ECOLOGICAL ECONOMICS Ecological Economics 13 (1995) 115-123
Extinction and market forces: two case studies Scott Farrow
H. John Heinz III School of Public Policy and Management, Carnegie Mellon University, Pittsburgh, PA, USA and Dames & Moore, Cincinnati, OH, USA
Received 30 May 1994;accepted 12 November 1994
Extinction defines a loss in biodiversity. An established economic model suggests that extinction can be avoided, even in common property settings, if the initial stock is sufficiently large that price and cost evolve to a non-extinction equilibrium. Alternatively, privatization has been suggested as a means to avoid extinction. The empirical validity of these conclusions are investigated by studying the collapse of two species that signaled the end of the United States frontier--the passenger pigeon and the buffalo. The historical studies suggest that the theoretical possibility of a non-extinction equilibrium is unlikely to hold in practice. Similarly, while privatization in a single species context may appear feasible, in a multi-species context the apparent profitability of privatization may be superseded and the species driven to extinction. The latter conclusion also depends on species-specific characteristics of minimum viable population size and habitat requirements. Keywords: Extinction; Non-extinction equilibrium; Privatization, species; Market forces; Common property, species;
American Bison; Passenger pigeon
1. I n t r o d u c t i o n
A testing ground for predicting extinction and integrating economic and ecological information lies in two events that ended the western frontier myth of resource availability: the extinction of the passenger pigeon and the near-extinction of the buffalo. Though recent interest in species survival focuses on biodiversity, these case studies in extinction provide information about markets for
* Address for correspondence: Dames & Moore, 644 Linn St., Suite 501, Cincinnati, OH 45203, USA. Tel. (513) 651-3440.
common property resources, incentives for privatization and the forecasting ability of natural-resource-based markets. Perhaps most importantly, when the opportunity cost of land resources is included in an established model of extinction, new results emerge that make extinction more likely. These findings have implications for biodiversity because: (1) biodiversity is reduced when a species is driven to extinction, (2) market behavior and some policy proposals apply to both extinction and biodiversity, and (3) extinction, like biodiversity, is shown to be inextricably linked to both the biological and the economic dimensions of habitat, or land, use. The near-extinction of the American Bison, to
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be referred to as the "buffalo", and the extinction of the passenger pigeon occurred virtually simultaneously during the closing of the United States frontier in the late 1800s. The plight of these species excited popular attention at the time (e.g., Hornaday, 1887). Regarding public policy, the case of the passenger pigeon was a major factor in the development of Federal wildlife law (Bean, 1983) while the buffalo remains a sufficiently powerful symbol today that it is the centerpiece of the seal of the US Department of the Interior. The historical case of common property harvesting of the buffalo and the passenger pigeon was defined by an inability to exclude hunters from a marketable resource. The passenger pigeon and the buffalo were clearly viewed as a marketable resource in the late 1800s. Buffalo were hunted on the public domain of the plains while pigeons were frequently hunted at their roosting sites in publicly accessible forests. Market prices for pigeons, buffalo hides and robes are in the historical record and are discussed in Section 3. Economic changes in the marketplace contributed to the rapid rise in the harvest of both the passenger pigeon and the buffalo. Schorger (1973) and Silverberg (1967) discuss some of these changes for the passenger pigeon. They indicate that the railroad expanded close to pigeon mass roosting sites while the higher speed of the railroad made profitable the shipping of iced-down game. Costs were further reduced by the emergence of wholesalers and the distribution of information about roosting. Commercial hunting of passenger pigeons, however, died out in the mid-1880s. Market factors also lie behind the near-extinction of the buffalo. One of these factors was the increased demand for meat for the workers of the railroads and the decreased transportation costs brought about by the railroads. A second factor in the early 1870s was a decline in the supply of traditional leather sources and a technological change in tanning that allowed buffalo hides to be used for some leather applications (Branch, 1929; Dary, 1974; see also Roe, 1970; McHugh, 1972). Large-scale hunting of the buffalo appears to have ended by 1884.
Common property resources are the frequent focus of extinction models and a policy concern in many developing countries, in coastal areas and in areas of the global commons. In the sections that follow, an established economic model of extinction is used to identify tile difficulties of predicting extinction given the historical case of common property access. Within economics, a substantial literature exists on extinction that predates concern with biodiversity (e.g., Smith, 1968; Clark, 1973a,b; Cropper, et al., 1979). Yet the event of extinction is the defining act that reduces diversity. While species richness and ecological integration (e.g., Norse, 1992; Wilson, 1992) are not initially addressed by concerns about extinction, it will be shown that modern extinction theories can inform the policy debate about biodiversity, particularly by emphasizing the importance of land in economic terms or habitat in biological terms. An alternative to common property ownership --privatization of the resource--is also analyzed. Privatization--the establishment of private herds and flocks--was technically feasible for both the passenger pigeon and the buffalo, but was successful only for the buffalo. Section 2 presents results from an established theory of extinction while Section 3 uses the results to investigate the actual case of common property ownership. Section 4 investigates the alternative case of privatization while Section 5 concludes.
2. The CroDper, Lee and Pannu model of extinction Both the passenger pigeon and the buffalo were hunted on the common property land of the west and midwest. Economic models of extinction often include common property ownership as a special case by associating an infinite discount rate with those who hunt on the common lands. In fact, the early mathematical, economic models of extinction such as those of Clark (1973a,b, 1976) predicted extinction rather easily due to common property and the assumption that prices
s. Farrow/ EcologicalEconomiCs ~3 (1995) t 15-123 were independent of the rate of harvest. Recent models have become more complex by allowing prices to change. Such change can preclude extinction in a common property setting. Cropper, Lee and Pannu (1979) obtain a result for a pricevarying model such that a species will not be driven to extinction, even under common property conditions, if the changes in cost and price lead to a lack of profitability. The case studies assess the ability to forecast a non-extinction equilibrium. This analysis is useful for concerns about the importance of government intervention to save marketable species such as fish stocks and the transformation of land from one set of harvestable resources to another set. The Cropper, Lee and Pannu model derives the optimal level of harvest and of the resource stock when an economic actor is maximizing the net present social value of a biological resource. The structure of their model is:
f0 If0v't'e ( y ) d y -
C ( X ( t ) ) Y ( t ) ] j e -rt dt
dX/dt=f(=F(X)-Y(t) Y ( t ) >_O, X ( t ) > 0
where Y ( t ) = harvest at time t; X ( t ) = resource stock, X ( t ) = 0 defines extinction; P ( Y ) = inverse demand curve; F ( X ) = net rate of growth of the stock in the absence of harvesting; F'(0) is the maximum growth potential, F(0) -- 0; r = discount rate; T = terminal time period. Cropper, Lee and Pannu derive three propositions that characterize the relationship between extinction [ X ( T ) = 0] and the parameters of the model based on the solution of the necessary conditions. These propositions are: 1. If r < F'(O), then it is never optimal to harvest the species to extinction. The proposition states that if the most rapid growth rate of the stock exceeds the opportunity cost of capital as measured by the discount rate, then the harvester will maximize present value net benefits by not driving the species to extinction. This proposition extends earlier results to this non-linear benefits case (Smith, 1968; Clark, 1973).
2. If r > F'(O), then extinction is optimal for all initial resource stocks such that 0 X 7 extinction is never optimal provided that it is not profitable to harvest some level of net births (sustainable yield). This last result follows from the change in net benefits as the large initial stock size is drawn down. The draw down of the initial stock results in large harvests that lead to decreased resource prices. Net benefits may also be reduced by increasing costs as the stock size is decreased. If the initial stock is sufficiently large, a non-extinction equilibrium can occur because total net benefits are reduced by any further harvest, l The theoretical insight provided by these propositions is two-fold. As with models with a constant price, if the species grows rapidly enough, it is not profitable to drive it to extinction. Conversely, even if the species is slow-growing, harvests from large stocks may depress price and raise cost sufficiently that the species is not driven to extinction, thus preserving one dimension of biodiversity. The usefulness of these propositions for forecasting extinction are investigated below by studying the stock sizes, growth rates and profitability for the passenger pigeon and the buffalo.
It is possible that in some initial time periods there is a temporary non-extinction equilibrium. Over time, demand may increase such that there is no non-extinction equilibrium. In that case the initial non-extinction equilibrium is not a steady state.
S. Farrow/Ecological Economics 13 (1995) 115-123
3. The historical case: forecasting non-extinction equilibrium with c o m m o n property
The passenger pigeon and the buffalo provide case studies for assessing the casual forecasting power of the model. The prediction of a non-extinction equilibrium in the common property case depends on the movement of price and cost toward a (potentially) non-profitable sustainable yield and on the initial stock size. A manager of the public domain might have tried to assess: • Whether the initial stocks of the resources were "large": i.e., would one have assumed X(0) >XI* ? • To what extent would the stock of the resource affect the cost of harvesting? • Would the price of the resource fall as large harvests occurred? Regarding measurements and perceptions of the initial stock size, the flock and herd sizes were proverbial for their size. Anecdotal stories and numerical estimates abound in reports of the time regarding the large size of even single flocks or single herds. Examples of these are reports that a flock of passenger pigeons would occupy a densely packed nesting site on the order of 30 square miles (Schorger, 1973) and that grazing herds of buffalo would occupy hundreds of square miles in a compact mass (Dary, 1974). A modern analyst would likely assume that the initial stocks were indeed "large". Alternatively, if these stocks were "not large", then it is unclear whether a market-based non-extinction equilibrium is possible in any relevant application. The question of the smallest stock size that is profitable is more complex and depends on the answers to questions two and three: the movement of costs and prices. The cost functions used to model renewable resources typically include the level of the stock as an argument. A negative partial derivative is assumed; increases in the stock size reduce the cost of harvest. Anecdotal evidence in a variety of sources (Branch, 1929; Dary, 1974)relates that search costs significantly increased as the population size of the buffalo was reduced. The costs associated with hunting passenger pigeons seems to have changed in a similar manner although the final remnants of
flocks were probably shot during the production of other wildlife harvesting activities. A resource manager might well conclude that costs for commercial quantities would increase as t h e stock size declined for both species. The revenue component o f d e c l i n i n g profitability requires an assessment of the decline in price, if any, during large harvests. Alternatively, prices increasing more rapidly than the rate of interest would provide an incentive for privatization. Qualitatively, both animals were used as a type of food for which there were substitutes while markets also existed for buffalo hides and robes. The presence of substitutes for all the products suggests a relatively fiat demand curve over a wide range of prices; small changes in price would lead to large changes in the quantity demanded. Furthermore, periods of market disequilibrium would be rapidly corrected because the market period for food and leather is relatively short; the resources were not long-lived durable goods and entry and exit from the industry was easy. These factors lead to an expectation that prices would not decline significantly over time though substantial short-term variation may have existed. These expectations are consistent with accounts of the time. For instance, Branch (1929) cites unemployment due to railroad lay-offs in 1872-1873 as the cause of a major increase in buffalo hunters, presumably due to reduced opportunity costs of the workers. Both Branch (1929) and Garretson (1938) then discuss a rapid decline in prices in 1873 though quantitative data are lacking. Schorger (1973) also cites an earlier witness to the effect that unusually large nestings could lead to a significant decline in price. Apparently these declines in price were of short duration. What is known with hindsight is that prices did not decline sufficiently for a non-extinction equilibrium to be reached for the common property stocks. Statistical analysis of price dynamics suffers from a lack of consistent data for given grades and locations of the commodities though sporadic data are available in newspapers for passenger pigeons (Schorger, 1973) and from a wholesaler for buffalo (Roe, 1970.) The data in these sources exhibit large variations in price throughout the
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Table 1 Prices for buffalo robes and hides " Year Robes Hides 1876 1.24 not available 1877 3.81 not available 1878 3.65 not available 1879 3.86 not available 1880 5.05 2.87 1881 6.50 3.35 1882 7.34 2.85 1883 5.23 3.07 1884 not available 3.25
Table 3 Trend analysis of prices Robes
Constant (t statistic) Time (t statistic) R2 Durbin-Watson
- 647.92 ( - 1.16) 0.35 (1.17) 0.10 2.53
- 188.61 ( - 3.31) 0.10 (3.35) 0.33 1.74
* Average annual prices paid by J. and A. BoskovitzCo., New York and Chicago (Roe, p. 461).
prices for the last observation on passenger pigeon prices is similarly well within the range of earlier values although that datum is not quite at the end of commercial hunting. The data further indicate that rapid price changes were possible in a short period of time. For instance, the mean price fell 27% in 11 days in June of 1882. Similarly, the highest price quoted in May of 1882 is over twice that of the lowest price in the same month. A trend analysis reported in Table 3 is, however, consistent with prices rising more rapidly than an arbitrary threshold rate of 10% as indicated by the coefficient on time. A trend of price increases makes movement toward a non-extinction equilibrium less likely although it also suggests an added incentive to privatize the resource. Given the ex-post evidence available on price and cost, it is uncertain whether a resource manager would have predicted a non-extinction equilibrium based on lack of profitability, especially when animals could be shot in the process of other activities. An alternative approach to forecasting extinction based on theory or limited price and cost data is to observe the actions of hunters as economics touts the self-interested forecasting powers of participants in a market. Evidence discussed below indicates that the market did not anticipate the end of commercial hunting: in other words, the expectations existed of either continued movement toward a non-extinction equilibrium or a longer time period to extinction. Hornaday (1887), a contemporary observer writing for the Smithsonian Institution, states that of the buffalo hunters remaining in the Fall of 1883, virtually all ended in bankruptcy having purchased supplies, but were then unable
period as indicated in Tables 1 and 2. It is interesting to consider the movement of price for the last recorded observation and also the time trend of prices, noting the limited extent of the data. While the buffalo robe and hide prices vary a great deal, the prices for the last observations on the buffalo are not the highest prices in the series. The price for hides rose only 6% in the last year of commercial hunting, the smallest annual change in price for the series. The level of Table 2 Passenger pigeon prices: Milwaukee " Date Price per dozen ($) Spring, 1871 0.40-0.85 September, 1871 0.50-0.75 Spring, 1872 0.75-0.85 September 3, 1872 1.00 Spring, 1873 0.70-1.50 May 4, 1874 1.25 Fall, 1874 0.60-0.75 Spring, 1875 0.65-1.25 Fall, 1875 0.50-0.75 Spring, 1876 0.35-1.25 Fall, 1876 0.60-0.75 Fall, 1877 0.60-0.75 Spring, 1878 0.40-0.90 Fall, 1881 0.60-1.00 March 1, 1882 0.75-1.00 April 6, 1882 1.25 May 1, 1882 0.60-1.00 May 23, 1882 1.00 May 24, 1882 1.00-1.25 June 2, 1882 1.00-1.25 June 13, 1882 0.75-0.90 December, 1882 0.90-1.00 " From the Milwaukee Sentinel as reported in Schorger(1973).
- 3453.81 (-4.34) 1.84 (4.36) 0.72 1.63
s. Farrow / Ecological Economics 13 (1995) 115-123
to cover these costs due the lack of buffalo. In the case of the passenger pigeon, the variety of theories proffered at the time for their disappearance and the persistence of commercial hunters after several years of unemployment (Schorger, 1973, p. 221) indicate that numerous actors in the market also did not anticipate the end of commercial hunting for the passenger pigeon. A hypothetical resource m a n a g e r seeking to predict extinction during the extraction period of a renewable resource is in a precarious position given the preceding evidence. Perhaps unsurprisingly, forecasts of extinction based on theory or on the actions of a market are likely to be unreliable and critically dependent on the availability of information for a combination of stock sizes, prices and cost that have not been previously observed. A resource m a n a g e r of a common property species today might plausibly maintain a working hypothesis that a non-extinction equilibrium would not exist. However, a market-driven reaction toward privatization may lead to species preservation and provide an alternative for those who are concerned about extinction as the result of common property ownership. If the technology and legal structure exist to privatize a resource, individuals in pursuit of their own self-interest may save a species from extinction. This alternative is investigated as the alternative case below.
4. T h e a l t e r n a t i v e c a s e : e f f i c i e n c y o f e x t i n c t i o n with private ownership
T h e social-welfare-maximizing solution can be considered an u p p e r bound to the privatization alternative. If it is efficient to drive a species to extinction when maximizing consumer surplus, the equivalent of a price-discriminating monopolist, then it is at least as likely that a private owner would drive a species to extinction because capturable benefits are less than or equal to those of society. As policy suggestions to privatize resources do not limit themselves to perfect competition, it is as well to consider the incentives for an imperfect competitor to privatize the resource. Proposition one of the Cropper, Lee and Pannu
model is a clear statement that if the species grows faster than the discount rate, then it would not be optimal for a price-discriminating monopolist to drive the species to extinction. 2 By studying the history of privatization efforts and the rates of growth, we may ask if the extinction of the passenger pigeon and the near-extinction of the buffalo are consistent with an economic incentive to privatize the resource, and hence preserve biodiversity. In the cases at hand, technological feasibility of private ownership is demonstrated by noting that some zoos and ranchers did establish private stocks of passenger pigeons and buffalo. The history of these private stocks emphasizes the importance of the minim u m viable population size in preservation efforts. G a r r e t s o n (1938), an active participant in the efforts to save the buffalo from extinction at the turn of the century, detailed the establishment of 18 buffalo herds during the period 18731919. O f these 18 herds, 9 were started with fewer than 10 buffalo and two began with as f e w as a pair of buffalo. None of these herds was noted to have died out. Some herds have grown so large in recent years that buffalo meat is again a commercial product. The situation for passenger pigeons provides a counter-example to the small, minimum viable population size of the buffalo. Schorger assesses the fate of three relatively well-documented captive flocks that were not subject to harvesting as well as reporting anecdotes regarding other captive flocks. One flock at the Cincinnati Zoological Gardens n u m b e r e d at least 20 including the last known passenger pigeon. 3 A second privately owned flock in Milwaukee contained at least 15 birds by an eye-witness account. This flock was later split with researchers at the University of Chicago. The Milwaukee flock was said to have started from a single pair. All of these flocks died
2 Clark (1973) derived a similar non-extinction condition for the case of a constant price, private resource that requires the maximum rate of growth to be twice the rate of discount. 3 Visitors may still be moved by the small memorial to the
passenger pigeon at the current Cincinnati Zoo and Botanical Gardens.
S. Farrow/EcologicalEconomics13 (1995)115-123 Table 4 A n n u a l growth potential *
Passenger pigeon l Buffalo 2
F'(0) 0.30-0.42 0.15-0.25
* T h e ranges presented are based on the expected life of the parent in a natural environment. T h e low part of the range corresponds to 4, annual, births; the high point of the range to 12, annual births. 1 Source (Cole, 1954). 2 Source (Cole, 1954; Halloran, 1968).
out from natural causes, indicating both the stochastic nature of predicting populations and the differences in minimum viable population size across species. These privatization efforts were not widespread, so they represent an alternative case to the dominant common property situation. The limited available evidence from biological studies regarding the maximum rate of growth of both the passenger pigeon and the buffalo is presented above in Table 4. These rates are estimated to exceed standard real rates of interest, indicating an expectation of the profitability of privatizing the species. While no estimates are available of the standard errors of these measurements, the mean value of the ranges are approximately 2 - 3 times an arbitrary real discount rate of 10%, consistent with a non-extinction equilibrium for a private resource in both this non-linear price model and in a constant price model (see footnote 2). In fact, the passenger pigeon appears to grow more rapidly than the buffalo and is, in terms of relative rates of growth, less likely to be driven to extinction though, in fact, the opposite occurred. The possible contradiction between the prediction of the model and historical fact, that a potentially private resource satisfying the condition for non-extinction was in fact driven to extinction, indicates that extinction is a more likely outcome than the original model predicts. The model can be modified however, to highlight the importance of the land resource in economic behavior leading to extinction. The modification indicates one reason why private ownership can lead to reductions in biological diversity. Since it was technically feasible to limit access
to a herd or flock, privatization was possible. A potential grower or resource manager, however, must consider not only the alternative use of funds implied by the existence of the resource stock and the rate of discount, but also the alternative use of any land resource d e d i c a t e d to pigeon or buffalo production. This is consistent with the increasing attention being paid to the role of habitat in the reduction of biodiversity as the types of renewable resources that are harvested from a given land resource are changed. The modification analyzes the opportunity cost of the land in an historical context. The Cropper, Lee and Pannu model is modified by considering that the land is "currently" being used to produce the species though at some switch date T, perhaps as soon as the following time period, the land can be used to produce an alternative crop, say cattle or chickens. 4 The present value of the production after the switch date depends on the date T and on the wildlife stock remaining on the land. This effect is modeled by an end-period term in Equation 1 that allows multiple periods of single species harvesting until some date, T, to be chosen. Define the present value of all future production at the switch date to be:
g( F( T), X( T) ) = e-'rg( X( T) )
Including this term alters the end period constraints of the Cropper, Lee and Pannu model. In particular, noting A - - P ( Y ) - C(X), an end point condition in the original model (that the present value surplus of harvest at the terminal date be equal to the foregone revenue from delaying harvest)
-- 0 l
4 It is important to note that this models a process that is fundamentally different than that of the Faustman-Samueison o p t i m u m forest rotation model. The growth/harvest cycle for the renewable resources studied here are taken to be one period, so that the optimum rotation is one period as long as harvesting continues.
S. Farrow/Ecological Economics 13 (1995) 115-123
becomes (Kamien and Schwartz, 1981, p. 147): lime-r, t--* T ×
A(F(X) -Y)] =0
The new condition indicates that the benefits of delaying harvest are reduced by the present value of lost interest earnings from the alternative crop and remaining stock. Extinction was infeasible in the Cropper, Lee and Pannu model when r < F'(0) because Equation 3, evaluated at X(T) -- 0 and Y(T) > 0, implies that average benefits equal marginal benefits. This is impossible in their model because marginal benefits are less than average benefits for positive levels of output with a downward sloping demand curve. In contrast, Equation 4 remains consistent with the model when X(T)= 0 and Y(T)> 0; in other words, a path of extraction leading to extinction and satisfying all the necessary conditions cannot be ruled out a priori. Further, Equation 4 can be given a reasonable economic interpretation. Substituting for A, F(0) = 0 and rearranging yields:
for")P(y) d y - P ( Y ( T ) ) Y ( T )
Equation 5 states that if extinction occurs, at the final time period the current value of the consumer surplus from harvest is just equal to the one period opportunity cost of using the land in its next best use, rg(O). If g(0) is the present value at T of an annuity, conceptually based on a profit-maximizing steady-state equilibrium from an alternative renewable resource, then g(0) is R / r where R is the one period value of the annuity. In that case, at extinction the value of the consumer surplus is just equal to the oneperiod annuity earnings of the alternative crop. The inconsistency between the high rate of growth and the lack of privatization is a reminder that the economic problem must include all the relevant opportunity costs. Contrary to previous analyses, a rapid rate of growth for a potentially private economic good is not sufficient for survival. The net benefits from the existing renew-
able resource must also dominate direct alternative uses of the land. In the context of current issues, even if it is profitable to privatize the common-property native resources of forest lands or coastal regions, if larger profits are obtainable from export or other sales, then extinction is likely to occur although a single species framework might suggest that the marketplace would lead to preservation.
5. Conclusions The conclusions presented here do not differ from the prevailing view that common property and reproductive characteristics were critical factors in the extinction of the passenger pigeon and the near-extinction of the buffalo. What results from a more detailed analysis, however, are the difficulties for a resource manager in determining the ex-ante existence of a non-extinction equilibrium in the common property case. The large data requirements for predicting a non-extinction equilibrium in the Cropper, Lee and Pannu model were described with limited evidence, highlighting the uncertainty surrounding a forecast of a non-extinction equilibrium. It is clear, however, that a significant number of hunters, voting for the marketplace, did not predict extinction. The historical cases suggest a working hypothesis for resource managers that no non-extinction equilibrium exists in a market-driven common property situation. Further difficulties occur if a common property manager chooses to privatize the resource believing that profitability in the marketplace will preserve the species. The importance of the relative profitability of alternative renewable resources was shown to be critical in the preservation of a species through privatization. In particular, an apparent refutation of a formalized extinction t h e o r y p t h e extinction of an economic good that likely grew more rapidly than the discount r a t e - - w a s reconciled by considering the alternative returns from other renewable resources. The fundamental uncertainties underlying extinction and its e f f e c t - - a loss in biodiversity--indicate the potential gains from integrating eco-
S. Farrow/Ecological Economics 13 (1995) 115-123
nomic and biological information particularly as they interact through the linkage of the l a n d - - o r habitat--resource. The current interest in identifying and quantifying the existing and future benefits from the use of a h a b i t a t - - t h e social and private demand function--is seen to be critical to any conclusion about the economics of managing the resource. The uncertainties discussed here also indicate the potential dangers in relying solely on the market to motivate privatization as a means of preserving species.
Acknowledgements Appreciation is extended to Gregory M. Duncan, Jeffrey Krautkraemer, James F. Shepherd and the reviewers for insightful comments, and to Mary Yuhoss for assistance on the historical context.
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Clark, C., 1973b. Profit maximization and the extinction of animal species. J. Polit. Econ., 81:1950-961. Clark, C., 1976. Mathematical Bioeconomics. John Wiley, New York, NY. Cole, L., 1954. Population consequences of life history phenomena. Q. Rev. Biol., 29(2), June. Cropper, M., Lee, D. and Pannu, S..1979. The optimal exiinction of a renewable natural resource. J. Environ. Econ. Manage., 6: 341-349. Dary, D., 1974. The Buffalo Book. The Swallow Press, Chicago, IL. Garretson, M., 1938. The American Bison. New York Zoological Society, New York, NY. Halioran, A., 1968. Bison (Bovidae) productivity on the Wichita Mountains Wildlife Refuge. Southwest. Nat., 13: 23-26. Hornaday, W., 1887. The Extermination of the American Bison. Smithsonian Report, pp. 367-548. Kamien, M. and Schwartz, N., 1981. Dynamic Optimization. Elsevier North Holland, Inc., New York, NY. McHugh, T., 1972. The Time of the Buffalo. Alfred Knopf, New York, NY. Norse, E. (Editor), 1993. Global Marine Biological Diversity. Island Press, Washington, DC. Roe, F., 1970. The North American Buffalo, 2nd edn. University of Toronto Press, Toronto. Schorger, A., 1973. The Passenger Pigeon. The University of Oklahoma Press, Norman, OK. Silverberg, R., 1967. The Auk, The Dodo, and the Oryx: Vanished and Vanishing Creatures. Thomas Crowell Co., New York, NY. Smith, V., 1968. Economics of production from natural resources. Am. Econ. Rev., 85: 409-431. Wilson, E.O., 1992. The Diversity of Life. W.W. Norton & Company, New York, NY.