possible scenarios at a crosswalk.
Because a certain type of pedestrian coming to a crosswalk, and a certain type of driver coming to a crosswalk are totally unrelated, independent events, we can find the probabilities for each situation by multiplying the driver and pedestrians' probabilities together.
So this gives us the following probability distribution:
P(Pnw/Dw) = 0.8*0.8 = 0.64
P(Pnw/Dnw) = 0.8*0.2 = 0.16
P(Pw/Dw): = 0.2*0.8 = 0.16
P(Pw/Dnw): = 0.2*0.2 = 0.04
So in this imaginary world I have created, 16% of all crosswalk encounters create a possibly dangerous showdown of pedestrian versus car, the most costly of the scenarios. 4% of the time there will be the boring situation of both driver and pedestrian wasting their time and/or gas. And the remaining 32% are efficient situations where either the driver or the pedestrian waste time/gas, but not both.
The first conclusion to be drawn from this hypothetical situation is that fewer costs will be incurred if all drivers and pedestrians knew what the rule was and followed it consistently. Let's imagine another world with different laws, where 100% of pedestrians were Pws and 100% of drivers were Dnws. Pedestrians would spend more time waiting than they do under the current rules, but the dangerous Pnw/Dnw scenario, and the extra time-and-gas-wasting Pw/Dw scenario would both be eliminated. This shows that there are clearly efficiencies to be gained from people behaving consistently as the result of clear property rights, regardless of who is given the rights in the first place. I believe this is the essence of the famous "Coase Theorem" in economics. In this case it would be cars that "own" the right of way. If pedestrians uniformly respected this property right, the result would be better than if pedestrians and cars didn't know or care about who has the right of way, resulting in accidents and delays.
With that being said, cars clearly should not have the right of way. The "transaction costs" (also a key element of the Coase Theorem) pedestrians face in crossing the street (e.g. the chance of getting run-over) are obviously much higher than those that cars face (e.g. wasting some gas). Thus to create a more efficient society, the law allocates the property right in a way that minimizes costs.
If drivers and pedestrians would just act like they understand who owns the crosswalk, it might be safer out there.

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