07 Nov 2012

How Chris Christie’s License Plate Scheme Adds Insult to Injury

Economics, Oil, Shameless Self-Promotion 26 Comments

[UPDATE: Actually, I am not sure the below is relevant, after thinking it through some more. What I will defend is the statement that if we had a long period of price ceilings, with new gasoline supplies being brought into the region but where the demand consistently were higher than the available quantity supplied, and there were no restrictions and how much you could buy once you made your way to the front of the line…then in that scenario, introducing license plate schemes would only make things worse. However, if you had a situation of a fixed total supply, a relatively short period of a price ceiling, and quantity restrictions (so you could only buy X gallons at a time), then in that scenario I could see how license plate restrictions added on to of all of these things, could reduce lines.]

Following up on an observation made by Ken B., I wrote the following in the comments of my previous post:

Major_Freedom wrote:

[I thought the license plate rationing scheme wouldn’t exacerbate the lines, because] I was assuming a constant distribution of plates. I was assuming that in any given neighborhood, or city, or whatever, there would be a 50-50 split.

[Bob now responds to Major_Freedom:] OK assume that. Now imagine an extreme scenario where in your neighborhood, the people with even plates for some reason don’t need to drive on Monday or Tuesday. But the people with odd license plates need to drive on both Monday and Tuesday.

If we just have the price ceiling, but no other rationing, then in practice the lines from the odd-plates will be evenly spread out over Monday and Tuesday. On Monday they might all go to fill up, until the lines encompass half of them and (since we assume rational expectations) they know that the lines will be just as long tomorrow, that’s when people decide to wait a day. (Or, people who really are running low on gas go on Monday, leading to long lines that encourage the others who can wait a day, to go on Tuesday.)

But then Chris Christie says, “If you have an odd license plate, you can only buy gas on M-W-F.”

Now everybody has to pile in on Monday, who can’t wait until Wednesday. So the lines that these people have to wait in, are longer than they would be in the other equilibrium.

And with our extreme assumption, there are no lines at all on Tuesday.

Yes if you assume away enough stuff, “on average” the license plate thing might not matter, but *at best* it won’t matter. There are all sorts of real-world complications that could make it cause worse delays.

Another way of putting it: It can’t possibly *reduce* lines by introducing another constraint, since the market would have an in-built mechanism to spread the lines out over time and minimize them. Thus, introducing a new constraint can at best do nothing, and in practice will lead to longer lines on average.

26 Responses to “How Chris Christie’s License Plate Scheme Adds Insult to Injury”

  1. Marc says:

    I get the point, but one tiny thing — who does your extreme assumption mean that there are no lines at all on Tuesday? You still have the evens going in on Tuesday, Thursday, and Sunday. So wouldn’t Even’s Tuesday be the same as Odd’s Monday?

  2. Marc says:

    Oh and one more thing — The reality is that New Jersey’s lines are basically over: http://www.northjersey.com/news/North_Jerseys_long_gas_lines_appear_to_be_over.html
    …while New York’s gas lines are still going strong (as I have witnessed).

    …Unless you say that New York has a gas shortage and Jersey doesn’t. And I’m not sure if that’s the case or not.

    • Dan(DD5) says:

      I live in NJ. There are still lines in most stations that are open but it’s not as bad as it were a couple of days ago. Driving for about 20 miles today home from work, I actually found a station open with no lines. (So I went in with 2/3 tank and topped up). There are no more cops in most stations and so nobody gives a damn about Christie’s rule anymore.

      • JFF says:

        Dan, did you make the trek south of I-195 at all last week? No lines down there.

  3. rob says:

    Other things being equal surely the license plate thing would discourage people from driving as much (since filling up would be much harder to plan) and cause the lines to be shorter.

    • Bob Murphy says:

      It’s not as obvious as you think Rob. I agree in this case it actually probably helped, but only because I think they had other quantity restrictions in place.

      • mike says:

        What about unintended consequences such as switching licence plates whether it is a second car or friends car.. So Govt solution creates yet another problem and has the same outcome long lines.

    • Ken B says:

      Random beatings of drivers would have the same effect. Is the goal shorter lines by any means necessary or amelioration of the problem?

      • Major_Freedom says:

        I think the point was not an advocacy, but a challenge to the assertion that odd-even plate days would exacerbate the length of line ups.

        • Ken B says:

          Well actually my claim was that it would make things worse. Worse has many dimensions.

          Rob’s effect is imposing an extra non-price cost at random on some drivers. If you think about that it should sit ill with advocates of odd/even. Banning bald drivers would cut lines too. That’s not the intended way for the scheme to work.

          • Major_Freedom says:

            Rob’s effect is imposing an extra non-price cost at random on some drivers. If you think about that it should sit ill with advocates of odd/even. Banning bald drivers would cut lines too. That’s not the intended way for the scheme to work.

            Again, what rob said clearly wasn’t an advocacy. He is only saying that odd-even plate days would not necessarily increase the line ups, but would shrink them.

            I am not necessarily agreeing with rob’s argument. I am just saying you don’t seem to be getting his point. You are taking it the wrong way.

            • Ken B says:

              I get his point. My comments acknowledge that that is a possible effect.

              I am not arguing that as a theorem in queing theory odd/even must in all cases make lines longer. I am arguing, as Bob sees, that in the real world odd/even will make the problems worse.

              • Major_Freedom says:

                Weird. You acknowledge that it is a possible effect, but then you say, as a seeming theorem, that it WILL make the problems worse, which of course would exclude said possibility.

                Can’t say it makes sense to me.

              • Ken B says:

                You out there DK? Since you had doubts about certain reading skills.

              • Major_Freedom says:

                Nice try, but this is ALSO a time when the problem is not my reading comprehension.

                Maybe you and DK could join a remedial class on argumentation and basic logic.

                Your problem is you don’t realize it when you are in the presence of superior argumentation, so you automatically assume the problem is with the other guy. Maybe it’s a self-esteem thing.

              • rob says:

                For the record, I am against both price controls and rationing.

                First assuming that the odd/even measure has no effect on total fills by the average driver and only affects the days they fill:

                With or without the measure the average length of line will be determined by (total number of fills / filling days).

                Intuitively it seems that the variance in queue length would be greater without the measure than with it (the group size is bigger and the maximum fills therefore also bigger) but maybe this is not statistically valid when the groups are really large like in NJ(?)

                If the measure does effect the total fills by the average driver then all bets are off. Some factors (like the one I mentioned) would lead to shorter lines. Others (like people always filling on the days they can even if they are not empty) would go the other way. One could not say which would win out overall.

  4. Ken B says:

    One question to ask is, will odd/even give me an incentive to line up to buy a smaller amount of gasoline that I otherwise would? It’s pretty clear that for many it will. After all the cost of missing a chance is higher the fewer chances you are allowed. So more small purchases mean longer lines. Since filling up involves some time overhead, this means more time in the line, for you and hence for others. A really simple model is each stop involves 1 time unit overhead, plus1 time unit for a small fill, and 2 time units for a big fill.

    It’s like old men with small bladders at the theatre.

  5. Don in NJ says:

    Odd/Even actually does not have any real effect or possibily a negative effect. As an example assume a 4 day period where a number of people have to get gas or plan to get gas. for simplicity lets assume there are 4000 people. that would be 1000 per day in line. But now lets put the restrictions in place – the same number of people have to get gas over those 4 days but on any given day only 2000 can get gas – so lets assume on average half go the first avalable day and the half the next available day- still 1000 car a day.

    Now add in the fact that this rationing is in effect in the first place- it causes panic- what if there is no gas when i need it???? i’ll just fill up today since i cant tomorrow. this results in even more people waiting in line with 1/2 to 3/4 full tanks. Lines get longer in this case.

    And we think these people can balance the budget – HA!

  6. Ken B says:

    The X gallon restriction is tricky. It could force me to line up more than once in a day to get sufficient gas, so by itself can makes lines longer. Lining up twice to buy 2X gas takes longer than lining up once to buy X, so everyone waits more.

    As I have remarked there are actually two things in demand here: gasoline and *spots in line*. Odd/Even has no direct effect on demand for gas (as rob notes it can have some disincentive effect). But it can strongly effect the demand for *spots.*

    • Ken B says:

      oops Twice for x vs once for 2X I meant

    • Bob Murphy says:

      Yeah that’s what I’m trying to nail down, Ken, before I write more on this. Surely even before the odd/even thing, if there is a humongous line and the guy at the front is not only filling up his tank, but also 50 gallons of additional containers, I’m thinking that would be prohibited.

      • Ken B says:

        I’m thinking so too, but I expect allowing it would shorten lines. I’m thinking in the comment above about X being less than a usual tank. So I can get a full tank, say 1.5X size, filled but in two stops.

        As long as there is overhead, and of course there is, and as long as the odd/even either
        1. turns someone away from an empty station
        2. causes him to make an extra stop
        then lines get *longer*

        If it unbalances lines then it makes things *worse* by increasing burdens on motorists. It will unbalance them if the odd/even is non uniform or if I must pass up short lines on my day off.
        Consider these 2 queues (no overhead) assumed to be in equilibrium (because of the odd even not allowing balancing)
        5 4 3 2 1
        3 2 1
        total waiting 21
        4 3 2 1
        4 3 2 1
        total waiting 20
        Overhead compounds the problem.

        Then there’s the whole issue of supplier incentives. Does it make sense to stay open past midnight? Under realistic conditions you get empty pumps, and drivers who cannot line up at 11:57.

        • Bob Murphy says:

          What do you mean by overhead?

        • Bob Murphy says:

          Ken don’t pull the trigger on this yet (assuming you’re even interested), but I am 95% sure I will write on this for an IER blog post. If I could outsource to your blog for a simple numerical example of how the odd/even thing can create more total waiting in line, that would be cool.

          However, if you did go down this path, you will have to try really hard to make it comprehensible to a lay reader.

          • Ken B says:

            I’ll hold off on doing anything Bob.
            By overhead I mean time other than filling. If the time at the pump were just time spent pumping then it would nbe proportional to the amount of gasoline. But it’s not, since there is time getting in and out of the car, paying etc. So when I construct an example I want 2 fills of size X to consaume more time than one fil of size 2X.

            That’s why my toy model has 1 unit overhead.
            In the example above everyone takes the same amount of time regardless of the amount they buy.

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