Bioeconomic factors of natural resource transitions:
The US sperm whale fishery of the 19th century
and the discovery of petroleum
Brooks A. Kaiser
Preliminary draft. Do not cite without permission.
Primary contact: Professor MSO, University of Southern Denmark, Department of Environmental and Business Economics, Niels
Bohrs Vej 9 - 10, DK-6700 Esbjerg; baka@sam.sdu.dk
Other affiliations: Affiliate Faculty, Department of Economics, University of Hawaii, Manoa, HI; Assoc. Prof., Gettysburg
College, Gettysburg, PA
2
19th century whales.nb
Abstract
This paper uses bio-economic modeling to investigate the transition from whale oil (a renewable, exhaustible natural resource) to
petroleum that occurred in the mid-19th century. The discovery of petroleum is often presented as a stochastic event that ‘saved
the whales’; we combine newer biological evidence (Whitehead 2002) with economic theory of natural resources to address this
long-standing controversy over whether sperm whale fishery dynamics would have been sufficient to preserve sperm whale
population without the discovery of petroleum (e.g. Davis et al, 1988; Maran 1974; Shuster 1973). We find that under most
economic conditions the dynamics, even without a substitute, would have prevented extinction; this result is different than that
usually determined for the better studied baleen whales, due in part to biological differences and in part to differences in their
economic productivity as harvested resources. The paper is part of a larger project investigating the timing of resource transitions
and how the increasing costs and demand for illuminants drove the search for substitutes and how successful drilling for
petroleum presented the best substitute from an array of interdependently developing resources and technologies, cementing the
decline of the US sperm whaling industry.
JEL Classifications: Q20; N50
Keywords: Sperm whale fishery; bioeconomic modelling; exhaustible biological resources; economic history of natural resources.
19th century whales.nb
3
I. Introduction
The literature to date on the intertwined fates of the American whaling and petroleum industry has focused mainly on the extent
to which the discovery of readily accessible petroleum supplies caused the decline of the whaling industry in the latter half of the
19th century (Daum, 1957; Hutchins, 1988; Maran, 1974; Shuster, 1971). In these works, the questions investigate the demand
and supply of whale oils in an industrial setting where the discovery of petroleum is exogenous, though once discovered, it has a
tremendous impact on whale oil markets. In this project, we seek to unify the two industries by examining theoretically the extent
to which the troubles in the whaling industry influenced the discovery of drillable petroleum in 1859 and the formation of the
industry that sealed whaling's fate. We discuss the two industries in terms of a transition from one exhaustible resource to
another, we exploit natural resource economics theory to evaluate the historical evolution of the industries. Along the way, we are
able to address other interesting questions about resource use, including how the whale population would have fared without the
advent of petroleum. This latter question is the focus of the immediate paper.
We consider whale oil a renewable but exhaustible resource, and drilling for petroleum a backstop technology with high initial
costs that decline for a considerable period of time before again rising, generating declining marginal costs for a substantial time
period (akin to Tsur and Zemel, 2003, but adapted for renewability of the original resource). These characteristics provide the
basis for determining the theoretically optimal time profiles of the primary (whale oil) and backstop (petroleum) resource supply
rates. These optimal time profiles will, in turn, be examined in light of the actual data in order to inform about the overall
exploitation of the primary resource in terms of its exhaustibility, i.e. will provide theoretical corroboration or rejection of the
empirical findings of Davis, Gallman and Hutchins (1988) that the stock of sperm whales was not, in fact, in jeopardy in the 19th
century.
We begin with a brief overview of the illumination business. We use data from several different sources to inform our research.
We have data on individual whaling voyages and biologists from which to build our cost (supply) function, and from industry
accounts of prices and quantities of whale oil and petroleum traded to build our demand function.
With respect to the whaling industry, we show, using standard theory of renewable but exhaustible resources, how whale oil
extraction should have optimally progressed if no alternative technologies were available (so that the present value of marginal
user costs were equal across time), and how they would have likely progressed given the estimated stocks of whales and the
growing demand for illumination (and lubricants). We discuss issues surrounding the open access nature of the fishery and other
aspects of a counterfactual assumption about the failure to discover cheap, plentiful petroleum.
4
19th century whales.nb
II. History and Background
Ÿ Short History of Illumination, 1800 to 1859.
Illumination up until 1830 was generally restricted to tallow for the common man (Williamson and Daum, 1959). Sperm whales
had been actively hunted since 1712, but the oil was expensive enough to be mainly for wealthy, and naval disruptions through
the war of 1812 hampered the industry tremendously. The demand for luminants was growing rapidly with industrialization,
however. Whale oil dominated the illumination market in the 1850 census (65.5% of the market in oil and gas illuminants (Daum,
1957)), but its competitors had decreased this share to 19% by 1860 Town gas (from coal), was introduced as a potential solution
to the illumination problem for urban areas, arriving in Baltimore first, in 1816, and then to New York and Boston by 1830, and
had a 16% share of the market by 1850, which grew to 38% in 1860. (Daum, 1957).
Several more cities turned to town gas 1830-1837; the financial panic of 1837 slowed this, then it picked up again in the mid
1840s. A tariff reduction for coal into the US in 1846 from $1.75 to $0.40 per ton increased coal use, and there were 56 or so
plants in operation in 1850 (Williamson and Daum, 1959).
But town gas was expensive to network into homes, and so slow-going. Households were still looking for alternatives. Meanwhile, lamps evolved to burn better and give more light. Lamps also started to be able to take different types of oil (sometimes
with a bit of conversion), reducing joint-product problems, in response to a number of potential new fuel entrants. Camphene
(from turpentine) was developed, but was highly flammable -- still it had 9% of the market in 1860. Lard oil markets expanded,
with 13.5% of the market in 1850 (falling to 8% in 1860). Europeans were working to produce coal oils from the mid 1830s, but
not much was going on in the US with converting minerals to oil until 1850. With no measurable share of the illumination market
in 1850, by 1860 coal oil (kerosene) had 20% of the market (Daum, 1957).
Coal-oil kerosene and lamps really dominated the growth in the mid- late 1850s, replacing the dangerous but cheap (and therefore
popular) camphene. This transformation put distilling and networks in place. Those working with distilled oils were aware of the
theoretical potential of petroleum, but didn't know how to get enough of it. The innovation of drilling, borrowed from salt wells
that had actually been producing petroleum as a by-product in the Mid-Atlantic region, was needed to settle the question of which
mineral or oil resource would capture the market at the lowest cost. In 1859, oil was struck at Pithole, PA, and quickly outcompeted other forms of illuminants.
Ÿ Demand for illumination
To model the demand for whales, we need to model the demand for illumination. Appendix I describes the instrumental variables model results from estimating a growing inverse demand function for illumination from oils, D-1 (qt ), where
qt = qwt + Æq bt ,so that qt is the total quantity of luminants demanded at time t, qwt is the quantity of in thousand gallons of sperm
oil, qbt is the quantity of the backstop resource, here petroleum, in thousand gallons. Æ is a coefficient translating illuminating
power, which we set here equal to approximately 0.64 based on reports of chemists suggesting that 1.57 gallons of petroleum oil
were needed to produce the same illumination quality and hours as one gallon of sperm oil (Silliman, 1871).
-Η
For parsimony and clarity, we choose D-1 (qt )=ΑeΓ×t+ΛI pt
for our functional form, so that quantity is a function of price, pt and
an industrial production index (Davis, 2004), I, growing over time as the market expands. Instruments are the shipping tonnage in
the whaling industry, the whale population, and a post-1859 dummy.
The elasticity of demand, Η, is estimated to be 3.58%. It may seem surprising that we would find such elastic demand, but
anecdotal evidence for a high elasticity of demand for sperm oil comes from as early as the mid 1760s, when spermaceti candle
manufacturers in New England tried (rather unsuccessfully) to restrict entry and keep down oil prices through a monopsonistic
cartel because oil input prices were rising faster than the market would allow candle output prices to grow. Between 1761and
1774, the premium on the highest quality oil had increased almost 7-fold while the price of candles had only increased about 20%
in Boston (Dolin, 2007). Elasticity of demand for petroleum was also fairly high in the early days of petroleum, with many
substitutes, uncertain customers, and evolving methods for storage and distribution.
19th century whales.nb
5
The elasticity of demand, Η, is estimated to be 3.58%. It may seem surprising that we would find such elastic demand, but
anecdotal evidence for a high elasticity of demand for sperm oil comes from as early as the mid 1760s, when spermaceti candle
manufacturers in New England tried (rather unsuccessfully) to restrict entry and keep down oil prices through a monopsonistic
cartel because oil input prices were rising faster than the market would allow candle output prices to grow. Between 1761and
1774, the premium on the highest quality oil had increased almost 7-fold while the price of candles had only increased about 20%
in Boston (Dolin, 2007). Elasticity of demand for petroleum was also fairly high in the early days of petroleum, with many
substitutes, uncertain customers, and evolving methods for storage and distribution.
The coefficient on the industrial production index is small and somewhat surprisingly negative, at -0.007. In combination with the
strong coefficient on time (0.31), this, however, only begins to shift the demand curve back after about 1880, when electricity
begins to come on the scene as an alternative for illumination.
Ÿ Whaling for oil: extraction of a renewable but exhaustible resource
è Marginal cost of sperm oil production
We assume that the marginal cost of supplying sperm oil is non-declining in the quantity of sperm oil, qwt, and decreasing in the
stock of sperm whales, nt . Supply (Price = marginal extraction cost in a competitive industry) is thus estimated as a function of
tonnage in the fleet, quantity of sperm oil (instrumented), quantity of whales available, price of the substitute whale oil, and price
of petroleum available. IV estimates are shown in Appendix II. While all of the variables have a significant influence on
marginal cost, the net effect of them on price when all except for whale population are held constant at their means is extremely
small. The coefficient on total harvest quantity, for example, is so small that the expected influence on price should be measured
in millions of gallons of whale oil. Thus we focus on the relationship between the whale population and the marginal cost to
obtain the marginal extraction cost function for the primary resource, whales, of:
C(nt , qwt) = C(nt ) =91.32-0.46*Ln(n2t ).
Thus costs are linear in quantity harvested and decreasing in the stock level of the resource, where the stock, nt , evolves over time
according to the growth function for the sperm whale population, discussed in Appendix III.
Having established the demand for illumination over time, and the costs of production as a function of the dynamic whale
population, we can proceed to our discussion of the discovery of petroleum.
III. Methodology and Simulation
1. The whale fishery
We now have virtually all the elements needed to model how the sperm oil industry would have fared without the discovery of
abundantly cheap mineral fuel oils, if the whale fishery were optimally managed (as opposed to the more realistic open access,
discussed briefly but left for further analysis elsewhere). This will illustrate, in a sense, the time frame that existed for new
discoveries, and show the pressures to discover new sources of illuminants.
To determine the optimal use of the sperm whale resource over time, we write the maximization problem as
V HN0 L º Max Ù SWt = Max Ù e-rt IÙ0 wt D-1 HzL â z - c Hnt L * qwt M,
¥
t
qwt
q
t=0
subject to
n = g Hnt L - qwt = Ρ nt I1 -
nt 1+b
M
KO
qwt ³ 0 ; nt ³ 0, and N0 given.
- qwt ,
6
19th century whales.nb
V HN0 L º Max Ù SWt = Max Ù e-rt IÙ0 wt D-1 HzL â z - c Hnt L * qwt M,
¥
t
qwt
q
t=0
subject to
n = g Hnt L - qwt = Ρ nt I1 -
nt 1+b
M
KO
- qwt ,
qwt ³ 0 ; nt ³ 0, and N0 given.
where social welfare, SWt , is the net surplus from consumption of the whales, qwt, given the inverse demand, D-1 HzL(see
appendix I) and the harvest costs as a positive, decreasing function of the population of whales, c(nt L (Appendix II) and constant
in the level of harvest, qwt . The system is subject to the equation of motion determined by the growth rate of the whales, n, which
is in turn a function of the intrinsic growth rate, Ρ , the current population, nt , the carrying capacity of the oceans, KO, and a
density dependent exponent, b, and illustrated in Appendix III.
The current value Hamiltonian for this problem is
H=Ù0 wt Dt HzL dz - c Hnt L qwt + @g Hnt L - qwtD Λt where Λt ³0.
-1
q
and the necessary conditions for an optimal solution are
¶H
¶Λt
= g Hnt L - qwt
n
t
=
Λ
t
= r Λt -
¶H
¶qt
¶H
¶nt
= r Λt + c¢ Hnt L qwt - g ' Hnt L Λt
= D-1
t HqwtL - c Hnt L - Λt £ 0, if < then qwt = 0, .
We define pt = D-1
t HqwtL. Rearranging the necessary conditions and combining them with the time derivative on price gives us
that the optimal harvest requires:
pt = (r + g'(nt ))*( pt - c(nt )) + (g(nt ))*c'(nt )
nt Š g(nt )- qwt, and
Λt =( pt - c(nt )),
and we have the following results, shown graphically below for three sets of conditions on growth.
Scarcity rent, Λt , is the difference between price and marginal harvest cost, and captures the dynamics of the model. If there is no
shortage of whales, Λt = 0 "t and the dynamic problem collapses to a static problem. If, on the other hand, a resource grows
scarcer over time, we expect the scarcity rent to rise, dramatically so in the case of a resource dwindling to zero, for example, as
is the case if the whales are pushed to extinction. Note that this can only happen if the growth function for the population of
whales is critically depensated, which is not the biologists' assumption in the case of sperm whales, or if the costs of hunting the
last whales does not rise toward infinity, contrary to what is generally assumed for most fish species. If costs increase toward
infinity, additional harvesting becomes infinitely unprofitable at low enough populations(Clark, 2005). In a case where it is
profitable to 'overharvest' - that is, to harvest to a point below maximum sustainable yield (MSY), then increased pressure from
growing demand will result in either a series of oscillations in the harvest (and therefore in price and cost) over time or a somewhat tenuous equilibrium at an unstable steady state. Because the evidence regarding the behavior of the sperm whale populations at low levels has significant uncertainty, we expect that reaching the period of chaotic behavior may well lead to unrecoverable stocks of the whales.
We analyze the question from the standpoint of 1800, at which point we assume that the sperm whale population has already
been drawn down to about 71% of its estimated carrying capacity (Whitehead, 2002), but is still above MSY. We do this to
nt Š g(nt )- qwt, and
Λt =( pt - c(nt )),
19th century whales.nb
7
and we have the following results, shown graphically below for three sets of conditions on growth.
Scarcity rent, Λt , is the difference between price and marginal harvest cost, and captures the dynamics of the model. If there is no
shortage of whales, Λt = 0 "t and the dynamic problem collapses to a static problem. If, on the other hand, a resource grows
scarcer over time, we expect the scarcity rent to rise, dramatically so in the case of a resource dwindling to zero, for example, as
is the case if the whales are pushed to extinction. Note that this can only happen if the growth function for the population of
whales is critically depensated, which is not the biologists' assumption in the case of sperm whales, or if the costs of hunting the
last whales does not rise toward infinity, contrary to what is generally assumed for most fish species. If costs increase toward
infinity, additional harvesting becomes infinitely unprofitable at low enough populations(Clark, 2005). In a case where it is
profitable to 'overharvest' - that is, to harvest to a point below maximum sustainable yield (MSY), then increased pressure from
growing demand will result in either a series of oscillations in the harvest (and therefore in price and cost) over time or a somewhat tenuous equilibrium at an unstable steady state. Because the evidence regarding the behavior of the sperm whale populations at low levels has significant uncertainty, we expect that reaching the period of chaotic behavior may well lead to unrecoverable stocks of the whales.
We analyze the question from the standpoint of 1800, at which point we assume that the sperm whale population has already
been drawn down to about 71% of its estimated carrying capacity (Whitehead, 2002), but is still above MSY. We do this to
determine whether the previous rates of harvest were too high or too low to maximize dynamic efficiency, given demand. If
harvests were too high, we should find a period of lower harvests where the fishery can recover before it is more rapidly
exploited to meet higher future demand. If harvests were too low, we should find a rapid drawdown of the population with no
period of conservation.
The essential counterfactual question is how fast would the demand for illumination grow without the advent of cheap petroleum
illuminant. We investigate several possibilities that are based around the growth rate of the 19th century. The growth rate in
industrial production (Davis, 2004) is on average 5.6% for the century while overall GDP growth is on average 4%. Rather than
assume there is no technological change (e.g. the utilization of other illuminants as we see occuring from 1850-1860 before
petroleum) we build the demand for illumination above as if fuels were available, incorporating the advances those brought in
efficiency to the production of light, but then assume the fuel itself would need to be provided by the whales. This defines the
scope of the counterfactual more reasonably than Assuming no advances in technology or production of such an important good.
Ÿ Growth in demand sustained at 5 %
Figure 1 illustrates the optimal population of whales over time if we assume that the growth in demand can be maintained at 5%
for the period without the advent of other particularly cheap illuminant sources, we find that the whale population should be
drawn down to a population of about 285,000 whales over a period less than 200 years (183 years, Figure 1A). This includes,
however, a period of about 50 years where the resource is used more lightly than it had been under the open access of the 1700s
(Figure 1B). At a population of about 285,000 whales, the industry costs exceed price and a period of somewhat dramatic
oscillations appears to follow before settling down to a harvest around the growth rate of about 2150 whales (I think. I am still
working on checking everything. But in any case, whaling can last 183 years even with 5% growth in demand and not become
chaotic). In Figure 3A, we show the population path to chaotic behavior in 183 years, while in Figure 3B we show a close-up of
the conservation over the first 50 years (note the time axis in Fig. 1B does not intersect the population axis at n=0).
Figure
1A:
Whale
population
from
demand.
Optimal Population, No Substitute
Whales
800 000
600 000
400 000
1800
to
1983,
5%
growth
in
Figure 1 illustrates the optimal population of whales over time if we assume that the growth in demand can be maintained at 5%
for the period without the advent of other particularly cheap illuminant sources, we find that the whale population should be
8
19th century whales.nb
drawn
down to a population of about 285,000 whales over a period less than 200 years (183 years, Figure 1A). This includes,
however, a period of about 50 years where the resource is used more lightly than it had been under the open access of the 1700s
(Figure 1B). At a population of about 285,000 whales, the industry costs exceed price and a period of somewhat dramatic
oscillations appears to follow before settling down to a harvest around the growth rate of about 2150 whales (I think. I am still
working on checking everything. But in any case, whaling can last 183 years even with 5% growth in demand and not become
chaotic). In Figure 3A, we show the population path to chaotic behavior in 183 years, while in Figure 3B we show a close-up of
the conservation over the first 50 years (note the time axis in Fig. 1B does not intersect the population axis at n=0).
Figure
1A:
Whale
population
from
demand.
Optimal Population, No Substitute
1800
to
1983,
5%
growth
in
Whales
800 000
600 000
400 000
200 000
50
100
Years
150
Figure 1B: Whale population from 1800 to 1900.
Optimal Whale Population, No Substitute
Whales
810 000
800 000
790 000
780 000
770 000
0
20
40
60
80
100
Years
This has corresponding harvest and price paths over time as illustrated in Figures 2&3. Figure 2 shows harvest rates for the entire
period, which grows rapidly until just prior to a fisheries "collapse", when prices first collapse (figure 3) and harvesting stops.
Note that open access harvesting is expected to hasten these outcomes and to forgo the initial conservation. (We are working to
incorporate this directly into the model but have not yet done so). Since the open access problem is one of missing property rights
and enforcement, we might anticipate a partial regulatory solution that would result in behavior tending toward this optimal path
as a less expensive solution than resource collapse; though competition was fierce within the industry, the concentration of the
fleet in a few locations (first Nantucket, MA, then New Bedford, CT, then San Francisco, CA) may lead one to expect considerable success from either self-regulation or state mandated regulation. This is an intriguing possibility and presents an interesting
counterfactual challenge; in future work we expect to investigate the implications of the endogeneity of resource regulation and
enforcement (see for example Kaiser and Roumasset, 2007 and Roumasset and Tarui, 2010 for more on this general issue).
Figure 2: Optimal harvest path, 5% growth in demand.
Optimal Quantity Harvested over Time, No Substitute
Whales Harvested
12 000
10 000
8000
6000
This has corresponding harvest and price paths over time as illustrated in Figures 2&3. Figure 2 shows harvest rates for the entire
period, which grows rapidly until just prior to a fisheries "collapse", when prices first collapse (figure 3) and harvesting stops.
19th century whales.nb
9
Note that open access harvesting is expected to hasten these outcomes and to forgo the initial conservation. (We are working to
incorporate this directly into the model but have not yet done so). Since the open access problem is one of missing property rights
and enforcement, we might anticipate a partial regulatory solution that would result in behavior tending toward this optimal path
as a less expensive solution than resource collapse; though competition was fierce within the industry, the concentration of the
fleet in a few locations (first Nantucket, MA, then New Bedford, CT, then San Francisco, CA) may lead one to expect considerable success from either self-regulation or state mandated regulation. This is an intriguing possibility and presents an interesting
counterfactual challenge; in future work we expect to investigate the implications of the endogeneity of resource regulation and
enforcement (see for example Kaiser and Roumasset, 2007 and Roumasset and Tarui, 2010 for more on this general issue).
Figure 2: Optimal harvest path, 5% growth in demand.
Optimal Quantity Harvested over Time, No Substitute
Whales Harvested
12 000
10 000
8000
6000
4000
2000
50
100
150
200
250
Years
Figure 3A shows the price path for the period. The price for a whale's worth of oil, without a substitute, unsurprisingly reaches
very high levels at the end of the period and then collapses, signaling the beginning of price and harvest oscillations. Figure 3B
shows the first 100 years' optimal price path, corresponding to the population levels in Figure 1B.
Figure 3A: Optimal price path, no substitute, 1800-1983, 5% growth in demand.
Optimal Price
Dollars
40 000
20 000
50
100
150
Price
Years
-20 000
Figure 3B: Optimal price path, no substitute, 1800-1900, 5% growth in demand.
Optimal Price over Time, No Substitute
Price
800
600
400
200
20
40
60
80
100
Years
Because costs of harvest are relatively low compared to the intertemporal benefits of the whale oil until the very end of the time
period, the scarcity rent, Λt , is only very slightly smaller than price; the graph is virtually indistinguishable from those in Figure 3
and therefore is not reproduced here.
50
100
Price
Years
150
10
19th century whales.nb
-20 000
Figure 3B: Optimal price path, no substitute, 1800-1900, 5% growth in demand.
Optimal Price over Time, No Substitute
Price
800
600
400
200
20
40
60
80
100
Years
Because costs of harvest are relatively low compared to the intertemporal benefits of the whale oil until the very end of the time
period, the scarcity rent, Λt , is only very slightly smaller than price; the graph is virtually indistinguishable from those in Figure 3
and therefore is not reproduced here.
Ÿ Effect of alternative growth rates on whale populations
1. Lower Growth in Demand
A. Slower growth, but greater than the discount rate
The failure to discover alternative cheap illumination sources might likely have slowed growth in the market for illuminants. If
growth were only 3.3%, (recall our discount rate is 3%) the whales are no longer optimally overharvested. Instead, there is a
period of conservation, for about 380 years, where the population grows slowly back to just shy of 910,600 whales, and then a
long chaotic period of decreasing oscillations until the population settles at 776,370 whales (Figure 4) with an annual catch and
growth rate of 1587 whales. In other words, there is a long opportunity to evolve new technologies and illuminants.
Figure 4: Optimal population over time, 1800-steady state, no substitute, 4% growth in demand
Optimal Population
Whales
778 500
778 000
777 500
777 000
776 500
776 000
775 500
2000
4000
6000
8000
10 000
Years
Prices rise throughout (not shown).
B. Very slow growth
If, however, the growth rate is only 2% per annum, the dynamics of the system change yet again and instead of settling at a
constant harvest rate after a long fluctuation, there is simply a long slow progression away from whale harvesting. There is a
monotonic reduction in harvest over time from 1800 levels that eventually leads to a very low, positive rate of harvest that is
asymptotically approaching zero over time. Figures 5 and 6 illustrate the optimal population and extraction over time. As shown,
the population rises monotonically, approaching carrying capacity.
Figure
5:
(K=1,110,000)
Optimal
Whale
Optimal Population
Whales
1.110 ´ 106
Population,
2%
growth
in
demand.
19th century whales.nb
11
B. Very slow growth
If, however, the growth rate is only 2% per annum, the dynamics of the system change yet again and instead of settling at a
constant harvest rate after a long fluctuation, there is simply a long slow progression away from whale harvesting. There is a
monotonic reduction in harvest over time from 1800 levels that eventually leads to a very low, positive rate of harvest that is
asymptotically approaching zero over time. Figures 5 and 6 illustrate the optimal population and extraction over time. As shown,
the population rises monotonically, approaching carrying capacity.
Figure
5:
(K=1,110,000)
Optimal
Whale
Population,
2%
growth
in
demand.
Optimal Population
Whales
1.110 ´ 106
1.108 ´ 106
1.106 ´ 106
1.104 ´ 106
1.102 ´ 106
1.100 ´ 106
2000
4000
6000
8000
10 000
Years
Quantity harvested falls to under 50 whales after about 400 years. Price still rises monotonically as expected.
Figure 6: Optimal Harvest, 2% growth in demand.
Optimal Quantity Harvested over Time, No Substitute
Whales Harvested
600
500
400
300
200
100
100
200
300
400
Years
We see a clear trade off between the whale population and economic growth; high rates of growth drive the fishery to overfishing
and unstable conditions, where the length of time before this instability occurs shortens as growth increases (at 7% growth, the
time until the costs are driven too high is only 97 years, while at 9% growth, not unreasonable given the pace of industrialization
in the 19th Century, the time frame is only 69 years. The paths look like condensed versions of figures 1-3). Lower rates of
growth that exceed the discount rate, so that the value of the fishery overall is not in decline, can lead to a long run steady state
harvesting something along the lines of 1000-2000 whales a year, which may be much like the 18th Century, before growth in
demand soared. Even lower rates of growth lead to the eventual virtual abandonment of the resource over time, not because costs
or prices rise too much but because the overall value of the output is not of much significance. This last result is not particularly
interesting except to highlight the important interaction between the choice of the discount rate and growth in long run models of
resource use. Clearly a better discounting model is needed.
We note that for the sperm whale population, at least, if our estimates of the biological processes and the costs are essentially
correct, it would have been hard to drive the population to extinction. If, however, the biology is significantly more complicated,
and in particular if there is a high threshold (around 200,000 whales) at which mates have trouble finding each other in the vast
oceans and reproducing, it would be possible to crash the population irrevocably. This is likely the case with several baleen
12
19th century whales.nb
We see a clear trade off between the whale population and economic growth; high rates of growth drive the fishery to overfishing
and unstable conditions, where the length of time before this instability occurs shortens as growth increases (at 7% growth, the
time until the costs are driven too high is only 97 years, while at 9% growth, not unreasonable given the pace of industrialization
in the 19th Century, the time frame is only 69 years. The paths look like condensed versions of figures 1-3). Lower rates of
growth that exceed the discount rate, so that the value of the fishery overall is not in decline, can lead to a long run steady state
harvesting something along the lines of 1000-2000 whales a year, which may be much like the 18th Century, before growth in
demand soared. Even lower rates of growth lead to the eventual virtual abandonment of the resource over time, not because costs
or prices rise too much but because the overall value of the output is not of much significance. This last result is not particularly
interesting except to highlight the important interaction between the choice of the discount rate and growth in long run models of
resource use. Clearly a better discounting model is needed.
We note that for the sperm whale population, at least, if our estimates of the biological processes and the costs are essentially
correct, it would have been hard to drive the population to extinction. If, however, the biology is significantly more complicated,
and in particular if there is a high threshold (around 200,000 whales) at which mates have trouble finding each other in the vast
oceans and reproducing, it would be possible to crash the population irrevocably. This is likely the case with several baleen
species of whale, that had much smaller initial populations and were hunted more aggressively at the end of the 19th Century for
their baleen, which had yet to have successful alternatives developed. Further comparison of the two very different species
groups is warranted to better understand the importance of biological growth in renewable resource use.
IV. Brief comments on the transition to petroleum
We imagine the early petroleum industry as a market for knowledge, and, elsewhere, describe how knowledge in the industry
decreased the marginal costs of supplying petroleum. In the process, we show how much greater in magnitude the petroleum
industry was than the whale fishery, already in decline and being replaced by the similar but higher cost coal-oil industry. This
increase in order of magnitude probably indicates that our estimates of demand growth for luminants is greatly understated at 5%
in the case of the whale fishery. Efforts to truly match the rate of growth implied by these magnitudes would have likely driven
the whale fishery to a low population of whales with prohibitively high costs in many fewer years -- 69 years at 9% growth, for
example. With such growth driving the incentives for discovering new technologies, it is unsurprising that petroleum was in fact
discovered and it would be rather surprising, and a poor counterfactual, if no cost-lowering technologies were anticipated.
V. Discussion and Conclusions
We examine the sperm whale fishery in America in the 19th century as part of a larger project to investigate the conditions
governing the transition between the sperm oil and petroleum resources.
We build demand and supply curves relevant to the sperm whaling industry, where sperm whale oil is primarily an illuminant
being replaced by alternative fuels over the course of the 19th century. The marginal cost of providing sperm whale oil is estimated as a function of the expected number of whales and we use data on individual whaling voyages to estimate costs, which
were rising considerably during the first half of the century. This increase in costs did not always translate to increases in price
due to the competitive nature of the industry and considerable technological change in illumination options. The industry was
already in decline before the advent of drilled, cheap petroleum in 1859.
We establish that the sperm whale fishery was on track to be overharvested, and under conditions that would have allowed for
industrial development along the lines as actually occurred, had petroleum not been discovered, the fishery would have been
overharvested to the point of instability within two centuries at the most, given institutional changes shifting governance toward
optimal management of the fishery. However, while economic growth would have significantly lowered whale populations, at
least for the sperm whale, it would probably not have rendered them extinct, because costs (and prices) would have risen too
rapidly. The time frame for the discovery of new resources is, as one would expect, shortened by higher rates of growth.
19th century whales.nb
13
We examine the sperm whale fishery in America in the 19th century as part of a larger project to investigate the conditions
governing the transition between the sperm oil and petroleum resources.
We build demand and supply curves relevant to the sperm whaling industry, where sperm whale oil is primarily an illuminant
being replaced by alternative fuels over the course of the 19th century. The marginal cost of providing sperm whale oil is estimated as a function of the expected number of whales and we use data on individual whaling voyages to estimate costs, which
were rising considerably during the first half of the century. This increase in costs did not always translate to increases in price
due to the competitive nature of the industry and considerable technological change in illumination options. The industry was
already in decline before the advent of drilled, cheap petroleum in 1859.
We establish that the sperm whale fishery was on track to be overharvested, and under conditions that would have allowed for
industrial development along the lines as actually occurred, had petroleum not been discovered, the fishery would have been
overharvested to the point of instability within two centuries at the most, given institutional changes shifting governance toward
optimal management of the fishery. However, while economic growth would have significantly lowered whale populations, at
least for the sperm whale, it would probably not have rendered them extinct, because costs (and prices) would have risen too
rapidly. The time frame for the discovery of new resources is, as one would expect, shortened by higher rates of growth.
The whale fishery and petroleum industries were extremely integrated, in the sense that increasing prices and costs in the whale
fishery signaled the need for increases in investment in knowledge in substitute resources. The open access nature of the whale
fishery, so that price (equal to marginal cost) was below the optimal price which includes scarcity rent, would potentially have led
to a muted signal to begin investments in knowledge. However the external costs of the whale fishery, in terms of labor difficulties, lost lives, and long journeys with uncertain payoffs, are likely to have proxied for these shadow values better than is often
the case. These same conditions are surfacing now as we search for alternative technologies for petroleum; the case of the
transition from whale oil should give cause for optimism and highlight the importance of investigating a basket of alternatives to
find the next resource.
Note to readers: Obviously this paper is still in progress, but I hope that you see that there is plenty here to discuss!
Works Cited
Allen, A.H. (1883). On the Chemistry and Analytical Examination of Fixed Oils. Journal of the Society of Chemical Industry,
II(2): 49- 58.
Allen, R. C. and I. Keay. (2001). The First Great Whale Extinction: The End of the Bowhead Whale in the Eastern Arctic,
Explorations In Economic History 38: 448-477.
Allen, R. C. and I. Keay. (2004). Saving the Whales: Lessons from the Extinction of the Eastern Arctic Bowhead, Journal of
Economic History 64(2): 400-432.
Baum, C., Shaffer, M. E., and S. Stillman (2007). Enhanced Routines for Instrumental Variables/GMM Estimation and Testing,
Boston College Working Papers in Economics, wp 667. Boston College Department of Economics, revised 05 Sep 2007
Beaton, K. (1955). Dr. Gesner's Kerosene: The Start of American Oil Refining. The Business History Review 29(1): 28-53.
Black, B. (2007). Petroleum History, United States. In: Encyclopedia of Earth, eds. C.J. Cleveland. Washington, DC: Environmental Information Coalition, National Council for Science and the Environment.
Black, B. (2000). Petrolia: The Landscape of America's First Oil Boom. Baltimore: Johns Hopkins University Press.
Chandler, C.F. (1886). Petroleum, in Johnson's (Revised) Universal Cyclopaedia: A Scientific and Popular Treasury of Useful
Knowledge, eds. in chief F.A.P. Barnard and A. Guyot. New York: A.J. Johnson & Co.
Clark, C.W.; Clarke, F.H.; and G.R. Munro (1979). The Optimal Exploitation of Renewable Resource Stocks: Problems of
Irreversible Investment. Econometrica 47(1): 25-47.
14
19th century whales.nb
Clark, C.W.; Clarke, F.H.; and G.R. Munro (1979). The Optimal Exploitation of Renewable Resource Stocks: Problems of
Irreversible Investment. Econometrica 47(1): 25-47.
Clark, C.W. and R. Lamberton (1982). An Economic History of Pelagic Whaling. Marine Policy 6(2): 103-120.
Clark, C.W. (2005). Mathematical Bioeconomics: Optimal Management of Renewable Resources, 2nd Ed. New York: WileyInterscience.
Conrad, J. (1989). Bioeconomics and the Bowhead Whale. Journal of Political Economy 97(4): 974-987.
Daum, A.R. (1957). The Illumination Revolution and the Rise of the Petroleum Industry, 1850-1863. PhD Dissertation, Columbia
University.
Davis, J.H. (2004). An Annual Index of U.S. Industrial Production, 1790-1915. The Quarterly Journal of Economics 119(4):
1177-1215
Davis, L.E.; Gallman, R.E.; and K. Gleiter. (1997). In Pursuit of Leviathan. Chicago: University of Chicago Press.
Davis, L.E.; Gallman, R.E.; and T. Hutchins. (1988). The Decline of US Whaling: Was the Stock of Whales Running Out? The
Business History Review 62(4): 569-595.
Davis, L.E.; Gallman, R.E.; and T. Hutchins. (1987). Productivity in American Whaling: The New Bedford Fleet in the Nineteenth Century, NBER Working Paper Series, Working Paper No. 2477.
Dolin, E.J. (2007). Leviathan: The History of Whaling in America. New York: W.W. Norton & Co.
Hutchins, T. (1988). The American Whale Fishery 1815-1900: An Economic Analysis, PhD Dissertation, UNC Chapel Hill.
Lund, Judith N., Elizabeth A. Josephson, Randall R. Reeves and Tim D. Smith. "American Offshore Whaling Voyages: a
database." World Wide Web electronic publication. http://www.nmdl.org.
Kaiser, B.A. (2011). Estimation of Demand for Illumination in the 19th Century. Manuscript, available from author.
Kaiser, B.A. and J.A. Roumasset (2007). From Rites to Rights: the Co-evolution of Political, Economic and Social Structures.
University of Hawaii Economics Department working paper 200703. Available at http://ideas.repec.org/p/hai/wpaper/200703.html
Maran, M.J. (1974). The Decline of The American Whaling Industry. PhD Dissertation, University of Pennsylvania.
Nordhaus, W.D. (1997). Do Real-Output and Real-Wage Measures Capture Reality? The History of Lighting Suggests Not, in
T.F. Bresnahan and R.J. Gordon, eds. The Economics of New Goods, Chicago: University of Chicago Press, p. 29-66.
Roumasset, J.A. and N. Tarui (2010). Governing the Resource: Scarcity Induced Institutional Change. University of Hawaii
Working Paper 201015. Available at http://ideas.repec.org/p/hai/wpaper/201015.html.
Shuster, G.W. (1972-1973). Productivity and the Decline of American Sperm Whaling. Environmental Affairs 345-358.
Silliman, Benjamin (1833). Notice of a Fountain of Petroleum, called the Oil Spring. The American Journal of Science and Arts,
23: 98.
Silliman, Benjamin Jr. (1871). Report of the Rock Oil, or Petroleum, from Venango Co., Pennsylvania, With Special Reference
to its Use for Illumination and Other Purposes. American Chemist, July: 18-23.
Starbuck, Alexander (1878). History of the American Whale Fishery, Waltham, MA.
Tower, W. S. (1907). A History of the American Whale Fishery. Publications of the University of Pennsylvania Series in Political
Economy and Public Law. Philadelphia: John C. Winston Co.
Tsur, Y. and A. Zemel. (2003). Optimal Transition to Backstop Substitutes for Nonrenewable Resources. Journal of Economic
Dynamics and Control 27: 551-572.
19th century whales.nb
15
Tsur, Y. and A. Zemel. (2003). Optimal Transition to Backstop Substitutes for Nonrenewable Resources. Journal of Economic
Dynamics and Control 27: 551-572.
Whitehead, H. (2002). Estimates of the current global population size and historical trajectory for sperm whales. Marine Ecology
Progress Series 242: 295-304.
Whiteshot, C. A. (1905). The Oil-Well Driller: A History of the World's Greatest Enterprise, the Oil Industry. Mannington, WV.
Wright, G. (2006). Output of Whaling Products: 1816-1905. Table Db371-376 in Historical Statistics of the United States,
Earliest Times to the Present: Millenial Edition, eds. Carter, S.B.; Gartner, S.S.; Haines, M. R.; Olmstead, A.L.; Sutch, R. and G.
Wright. New York: Cambridge University Press. http://dx.doi.org/10.1017/ISBN-9780511132971.Db273-37810.1017/ISBN-9780511132971.Db273-378
16
19th century whales.nb
Appendix I
Estimation of Demand for Illumination in the United States, 1800-1900
We use Instrumental Variables to estimate the demand for illumination in the 19th century. We combine data from American
whale oil prices and production, and after 1859, petroleum prices and production, with characteristics of the economy to estimate
a demand for illuminating oils.
To create a consistent quantity of illuminating oils, we assume that one gallon of sperm whale oil is equivalent to 2.5 lbs of
spermaceti candles. One gallon of kerosene (refined petroleum) is equivalent to 14.5-20 pounds of candles, or about 5.8-8 gallons
of sperm oil. One gallon of kerosene comes from refining about 6 2/3 gallons of crude oil. Sperm oil is approximately equal to
1.57 gallons of petroleum for illuminating purposes (Silliman, 1871; Chandler, 1886), and sum quantities exchanged on the
American market accordingly. To create a consistent price representing demand, we use sperm oil prices until 1859, and then
choose the lower weighted price of the two fuels (usually petroleum) thereafter. We test demand as a function of per capita
income, population, industrial growth, time, and the price of the inferior substitute whale oil. We instrument for shifts in supply
with the tonnage of the whaling fleet, the whale population (ln), and a dummy variable for dates after 1859, when petroleum was
discovered in large enough quantities to fuel the new industry.
Table I.1: IV (GMM) Estimates for Demand of Sperm Oil
Variable
Price of illumination HlogL
I
-3.58 ***
H1.25L
II
-3.30 ***
H1.20L
Price of Whale oil HlogL
Per Capita income HlogL
Year
Index of industrial production
Constant
Adj.R2
Nobs.
Wald H Χ2 L-stat
Instruments
III
Variable Provenance
-5.02 **
H1.96L Whales: Tower H1907L;
Petroleum: U.S. Bureau
of Mines, Mineral
Resources of the United
States HannualL @Series
Db56 in Historical
Statistics of the USD;
HDeflator: CPI, Sahr H2010L
1.50
H1.71L
Tower H1907L
4.28
H2.83L
Series Ca11 in Historical
Statistics of the US
0.31 ***
H0.02L
-0.007 ***
H0.001L
0.25 ***
H0.04L
-0.007 ***
H0.001L
0.32 ***
H0.02L
-0.008 ***
H0.001L
-538.92 ***
H30.61L
0.88
101
1783 ***
-465.59 ***
H48.05L
0.88
101
2047 ***
-554.47 ***
34.34
0.87
101
1408 ***
Tonnage
Tonnage
Tonnage
Whale Population HlnL Whale Population HlnL Whale Population HlnL
Post1859 dummy
Post1859 dummy
Post1859 dummy
Series Ca19 in Historical
Statistics of the US
Tower H1907L
Whitehead H2002L
19th century whales.nb
17
Appendix II
Estimation of Marginal Cost of Sperm Whaling, 19th Century
We use instrumental variables to estimate the marginal cost of harvesting sperm whales. Using data from the American Offshore
Whaling Voyage Database collected by Lund et al. (2011) and stored at the National Maritime Digital Library, we have over
9800 observations of whaling voyages for the 19th Century that we match with annual data on estimated whale populations, price
and economic conditions to estimate the marginal cost of sperm whaling as a function of whale population and other economic
variables. Whaling is a competitive industry and so we assume that price is equal to marginal cost. We instrument for quantity
with the industrial production index, GDP per capita, and a post1859 dummy to mark the presence of cheap petroleum as an
alternative fuel. We control for vessel-specific idiosyncrasies by treating vessel observations as cluster groupings.
Table II.1 IV (GMM) Estimates of the Marginal Cost (Ln Price)
PriceHdollarsgallL
Q sperm oil
Time periodH1770=1L
Total months away
Max. of ship's tonnage
Total oil arriving in port that year
Real price of whale oil
Whale population sq.HlnL
Constant
R2 HuncenteredL
Nobs.
N. Clusters
F-stat H7,1302L
Instruments
z P>ÈzÈ
Coef. Std.Err.
7.1
0
0.0016 *** 0.0002
0.004 -10.02
0
-0.045 ***
0.005 -7.01
0
-0.037 ***
2.12 0.034
0.0003 ** 0.0002
0
-4.99E-06*** 6.94479 -9.74
0.004
7.68
0
0.030 ***
0.045 -10.3
0
-0.463 ***
8.82 10.39
0
91.63 ***
0.31
9803
1303
87.3 ***
Per Capita GDP
Index of Ind. Prod'n HDavisL
Variable Provenance
Tower, 1907
NMDL
NMDL
NMDL
Tower, 1907, Deflated CPI, Sahr 2010
Whitehead, 2002
Series Ca11 in
Historical Statistics of the US
Series Ca19 in
Historical Abstracts of the US
Post 1859
Marginal costs to a vessel are thus increasing in the quantity harvested and the price of the substitute good they could be harvesting, (baleen) whale oil, as well as to a limited extent the ship's tonnage, perhaps because of higher labor and other operating
costs. The time at sea (total months away) decreases the marginal cost (ships having success stay longer, or ships staying longer
return with more product) as does the total oil in to port in a given year (as more ships are being more successful). While all of
the variables have a significant influence on marginal cost, the net effect of them on price when all except for whale population
are held constant at their means is extremely small. The coefficient on total harvest quantity, for example, is so small that the
expected influence on price should be measured in millions of gallons of whale oil.
Importantly, however, the greater the estimated log of the whale population (squared), the lower the costs. A nonlinear relationship is assumed here to incorporate the nonlinear biological growth. Demand is instrumented with per capita GDP, the index of
industrial production, and a dummy indicating the time period after 1859 and the rise of petroleum.
18
19th century whales.nb
Appendix III
Figure III.1 shows the estimated growth function for sperm whales generated from Whitehead (2002). He estimates that carrying
capacity, or the population of whales before harvesting (N0 L began in 1712, was 1,110,000 whales. Using population estimates
n 1.4
and harvest records from 1800 to 1999, he estimates the annual biological growth function to be n = 0.011 nt J1 - Nt N . Thus the
0
maximum sustainable yield, or the highest number of whales that can be taken in a year without causing harvest to exceed
growth, is estimated to be 2,392 whales per year (shown on Figure).
Note that this is considerably lower than the MSY estimate of 13,893 whales used by Hutchins (1988), which is based on higher
initial expected populations of between 1.8 and 2.4 million and a higher growth rate. In fact, using the upper bounds estimated by
Whitehead (2002), the highest his data allows MSY to be is 5,172 whales, still less than half the value used by Hutchins (1998)
and Davis et al (1988). This throws their finding that sperm whales were not being overhunted into doubt.
Figure III.1: Sperm Whale Growth Function
Growth HgHNLL
MSY
2000
1800 population
1500
1000
500
200 000
400 000
600 000
800 000
1 ´ 106
Population HNL