DANIEL FIFE is a postdoctoral fellow in the department of biostatistics, School of Public Health, University of Michigan.

Transcription

1 KILLING THE GOOSE By Daniel Fife DANIEL FIFE i a potdoctoral fellow in the department of biotatitic, School of Public Health, Univerity of Michigan. Environment, Vol. 13, No. 3 In certain ituation, "indutrial elf-regulation" i not merely quetionable, it i farcical. THE TRAGEDY OF THE COMMONS conit of the irrevocable working out of the following ituation a quoted in a recent paper by Garrett Hardin. 1 The formulation given here date from The tragedy of the common develop in thi way. Picture a pature open to all. It i to be expected that each herdman will try to keep a many cattle a poible on the common. Such an arrangement may work reaonably atifactorily for centurie becaue tribal war, poaching, and dieae keep the number of both man and beat well below the carrying capacity of the land. Finally, however, come the day of reckoning, that i, the day when the long-deired goal of ocial tability become a reality. At thi point, the inherent logic of the common remorelely generate tragedy. Each herdman eek to maximize hi gain. More or le conciouly, he ak, "What i the benefit to me of adding one more animal to my herd?" There i a benefit, which i offet by a lo. The benefit i a function of the increae in the herd by one animal. Since the herdman receive all the proceed from the ale of the additional animal, the benefit can be repreented a +1. The lo i created by the additional overgrazing by one more animal. Since, however, the effect of overgrazing are hared by all the herdmen, the lo for any particular deciion-making herdman i only a fraction of -1. Comparing benefit and loe, the herdman conclude that poitive gain remain even after loe are taken into account, and conclude: the only enible coure for him to purue i to add another animal to thi herd. And another; and another... But thi i the concluion reached by each and every rational herdman haring a common. Therein i the tragedy. Each man i locked into a ytem that compel him to increae hi herd without limit - in a world that i limited. Ruin i the detination toward which all men ruh, each puruing hi own interet in a ociety that believe in the freedom of the common. Freedom in a common bring ruin to all. There are three important aumption in the above decription of the tragedy of the common: One, each herdman (entrepreneur) act eentially alone for hi own good without regard for the good of the other; there i no community. Two, each herdman (entrepreneur) when faced with a chance to increae profit i under great preure to do o and will eventually act in accordance with that preure. Three, the ruining of the common caue ruin for the entrepreneur. The firt two aumption fit many area of the buine world rather well. However, there are many ituation in the buine world where the third aumption might eem to apply, but where in fact ruining the common doe not bring ruin to the entrepreneur. The lat line of the quoted tragedy of the common i not trictly correct. lt hould read "... bring death to the common." If death to the common bring ruin to the -2-

2 entrepreneur then we have the tragedy of the common. However, we can write a mathematical tatement of the condition under which death coming to the common doe not bring ruin to all the entrepreneur. Where thee condition apply, the tragedy of the common may appear to be occurring but in fact omething quite different i really happening. The common i being killed but omeone i getting rich. The gooe that lay golden egg i being killed for profit. The Inequality I have no pretenion to neutrality, o the notation will be a little propaganditic. Let u ay that a buine i run reponibly if it i run in uch a way that it could continue to run indefinitely. In many buinee profit can be raied for a period by running the buine in a way which i not reponible. For example, a farmer might double profit for a period by overue of the land. When a buine abandon reponible tactic a defined above in favor of higher temporary profit we will ay it i running irreponibly or fat. Let u imagine a buine which derive it profit from the exploitation of ome natural reource which renew itelf - a whale fihery, perhap. When thi buine i being run reponibly, it make a certain profit. For a limited period of time, until the reource i depleted, it can be run irreponibly at a higher rate of profit. Thi profit can then be inveted, and a regular dividend collected from the invetment. It i clear that, if the available invetment provide ufficient return at no greater rik than that of a reponible buine, and if the increaed profit from irreponible operation are great enough, the return from the invetment of thee profit will be greater than the buineman could obtain from reponible operation of hi buine. That i, if the ratio of profit from an irreponible buine to the profit of a buine reponibly run i great enough under given condition of invetment, it pay to run irreponibly and invet the higher profit a fat a they come in. It pay for the buineman to kill hi buine. The condition under which it pay to be irreponible are tated in the form of an inequality given a (1) in the box at the end of thi article. The inequality define the condition under which a buineman can expect to be at leat a rich from running hi buine fat a by running it reponibly, at every time from the beginning of the proce onward (no matter how long). He can expect to be ahead not merely for the next five year. He can expect to be ahead forever. In addition, he no longer ha to run the buine. For the convenience of any buinemen reading thi paper, I have compiled the following table. In order to ue the table, firt etimate the rate of profit you might receive if you ran your buine irreponibly, and then calculate the ratio of thi rate of profit to that derived from reponible operation. If the value of thi ratio i greater than the "golden number" in the right hand column of the table, then it pay to run your buine fat. To find your golden number, etimate the number of year (m) the buine can run fat before the reource you depend on i depleted, and multiply it by the rate of invetment return () available to you at a rik imilar to the rik involved in your buine run reponibly. Locate the product (m) of thee two number in the left hand column of the table; your golden number will then be the correponding one in the right hand column. (The ymbol at the head of the column are thoe ued in the derivation of the inequality given in the box.) -3-

3 m golden number e m /(e m!1) Approximation In writing thi article I have made everal rather coare approximation. I have aumed that in an irreponibly run buine money will come in at a fixed rate and then uddenly top. Perhap one could get a better approximation by auming a linear or exponential decreae beginning after ome period of income at a fixed rate. I have alo written in the inequality a condition under which running irreponibly leave the buineman ahead for all time. Thi i perhap tronger than neceary. A buineman could profitably decide to run irreponibly if it would put him ahead at ome future time rather than at all future time. If a more careful verion of the inequality were derived uing either of thee idea we might find everal buinee in which, uing the above table, it appeared that it did not pay to run irreponibly, but uing the harper verion it would turn out to pay after all. In mathematical language, the inequality tated here give a ufficient condition, but not a neceary condition, for killing the gooe profitably. Throughout thi paper I have ignored two major effect, namely the effect of taxe and the problem of extracting inveted capital. Large corporation can often deal efficiently with tax problem. For a buine which cannot do o, the inequality may have to be applied by computing after taxe. The econd problem, extracting inveted capital, may caue a buine which appear to be able to run irreponibly to have to run reponibly after all. Thi would be epecially true in a buine involving a large capital invetment in a phyical plant which i not readily modified. Concluion A condition ha been decribed under which a buine depending on a renewable reource may be run irreponibly (detroying the reource) and not reult in lo of income to all of the buinemen involved. Taking advantage of uch a ituation ha been termed "killing the gooe" and i different from the tragedy of the common. The characteritic difference i that the long-term economic interet of at leat one of the entrepreneur are not harmed by detroying the reource. A there are buinee which have demontrably depleted the reource on which they depend (whaling, for intance), killing the gooe i not purely hypothetical. There may be buinee doing it now. -4-

4 It i a common practice of conervationit to iue warning of the coming tragedy of the common to buinemen engaged in detroying a renewable reource. It i a common practice for buinemen to ignore them. Perhap thi article ha hed light on the reaon. The buineman may have realized more or le explicitly that he i in a poition to kill the gooe and that the conervationit' economic argument are imply fale. Further economic argument by the conervationit i then pointle. He mut go back to hi real reaon for arguing and try to convince ociety to protect the reource. If he cannot do o he fail and the reource will be detroyed. Thi article alo indicate that in certain ituation, namely thoe where it may pay to kill the gooe, "indutrial elf-regulation" i not merely quetionable, it i farcical. It i in fact equivalent to a policy of detroying the reource in quetion. In uch ituation ociety i the only poible protector, of the reource, and any, effort directed to protecting the reource without government intervention are doomed to fail in the long run. NOTES 1. Hardin, Garrett, "The Tragedy of the Common" 162: , December 13, Deriving the inequality We define the following term: N r = profit rate for reponibly run buine (dollar per year). = profit rate for irreponibly run buine (dollar per year). = dividend (interet) rate on available invetment (dollar per dollar year). m = time buine can be run at profit (year). We will how that if e m (1) N r e m! 1 then it pay to run irreponibly and invet the (higher) profit at the rate "" a fat a they come in. Let N be a profit either or N r. Let t repreent time and T(t) the total money accumulated at time t under the profit N. Thu T r correpond to N r and T i to. dt i the rate of accumulation of money. dt Money come in from profit at a rate N and from invetment at a rate T(t) [ince T(t) i the total that i inveted at time t]. Let u aume T(O) = 0.Then we have dt = N + T dt (2) T(O) = 0 It i well known that uch a ytem ha only one olution, T(t). -5-

5 Since dt N = (e t! 1) olve ytem (2) it mut be the (only) olution. dt (3) T(O) = 0 Therefore if we aume a reponible buine, the total money accumulated by time t will be given by N r (5) T r (t) = (e t! 1). If we aume an irreponibly run buine, then at the end of m year the total will be (6) T i (m) = (e t! 1). After t > m the only income will be from interet and equation (2) mut be replaced. dt i = T i dt (7) T i (m) = (e m! 1) whoe olution i (8) T i (t) = (e m! 1)e (t!m) (t > m). We are intereted in finding out under, what condition T i (t) T r (t) for all t. If t # m clearly T i (t) T r (t), o we need only conider t > m. Then ubtracting (5) from (8) T i (t)! T r (t) = (e m! 1)e (t!m)! (e t! 1) 1 (9) T i (t)! T r (t) = e (t!m) { (e m! 1)! N r e m + N r e (m!t) }. N r Since N r e (m!t) i never negative, -6-

6 1 (10) T i (t)! T r (t) e (t!m) { (e m! 1)! N r e m }. The right ide of (10) i poitive if (e m! 1)! N r e m 0, i.e., if e m (1) N r e m! 1 which i inequality (1).