Banking on Extinction: Ivory Storage and Elephant Conservation*
Erwin H. Bultea, Richard D. Horanb, and Jason F. Shogrenc
aDepartment of Economics, Tilburg University
P.O. Box 90153, 5000 LE Tilburg, Netherlands, email@example.com
bDepartment of Agricultural Economics, Michigan State University
East Lansing, MI 48824-1039, firstname.lastname@example.org
cDepartment of Economics and Finance, University of Wyoming
Laramie, WY 82071-3985, email@example.com
20 March 2001
Selected paper, 2001 AAEA Meetings
*We thank Michael Kremer for his comments.
Copyright 2001 by E. Bulte, R. Horan, and J. Shogren. All rights reserved. Readers may
make verbatim copies of this document for non-commercial purposes by any means,
provided that this copyright notice appears on all such copies.
Ivory poachers threaten with extinction the half million elephants roaming the
African range states (Said et al., 1995). High prices in international black markets tempt
poachers to risk their lives harvesting ivory, despite or because of international
agreements banning such sales.1 In response, Kremer and Morcom (2000) offer a novel
solution to reduce the risk of extinction—a local government can stockpile ivory and
threaten to dump it on the market if the elephant population falls too low (also see Brown
and Layton, 2001, on illegal sales of black rhino horns). This time consistent stockpiling
policy works by lowering the expected returns from illegal ivory sales, thereby driving
otherwise fearless poachers out of the business.2
Herein we explore the downside to this storage policy. We show that ivory
stockpiling is detrimental to elephant conservation if sufficiently large stocks trigger
strategic extinction by African governments. Three realities of ivory storage and trade
increase the odds that strategic extinction could occur. First, most African elephants
inhabit a few nations, which opens the door for collusion between governments trying to
maximize joint interests.3 Second, while “avoiding extinction at low cost” is a
reasonable goal of the broader international community, the preferences in poverty-struck
1 Wildlife policy in some nations empowers wildlife agents to shoot poachers on sight.
2 Ivory storage matters in international negotiations. Large quantities of ivory have been stored in the past
for speculative reasons, at considerable cost (Milliken, 2000). Negotiators at COP 10 (Conference of the
Parties) of CITES (Convention on International Trade in Endangered Species of Wild Fauna and Flora),
decided to lower these costs by allowing for buy-outs by non-commercial donors. The North donors can
now buy ivory from the South to reduce their financial and security liabilities associated with stockpiles,
and to generate funds for elephant conservation purposes. But these buy-outs were conditional on “none of
the [thus traded] ivory could be re-sold in any form at any time in the future” (Milliken 2000). No buy-
outs have yet transpired under this mechanism, and the issue of costly ivory storage arose again at COP 11.
3 We consider perfect collusion as a convenient benchmark. Alternative specifications may be more apt,
including “cartel & fringe models.” If African range states behave non-cooperatively, externalities in
conservation and exploitation emerge when decisions to lift the trade ban are based on the sum of elephant
stocks across countries. If one government pursues a path of extinction, it becomes more costly for the
other governments to allow their populations to grow to equal the common threshold. This would likely
African range states might be less lofty. Pressing problems like securing potable water
and reducing AIDS can force a nation to worry more about the discounted value of
monetary revenues than about the survival of a species considered by many locals as
pests.4 Third, all international sales of ivory, private and public, were banned in 1989 by
CITES.5 Nations should expect the trade ban to be lifted either (i) at a future date when
the in situ elephant population becomes sufficiently abundant, reaching a certain
threshold value set in the international arena;6 or (ii) immediately if extinction occurs.
Though not guaranteed, the international community might dispense with a costly trade
barrier when it serves no purpose.7
Governments compare the expected returns from two rules—a conservation and
an extinction strategy. The conservation strategy means that African nations invest in
anti-poaching enforcement and store any confiscated ivory or ivory from culled problem
animals. The extinction strategy implies the nations forego enforcement and could even
promote hunting the species to extinction. Using realistic parameters, our results suggest
that conditions exist in which African nations prefer the extinction strategy. With
extinction, African nations switch to a Hotelling depletion path for their stockpiled ivory.
The extinction interval is shorter than the period it takes for the elephant population to
recover to the threshold level, causing the discounted value of the extinction strategy to
increase the probability of extinction in the other countries as well.
4 This perspective is consistent with that of Anderson (1992: 42) who writes that conservationists in the
North “have been prepared to insist on a ban on raw ivory trade in large part because they have not been
required to compensate the losers.”
5 CITES is the Convention on International Trade in Endangered Species of Wild Fauna and Flora.
Governments can dump commodities on domestic markets, depressing local prices, but this will not scare
off poachers illegally catering to international black markets.
6 Conservationists argue that a strong link exists between legal sales of ivory and poaching. Legal trade
abets the laundering of illegal ivory, lowering transaction costs and stimulating poaching. The alleged link
between legal and illegal harvesting is a key reason why the trade ban is in place and makes it difficult to
predict when the ban will be lifted.
exceed that of the conservation strategy. This result suggests an alternative strategy to
enhance the viability of elephant stocks in Africa—international conservation
organizations rather than governments should hold the stockpiles.
2. A Model of Strategic Conservation and Extinction
Assume a government has a store of ivory, s, and can increase this store by
directly influencing harvesting activities, h, associated with elephant stocks, x. We
simplify the interaction between government and poachers by presuming the government
can control poachers at a cost. This allows us to focus on government decision-making
as constrained by the exogenously imposed trade ban. Harvests are divided into
immediate sales, q, and stores, v, i.e., h = q + v. Due to international agreements,
however, ivory cannot be sold until the stock of elephants is deemed safe at a level x*
(then, in CITES terminology, the species is downgraded from Appendix I to Appendix
II). Thus, ivory sales, denoted z = y + q, where y denotes sales from stores, can occur as
long as x ≥ x*.8 Assuming no depreciation, ivory stores evolve according to
Assume the initial stock of elephants, x0, is such that ivory sales are not allowed initially,
i.e., x0 ≤ x*. When and if sales do occur, revenues from these sales are defined by p(z)z,
where p(z) is the downward sloping demand for ivory, p′<0, where primes denote the
7 Commercial trade in ivory from mammoths is perfectly legal, for example, albeit subject to import
8 It may be more accurate to model the trade ban in a probabilistic sense. For example, in times with the
trade ban in effect, the ban may be lifted according to the stock dependent probability α(x), and in times
with the trade ban lifted, the ban may be reintroduced according to the stock dependent probability η(x).
The elephant population grows over time according to the equation of motion
where g(x) represents elephant reproduction. Assume g′′<0, and g(0)=g(X)=0, where X is
the carrying capacity of elephants in the environment. Harvesting costs are denoted by
the well-behaved cost function c(h,x), where ch>0; cx≤0; chh, cxx ≥0; chx≤0, where
subscripts denote relevant partial derivatives.
Without trade, net benefits during a trade ban are the sum of stock related benefits
and damages, possibly minus harvesting costs,
(3) NB(t) = F(x) – c(h,x),
where F(x) measures the sum of wildlife–related tourism benefits, R(x), agricultural
damages and other nuisance effects, D(x), and anti-poaching enforcement, E(x). Assume
F(x) can have positive and negative values. This structure implies the government is not
simply self-serving, it also accounts the benefits and costs affecting its constituents, as
manifested by F.9 With trade, net benefits now include the demand for ivory, and are
(4) NB(t) = p(z)z + F(x) – c(h,x).
The government considers two strategies to maximize the present value of net
benefits over time. First, the conservation strategy is defined as when stock, and possibly
stores, are allowed to grow until x* is reached and sales can occur legally. Second, the
extinction strategy is defined as a purposeful extinction of the stock, with a corresponding
Such a rational expectations model would complicate the analysis without affecting the primary results.
9 We explore the case of a self-serving government, F=0, in the numerical analysis below.
10 We consider revenues and not consumer surplus since ivory consumers are mainly outside of the range
states. Likewise, we do not consider non-use (existence) values as these are mostly external as well.
increase in stores, triggering an immediate lifting of the trade ban.11 We now consider
when the government will choose the extinction strategy over the conservation strategy.
We do so by comparing the present value of net benefits under both strategies. If
extinction is rapid, relative to restoration of the population to safe levels, an impatient
government may prefer the returns of a finite depletion path—strategic extinction, to the
returns of an infinite sustainable culling scenario that starts at a later date—strategic
First, consider the conservation strategy. Here the elephant stock always remains
larger than x* after some time T, which is chosen endogenously.12 Ivory sales are always
legal after T. Ignoring illegal ivory sales, the government’s problem is
, (2), (1), s.t.
∫ ∫∞−−− +−++++−=
Now define the extinction strategy. This strategy presumes the stock never grows past
x*.13 The optimal extinction scenario is defined by the solution to the problem
11 Alternatively, the government may choose to refrain from antipoaching enforcement, E(x)=0, allowing
poachers to wipe out the species. Although the distributional consequences are obviously different, the
economic intuition is unaffected.
12 Under the conservation option in which extinction never occurs, there is no reason to temporarily deplete
the stock once x>x* as there are no fixed flow costs in the model. Otherwise, so-called “pulse harvesting”
may be optimal (see Clark 1990).
13 An alternative extinction strategy is that the stock temporarily exceeds x* and is optimally depleted
thereafter. This plan may be optimal if the stock related benefits and costs are sufficiently small (i.e., if
F(x) is close to zero) and the discount rate r is sufficiently large. Because of the discontinuities involved
with the threshold stock, x*, the problem for each extinction option is formulated differently. We therefore
focus on the first plan. If this second strategy were in fact optimal, the benefits of an extinction strategy
would be even greater than what we indicate here. The set of initial elephant stock and ivory store levels
for which extinction is optimal relative to conservation would likely be increased if this second plan was
considered. For the simplest conceptualization, we would have to choose the optimal time at which x>x*
so that the ban is temporarily lifted, and also the optimal time at which x again falls below x* on its way
towards extinction. The problem is more complex if we allow for additional ‘cycles’ in which the trade ban
is lifted temporarily. Extinction is more likely to be optimal if s0 is sufficiently small. In this case, there
may be gains from allowing the elephant stock to increase in order to increase ivory stores.
, (2), (1), s..t.
])([)],()([ 1 2
dteyypedtexvcxFNPVMax T T
TTyv ∫ ∫ −−− +−=
where T1 is the time at which extinction occurs, and T2 is the time at which stores are
depleted. We now compare the returns from these two strategies with a numerical
3. Numerical results
We compare extinction and conservation strategies for the African elephant
(Loxodonta Africana). Our parameters are derived from existing estimates of biological
growth, and the economic characteristics of ivory harvesting costs and international
demand (see Milner-Gulland et al. 1992; Bulte and van Kooten 1999). First, consider the
biological growth and stock parameters. Recent estimates suggest that about 550,000
elephants exist in Africa (Said et al. 1995). Elephant population growth is given by the
logistic function g(x) = 0.067x(1-x/3,000,000). African governments have been storing
ivory for a number of years. A recent report indicates 460 tons of ivory have been
declared, and it is believed that another 350 tons remain undeclared (Milliken 1997). We
therefore presume that 700 tons of ivory is stored in Africa. Assuming 10kgs of ivory per
elephant, this translates into 70,000 elephants. The initial store of ivory, measured in
elephants, is s0= 70,000.
Next, consider the economic parameters. Assume the government can convert
living elephants into ex situ ivory at a maximum pace of 200,000 elephants per year.14
This maximum harvest level is only slightly greater than actual harvesting in the 1980s,
14 Note that, when harvesting is not allowed, the Hamiltonian is linear in the control variables, hence a most
rapid approach path to either extinction or the threshold level must be optimal.
even though illegal poachers were the main harvesters, e.g., some 120,000 elephants were
harvested in 1986, of which about 80% were illegal. We use the functional
specifications derived in Bulte and van Kooten (1999): tourism value: R(x) = 2.6×106
ln(x); crop and people damages: D(x) = 165x; ivory demand: P(z) = 6,397–0.044z;
harvesting costs: c(h,x) = 692,300h/x.
Assume the trade ban will be lifted under two conditions: (a) after the elephant
population exceeds x*=1.2 million, or the elephant population in 1980 (Barbier et al.
1990);15 and (b) if extinction occurs. With extinction, we assume the international
community delays lifting the ban until it verifies that the last elephant has been killed.
We assume a delay of five years, implying the total delay faced by range states in
resuming trade under the extinction strategy is T1+5. Our choice to include this delay
assumption biases the numerical estimate in favor of conservation.16 Finally, we bias our
numerical estimate further towards conservation by setting to zero both the (i) costs to
store and guard ivory (see Milliken 2000), and (ii) the costs of anti-poaching efforts.
Consider now our main result. Column 4 in Table 1 shows that that the net
present value of the extinction strategy exceeds that for the conservation strategy, given a
range of discount rates. Stockpiling ivory creates an incentive for governments to follow
the strategic extinction path for two reasons. First, it is faster to kill than to nurture
elephants—it takes eleven more years to grow the stock to x* under the conservation
strategy relative to the time required to eliminate elephants under the extinction strategy.
Second, the economic benefits of large elephant stocks are on-net negative in our model:
while more elephants lead to more tourism benefits, they also cause more damage to
15 We will also consider less stringent conservation policies.
16 Delay can also occur under a conservation strategy to verify that x* has been reached, but we do not
crops and people in the range states. Tourism benefits dominate only at small stock
levels that arise en route to extinction, whereas the damages take charge at the large stock
levels that arise under the conservation plan (Bulte and van Kooten 1999).17
Next we consider how four changes in the underlying conditions affect the
robustness of the strategic extinction result (Table 2). First, since it is faster to kill than
to rear an elephant, we make the conservation strategy more attractive by reducing the
required time to replenish the stock. Specifically, we reduce the threshold stock level by
40 percent, x* = 750,000. Table 2 shows, however, that the extinction strategy still
dominates, even though the length of time needed to reach x* is reduced by nearly sixty
percent, to 7 years from 17 years.
Second, we make large elephant stocks more attractive by presuming the
government is completely self-serving. It cares only about its ivory revenue, and nothing
about tourist benefits or local damages, i.e., F(x)=0. Again Table 2 shows that the
extinction strategy dominates at the ten percent discount rate. But note the differences in
net benefits are smaller than before, and can actually favor conservation at lower discount
rates. A five percent discount rate, for instance, reverses the result—now the net present
value of conservation exceeds extinction by about $700 million. A more patient
government that ignores stock effects might prefer the conservation strategy. The open
question is how likely this low-discount rate scenario reflects government actions within
the range states given their levels of poverty and capital scarcity. Many experts in
model this explicitly.
17 Recall we have excluded the costs of protection; adding these costs, however, would only reinforce the
main results because poaching would only prolong the replenishment interval and enforcement costs further
depressing the net present value of conservation.
development/resource economics would find this presumption as unrealistic (see for
example Pearce and Warford, 1993; Holdren et al., 1998).18
Third, would conservation be more attractive if ivory stores started at ground
zero, i.e., s0 = 0? Table 2 suggests the answer is no. While the benefits under both
strategies are lower, they are only moderately so. Apparently, the contribution of past
ivory stockpiling to future profits is modest, swamped by benefits of ivory stockpiling
during the extinction phase.
Finally, we explore the effects of ivory stockpiling further by presuming that
stocks cannot be increased during the extinction phase. This captures the scenario in
which the government, trying to avoid the international political heat of an explicit
extinction policy, lets poachers do the work for them. Here the government announces a
“no enforcement” policy, which then triggers an inflow of rational poachers who kill off
the elephants for private profit (see Burton,1999). Poachers now kill and trade the
elephants, rather than the government, i.e., sT1 = s0. Because the ex situ stock of ivory
does not grow during the extinction phase, the profits of successive sales will be
substantially reduced, whereas the net revenues from the conservation strategy are the
same. Table 2 shows, however, that the net value of the extinction strategy still exceeds
that of the conservation strategy by $732 million.
We see that our main result holds up to changes in the underlying conditions—
ivory storage by African range states enhances the relative profitability and probability of
18Also see Poulos and Whittington’s (1999) contingent valuation survey of individual time preferences in
six less developed nations including the African nations of Uganda, Mozambique, and Ethiopia. Their
results suggest the respondents attached much less value to lives saved in the future than to lives saved
today. Few people in their study attached any value to saving lives ten years in the future. For instance,
the median discount rate for Ethiopia was 49 percent for 2 years; 39 percent for 5 years; and 28 percent for
10 years. Also, the median Ethiopian respondent said saving seven lives in five years was equivalent to
an extinction strategy. We now ask what conditions would have to exist to reverse this
result? We consider alternative parameters to determine what conditions would have to
exist, and considered whether they seem reasonable. First, we find that there is no
market price for ivory, either large or small, that causes the conservation strategy to
dominate the extinction strategy. Second, we do find that conservation dominates if the
coefficient for tourism benefits increases nearly six fold, to at least $14.4 million from
$2.6 million, such that R(x) = $14.4×106 ln(x). Finally, we find that conservation
dominates if the coefficient for damages is decreased nearly eight fold, to $23 from $165,
such that D(x) = 23x. Given the data currently available, it is our best judgment that these
alternative specifications for R(x) and D(x) are unrealistic.
Here is why. For tourism benefits, the threshold value for the coefficient in which
conservation becomes profitable is bT = $14.4 million. But consider how this compares
to an upper bound estimate of the net gain from elephant tourism within the range
nations. We start by noting that the net gain to Kenya of wildlife tourism is estimated to
be about $45 million in 1995 (Earnshaw and Emerton, 2000). Now assume Kenya
attracts about 15 percent of the wildlife receipts earned in Africa, and that the relation
between receipts and net benefits is equal across the board in different countries. Then,
total wildlife benefits in all of Africa equal 6.67 times $45 million = $300 million. Let us
optimistically assign half of the wildlife benefits to elephants and elephants alone—and
divide the other half amongst popular species like lions, rhinos, leopards, buffalos,
gazelle, African dog, ostrich, and so on. In this case, tourism benefits from elephants
equals, R(x) = $150 million. But given bT = $14.4 million, one would predict that the
saving one life today, as compared to the median US respondent who said that saving two lives in five
years was equivalent to saving one life today (see Cropper et al., 1994).
benefits of elephant tourism alone amount to no less than $190 million [R(x) = $14.4
million * ln(500,000 elephants)]. This suggests that the pro-conservation threshold value
overestimates our upper bound benefit estimate by $40 million annually ($190 million vs.
$150 million).19 While recognizing this is a rough benchmark based on the best available
data, overestimating benefits by nearly 25 percent causes us to suspect that the pro-
conservation threshold value, bT, is too high.
Kremer and Morcom (2000) used ivory stockpiling to merge the theories of
renewable and nonrenewable resources, a valuable contribution to our understanding of
the efficiency of natural resource policy. They revealed how a policy of stockpiling and
dumping could be used to reduce the risks to species threatened by poachers. But for
their strategy to work, African range states should stockpile large quantities of ivory.
Recall that range states have accumulated about 700 tons of ivory in stores, the 1989
equivalent. Holding other supplies and demand constant, dumping all stockpiled ivory on
today’s markets would imply an 1989 price level of about $300 kg-1. Unfortunately,
even without the CITES ivory trade ban, this price is unlikely to be sufficiently low to
drive out poachers, as one can illustrate using data on poaching revenues, production and
costs from Milner-Gulland and Leader-Williams (1992). Prices must be much lower to
discourage entry under open access. We fear current stores are insufficient to push the
price low enough to force the exit of poachers.
19 Alternatively, one can solve for the coefficient in R(x) = b *ln(x) as b = $150 million/ln(500,000) =
$11.43 million, which is 4.4 times larger than our current value of b = $2.6 million, and is based on the
courageous presumption that elephants generate 50 percent of all wildlife benefits.
But we contend that the price is certainly large enough to make it profitable for
governments to deplete in situ stocks––facilitating legal sales out of ex situ stocks. We
have shown for a wide range of plausible scenarios that this strategic depletion could be
profitable relative to a conservation strategy. Stockpiling ex situ resources may enhance
depletion of in situ stocks if trade in the ex situ stock is restricted due to considerations
pertaining to the in situ stock, which is true for most species protected by CITES.
In this light, we offer an alternative set of policy measures to enhance the viability
of elephant stocks in Africa. First, set the threshold population that allows switching to
legal trade (i.e., lifting of the ban) at a relatively low level. Low threshold levels reduce
the time during which range states only bear the costs of conservation, thereby increasing
the relative profitability of conservation. Tough conservation measures—high threshold
values—are counterproductive for conservation.
Second, encourage non-commercial donor buy-outs. The international
community could invest in purchasing ivory from range states, both for fairness and for
efficiency. Buying stockpiled ivory contributes to conservation, which promotes global
welfare since it undermines the profits of the extinction strategy. Similarly, restricted and
controlled commercial trade under certain conditions should be encouraged. Recent
experiences with non-commercial buy-outs have been disappointing, but COP 11’s
resumption of restricted trade is encouraging. A conservation-motivated international
community could agree to buy all existing stocks and to promise to lift the trade ban
should the extant population exceed the relatively modest objective of 600,000 elephants.
The international community would have to design an incentive-compatible and
individually rational ivory contract for the governments of the range states, such that the
contract such that the nations are just as well off or better off relative to their next best
alternative—which is the strategic extinction option. Good intentions backed with cash
and incentives could better serve to protect treasured species at risk.
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Table 1: Numerical results of the extinction and conservation strategies to elephant
Conservation Strategy Difference in NPV
(r) T1 T2 NPV (×$106) T NPV (×$106) ∆NPV (×$106)
0.05 6 34 1,215.2 17 -668.0 1,883.2
0.1 6 29 500.0 17 -670.3 1,170.3
0.15 6 27 210.4 17 -543.7 754.1
Table 2: Alternative scenarios (r=0.1): NPV of extinction and conservation strategies
Conservation Strategy Difference in NPV
Scenario T1 T2 NPV (×$106) T NPV (×$106) ∆NPV (×$106)
x*=750,000 6 29 500.0 7 235.4 264.6
F(x) = 0 6 29 546.3 17 472.5 73.8
s0=0 6 28 471.6 17 -685.1 1,156.7
No enforcement 6 16 61.9 17 -670.3 732.2