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So from what I see, it would be insane and IMO you out yourself as a nut if you tried to defend it to expect a actual step change in outcomes pollution level on the passing of one of these laws. The distance between two points is the straight line connecting the points. Atiyah Gromov. Back to Top. A few things to keep in mind: 1. When the polyline has multiple line segments the most common case , the closest line segment to the point is determined first, and then Rule 2 is applied to get the distance. Concepts Features.
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Need a translator? Translator tool. Browse rectangle. If the costs are indeed exponential then at some point the incremental cost exceeds the incremental benefit, and on an exponential graph it is easy to go well past that point in linear dollars. Something may cost fifty billion a year and be worth that cost, so you require it, then ten years later someone discovers a way to get the same benefit for ten billion. But the rule requiring the old method is still on the books. Graph the number of workplace accidents per capita on a log curve instead of a linear one. The alleged straight line goes away.
The lead line is rather instructive. Lead started being phased out by law in , but the big drop was probably the requirement of cars which accepted only unleaded gasoline. No matter how many laws you have you only have so much bureaucratic enforcement you an apply.
And at the same time industry only has so much capacity to make changes. So one model would be that you need a certain amount of legal overhang to keep making progress and that progress will eventually level off if the actual situation ever arrives at what the law says it should be.
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This seems right to me. My understanding is that the s amendments addressed much more than the four pollutants graphed, including Ozone, for example. And on the other, other hand, I wonder would happen if you took the Y-Axes in all of the graphs shown and divided them by something like the GDP, as well as controlled for other factors relating to globalization. All it takes is one company to lead the way, the others will have to follow if they are to stay competitive.
The cost of chip fabrication facilities has also always increased exponentially. This worked out okay as long as demand for CPUs also increased exponentially, but that stopped sometime after Since about , transistors per CPU—on the most-expensive CPUs—has increased much faster than transistors per dollar.
Also at that time, clock speed basically stopped increasing. This does not necessarily say anything about what that cost will be, either per component or overall. While the point is interesting, I feel like the transistor data is a bad example and relies on the presentation of the data.
First, the data presented is log-linear; if you were to put the vertical line before the shoulder of the exponential growth on a linear-linear plot it would emphasize exactly how important photolithography is. Second, there are only four data points before the vertical line. It not statistically significant to fit an exponential to such a small sample size. The presentation hides how noisy this is. Moreover, if you do a regression on the first 4 points, it suggests we should have at least two-orders of magnitude fewer transistors than we do today.
I want to second and elaborate on this point. This sounds like a fungibility sort of argument.
Ceteris paribus, seatbelts make people safer, but this effect is muted in practice  because people would prefer to drive faster and more recklessly while preserving roughly the same margins of safety. As far as trying to determine whether this sort of fungibility is responsible for straight lines, we should look at places where those sorts of control systems are not in place and see if the same lines exist there. I believe the spike on the steering wheel was due to Gordon Tullock, so either you were a student of his or your professor borrowed the idea.
But your summary is not quite right. There is no reason why people would want to preserve the same margins of safety. If you reduce the cost, people will do more of those things. But the implication is not that the highway death rate would stay the same, just that it would not fall by as much as a calculation which ignored the effect would predict.
The fact that the particular changes he was analyzing did leave the death rate about the same was a conclusion from the data, not anything implied by the theory. The main thing is that empirical safety margins should go up by less than their theoretical counterparts because people rationally value things besides safety and are to some extent willing to substitute safety for those things.
This same idea should hold when considering environmental impacts and pollution laws. In reality, improved safety of cars due to new technology allows for some combination of less deaths or improved transport per unit time.
The exact ratio of these two things is directly or indirectly revealed preference. You might be saying that people would crank up their carefulness in response to this added danger, just as we suppose they have cranked it down in response to various safety features, with the result that the actual expected value of injury or death is the same.
And that might well be true. And in that sense the point of the spike literally is to reduce deaths. His alternative proposal was to use the mechanism that is currently used to set off an airbag, but wired to a hand grenade instead. It was that if you made accidents much more dangerous individuals would rationally act to reduce the chance of an accident, whether by driving very carefully or not driving at all.
That depends on how much more carefully people drive as a result. It decreases the number of accidents, increases deaths per accidents.
The net effect could be an increase or decrease in deaths. But pedestrians are probably a lot safer when all the drivers have spikes instead of airbags!
Risk is convexly increasing in speed for given traffic and road conditions, so we would expect safety improvements to lead to both a decrease in injury and a slight increase in speed. This is especially the case in congested roads conditions so here we expect almost all of the gains to be realised as a safety improvement. Traffic laws also encourage people to realise the potential gains as a safety improvement, as increased speed has the cost of both increased risk and fines and license suspensions etc.
The obvious complication here is that motorists probably have very poor perception of actual risks, and it may be the case that some technology so greatly increases the perception of safety that actual risk rises even if risk would fall if the drivers had accurate risk perceptions — this may be a partial effect of modern cars that feel stable and free from noise and vibration even at high speed. The Wikipedia page states quite a lot of criticism of the strong version risk is kept constant , while the weaker version people adjust behavior and act a bit more risky, called Peltzman effect seems quite established.
It just refers to the likelihood of an unwelcome occurrence and the severity of consequences. Yes, exactly. I gave links to the history of the US ambient concentration standards for the four pollutants in the figure in a separate comment sorry that I saw your comment after. Also, it is very plausible that companies knew in advance what minimum regulations are likely to be passed and adapted slightly even before the law took effect. The regulatory standards for those 4 pollutants were set in the 70s and they did not change with the Clean Air Act amendments.
The concentrations were dropping because of the s regulations.
The first figure in this post is deceptive seems to be unintentional on the part of the author , and to a degree this discussion about the figure is moot. As I mention upthread, the first municipal air pollution regulation was put in place in The FDA can ratchet up requirements over times and across several areas in a gradual and non-synchronized fashion e. The process can as part of enforcement FDA and the law a lot of 77, some of 90 specifically target weak points e.