Backward Looking Coal Legislation Serves the Wrong Constituency

Following the death of 14 coal miners in two separate incidents in West Virginia this month, on January 26^th governor Joe Manchin signed a set of new mine safety rules into law. The new rules, passed unanimously through the state legislature, call for wireless communication and tracking devices to be carried by miners. They also call for additional stores of oxygen in mines and for the establishment of a statewide 24-hour accident response team. Had they been available, these measures may have aided the rescue of the recent victims. But for those West Virginians still employed in the coal industry, the new law may pose more harm than good--hurting the very people it is intended to protect.

Though obviously an emotionally-charged topic, worker safety must be evaluated from a pragmatic standpoint. An economic model is useful here. Consider a young man in a coal mining state who can decide between a high risk job like coal mining and a (relatively) low risk job like say auto repair. Due to the higher risk of injury and death in coal mining, he will choose mining only if he is sufficiently compensated for assuming the additional risk. Economists call this increase in pay a “compensating differential.” Operating in a competitive labor market, the coal company is obligated to pay a compensating differential to attract workers to its operation. Since higher risk implies higher wages, the firm internalizes the risk faced by its employees in its attempt to minimize labor costs.

This provides the proper incentive to lower risk through various safety measures. As additional safety measures are undertaken, the compensating differential and hence the total wage bill declines. The level of risk is reduced to the point at which the additional cost of safety is exactly equal to the saving in labor costs. At this point, the added benefit to the miners of any further safety measures would be offset by an even larger increase in the cost of providing such measures. The resulting level of safety is efficient: from a purely utilitarian standpoint, the net of benefits and costs of safety provision are maximized. The efficient level of safety is the level that the employees themselves would choose if they were charged with the decision of how much safety to provide and had to bear the cost.

Compensating differentials, however, may fail to promote the efficient level of safety under certain market imperfections. An imperfection exists if the mining company does not operate in a competitive labor market. This was likely the case in decades past when geographic mobility was limited and working in the mine was the only job available. Another impediment to an efficient market is a lack of information on the part of coal minors as to the risky-ness of their job. In either case, the mining company can lower wages and reduce safety relative to the efficient level and still recruit the necessary workforce.

Though not likely established explicitly for this purpose, workers compensation (WC) insurance can correct for such inefficiencies. WC collects funds from employers and pays damages to workers injured at work and to survivors of those killed. The premium paid by the employer is “experience rated,” so its magnitude depends upon the risky-ness of the work as measured by on-the-job injuries. Thus, WC improves information as all injuries must be reported to the insurer. Furthermore, it forces the employer to once again internalize worker risk in the form of higher premiums. Under WC, compensating differentials are smaller as the risk of employment is (at least partially) offset by insurance payments for damages. But the incentive exists for the employer to provide safety closer to the efficient level even in the presense of market imperfections.

If the coal companies internalize the benefits of greater safety through lower WC premiums and smaller compensating differentials, then why hadn’t they already adopted the measures mandated by the recent legislation? Because the costs would have exceeded the gains. A record low 22 American coal minors died on the job last year. While this may seem like a large number, the fact that it was an all-time low suggests that the most cost-effective safety measures have already been adopted. According to various news reports, industry experts question whether the wireless communication mandated by the new rules is even feasible. And it is not yet clear where the funds for the 24-hour rescue service will come from. What we do know, is that these additional measures will increase costs for the coal companies and any resultant reduction in risk will be accompanied by a decline in wages.

The passage of the law by the legislature indicates its preference for lower risk and lower wages. But the victims themselves understood the risks and chose to work in the mines instead of in a lower-paying, less dangerous job. Had they known such a tragedy would befall them, they would never have gone down the mine in the first place. The fact that they did indicates their willingness to incur some risk. We will never know whether or not the new safety measures would have saved their lives. But by increasing costs for coal companies and by transfering income from coal miners to the providers of safety, the new measures are certain to save lives in the future because fewer and fewer men will find employment as miners. If the legislation is intended to help miners, it would make sense to have consulted them. Had they done so, I doubt that the endorsement of the bill would have been unanimous.

Lessons in Oil Reserves from an Ancient Greek

With gas prices rising, Americans are more than ever questioning our dependence on oil. Beside rising costs, the worry is that current demand is unsustainable, oil reserves will soon be depleted, and the American standard of living will be eroded for all future generations. I am happy to put those worries to rest: the depletion our supply of oil is inevitable so long as we continue to rely on it. And I have the wisdom of over 2,000 years to back me up.

The Greek philosopher Zeno (circa 450 B.C.) formulated a famous paradox who’s solution can shed light on the situation. Zeno’s paradox can be paraphrased as follows: Suppose I want to cross a room of length D. In order to get across, I must first travel half the distance. But before reaching half the distance, I must first travel half of that distance. And before getting there, I must travel half of that distance and so on until I can’t actually go anywhere since doing so would involve an infinite number of intermediate steps. This logic calls into the question the very possibility of motion.

Since we know motion is possible, we resolve Zeno’s paradox by noticing the following. Suppose I could walk half the original distance, which would be ½D. I could then walk half the remaining distance, ¼D, again half the remaining distance, 1/8D, and so on. Continuing in this manner, how far would I eventually walk? Adding up all my individual steps gives us ½D+ ¼D + 1/8D +… or [ ½ + ¼ + 1/8 +...]D. The term inside the brackets is the well-known geometric series, the sum of which is simply: G(r)=r+r²+r³+…=r/(1-r) for any fraction r. Letting r= ½, we have G(r)=1. This is remarkable: not only is the sum of an infinite number of increments a finite number, but by taking smaller and smaller steps we can eventually get to our destination having traveled the entire distance D. Any bewilderment should be relieved by realizing that any finite distance, broken up into an infinite number of small parts, must have the small parts add up to the original distance. Zeno’s paradox is resolved by understanding that while the number of intermediate steps is infinite, they must still add up to something finite. So motion is possible—good news for commuters.

So what does this have to do with oil reserves? Suppose D is the existing supply of some natural resource, say oil. And suppose we are given the job of determining a rate of extraction so that we will always have some oil left over for future generations. Assume that the resource is non-renewable, so once we extract D, there is none left. But to extract D, we must extract half of D. And to extract half of D, we must first extract half of that and so on. From Zeno’s paradox, we know that continuing in this manner, we will eventually extract all of our oil reserves and there will be no more. Fearing this, we may want to reduce our rate of extraction. If we consume say 1/3 of our original stock, then 1/3 of the remaining stock and so forth, we can insure that there is always some amount left over, right? Wrong. As it turns out, any manner in which we extract a constant fraction of our available reserves ultimately result in the complete depletion of the resource. To see this, suppose we decide to extract some fraction r of our existing reserve in every year. In year 1, we will extract rD, leaving D-rD=(1-r)D in reserve for year 2. In year 2, we extract fraction r of our existing reserve (1-r)D for a total extraction r(1-r)D, leaving (1-r)D-r(1-r)D =(1-r)²D for year 3. Continuing in this manner, we will extract r(1-r)^t-1D in any given year t. Summing our per-year extraction over all years, we will eventually extract [1+(1-r)+(1-r)²+(1-r)³+…]rD total. The term in brackets is 1+G(1-r)=1+(1-r)/r=1/r. Thus, our total resource extraction will be [1/r]rD=D, and we use up all of our resource regardless of the rate at which we extract it! The same principle that guarantees you will eventually make it to work in rush hour traffic guarantees that someone in the future will run out of gas and never make it.

With regard to the current discussion over oil consumption, the issue is not whether oil reserves will eventually be depleted but when. The when should be determined by balancing the benefits of current consumption with such benefits in the future while taking into account the possible development of alternative energy sources. Since consumption decisions are made on the level of the individual consumer and producer, any reduction in oil consumption would require intervention by a central authority possibly through the imposition of a tax. A tax would serve to raise the price of gas and of any product produced using oil, reducing consumption of these products and indirectly of oil itself, but in doing so lower our standard of living. The development of an alternative energy source that rendered oil useless would stop the process of depletion resulting in left-over reserves without the need to cut back consumption. Of course the remaining oil would have no value by virtue of having been rendered useless.

So I went to a lot of trouble to prove something obvious. At least the math was fun.