Ann M. Carlos		    Frank Lewis
University of Colorado	Queen's University

I have yet to see any problem, however complicated, which, when you look at it in the right way, did not 
become still more complicated. (Indians, Animals, and the Fur Trade, p.61)

	That the beaver population was depleted during the fur trade period is generally accepted.  
	Irrespective of which part of the extensive body of literature that one might examine, the basic 
	theme is that the Indians in Canada overexploited the fur resource.  Indeed, this belief is so 
	widely held that no one has examined the timing, pattern, or scale of that exploitation.  This 
	paper addresses just these issues for the period 1700 to 1763, through an examination of the 
	Hudson's Bay Company's post records of the interaction between trader and Indian.  We ask whether 
	the company's records of the numbers of furs brought to the post indicate depletion of the beaver 
	population.  If depletion is indicated, we then ask over what period did this occur, under what set 
	of economic circumstances, and in which of the Hudson's Bay Company's post hinterlands?

	Although there was a Hudson's Bay Company presence around Hudson Bay from 1670, trade at company 
	posts, at least until 1713, depended on the success or failure of its military campaigns against 
	the French.  Because of this, we focus on the years between the Treaty of Utrecht (1713) and the 
	Treaty of Paris (1763), which marked the end of French rule in Canada.  During these years, Hudson's 
	Bay Company policy in Canada was passive but vigilant in that the Company waited for the Indians to 
	come to trade at the Bay side posts rather than actively going out in pursuit of the Indians.  Such 
	a policy operated to the Company's advantage as long as no impediment cut the flow of Indians to the 
	Bay.  Because each river-mouth fort commanded a different region, a roughly radial trading pattern 
	developed.  In contrast, the French trade from the St. Lawrence can be thought of as linear.  
	Traders from the St. Lawrence were continually pushing further west in search of cheaper furs. 
	On a theoretical level, the organization of the two trades was similar in that the Hudson's Bay 
	Company had a technical monopoly of the beaver trade in the drainage basin of Hudson Bay, while the 
	French company, the Compagnie d'Occident, obtained in 1718 a monopoly of the beaver trade in the 
	St. Lawrence basin.  In other respects, however, the companies operated quite differently.  The 
	French monopoly issued conges (licenses) or leased out the use of its posts.  Both leasing and 
	licensing created an incentive for those involved to try to expand the trade as much as possible, 
	therefore it is not surprising that during the period after 1720, there was an expansion of the French 
	trade.  But it was not until the beginning of the 1740s that new French posts were established within the 
	western drainage basin of Hudson Bay.  Thus it was only for the period from 1740 until the mid 1750s that 
	these posts represented a threat to the flow of furs to Hudson Bay.  From 1755 to the British conquest, 
	French competition was a much less serious problem.

	In comparison to the licensing and leasing system of the French company, the Hudson's Bay Company 
	was organized on strictly hierarchical lines and attempted to set and maintain uniform rules for 
	the managers of its various forts.  The Company dictated the prices managers could charge for goods 
	traded  and for furs purchased.  These standards were known as the Official and Comparative Standards 
	and were denominated in the Company unit of account - a Made Beaver (MB).  However, because the nature 
	of the trade required price flexibility, the Company allowed some differences between its posted 
	schedules and those used in actual trade.  This difference was know as the Overplus.  But even here, 
	the head office demanded a full accounting of the actual trading prices and the amount by which the 
	managers had deviated from the posted schedules in order to ensure that no manager used the difference 
	for personal gain.  It is within this highly centralized structure that our discussion of depletion 
	takes place.

	The study of the fur trade in Canada has generated a large and varied literature, much of which is 
	qualitative.  Yet the absence of quantitative analysis, in some cases, has not been dictated by a lack 
	of available data.  The Hudson's Bay Company preserved its trading post records; and these records 
	allow us to form a good picture of some aspects of the fur trade including the economic relationship 
	between the Indians and the Company.  Arthur Ray and Donald Freeman in their seminal works on the fur 
	trade have already made use of some of these data.  In this paper, we also exploit these records to 
	address a number of questions including the specific issue of depletion.  By combining the Company 
	records with recent work on beaver ecology, we attempt to infer the change over time in the beaver 
	population and the impact of French competition on that population,  In addition, we use the current 
	economic literature on biological resource extraction to indicate the effect of the Hudson's Bay Company 
	pricing policies on the depletion of the beaver stock.

	Our analysis is based on a fisheries model of resource extraction that has been applied successfully 
	to fur-bearing animals.  The model assumes that the unexploited population follows a logistic growth 
	curve from which can be derived a quadratic relationship between the animal stock and the absolute 
	rate of natural increase:
		(1)    F(x) = aX - bX2,   a, b > 0
where X = the animal population and F(X) is the natural growth of the population per period.  In equation (1), 
parameter, a, is interpreted as the maximum proportional rate of growth of the population, a rate that decreases 
continuously as the population declines; and parameter, b, equals  where  is the (maximum) population if the 
resource is not harvested.

	The observed population dynamics of an exploited species will depend on the harvest rate and the extent 
	to which that harvest varies over time.  Combining equation (1) with the harvest rate, we derive the 
	change in population per period as:
		(2)     X = aX - bX2 - H,
where H is the harvest.  Whether the population is growing or declining depends on the relationship between natural 
	growth and the size of the harvest.  In particular  as  .  Also of interest in some resource analysis is the 
	population that yields the maximum sustainable harvest, Xm.  This is derived by maximizing H with respect to 
	X subject to = 0. One objective of the paper is to determine the extent to which the Hudson's Bay Company and 
	the Indians followed policies consistent with a population of Xm.

	We estimate the beaver population in three areas of the Hudson bay hinterland; the areas served by Fort Albany 
	(including Moose Factory), York Factory and Fort Churchill.  Fort Albany, located on James Bay, was furthest to 
	the southeast and hence faced the most competition from French traders.  York Factory, more than 500 miles to 
	the northwest, did not experience significant competition until the 1740s and Fort Churchill, which was even 
	further up the Hudson Bay coast from York Factory faced only modest French competition beginning in the 1750s.  
	The annual number of furs traded at these posts provide the basis of our population estimates.

	We derive estimates of the beaver population and the French harvest by combining fur trade data with recent 
	ecological findings on beaver life-histories and the way those histories respond to exploitation.  Central 
	to our calculation is the natural growth function, F(X).  To derive the parameters of that equation we use 
	the ecological studies which indicate that at maximum sustainable yield, 25 percent of the beaver stock 
	is harvested annually.  This is consistent both with the recent observed harvests and with the observation 
	that in an established lodge, 3 adult beaver of the 12 would leave each year to establish new colonies.  
	A harvest of 25 percent at maximum sustained yield implies parameter, a, in equation (1) is 0.5.  The value 
	of parameter, , depends on the maximum population a region can support and therefore will vary by trading area.

	Our estimates of  and the French harvest are derived by selecting plausible values and then determining if 
	those values generate a population pattern consistent with the observed Hudson's Bay Company harvests.  
	Because of the nature of the dynamic relationship between population and exploitation (equation 2), it 
	turns out that only a small range of values could have generated the harvests that we observe.  All 
	others either imply an extinction path or an implausibly large population towards the end of the period 
	when harvests were very low.  To illustrate the approach, consider the hinterland served by Fort Albany.  
	We begin by selecting a period when it most appeared that the Hudson's Bay Company was harvesting at a 
	maximum sustained yield basis.  That is 1718-24, when an average of just over 17 thousand furs were traded.  
	We then test different levels of French harvests, until we find one that generates a consistent population 
	series.  This turns out to be just under 4 thousand furs.  Thus we assume 21 thousand was the maximum sustainable 
	harvest in the Fort Albany hinterland.  Our estimates of the beaver population and the rate of French exploitation 
	are speculative, but at least they are consistent with the observed Hudson's Bay Company trade, the recent beaver 
	ecology literature, and the qualitative accounts of the fur trade.  If we are prepared to accept these 
	simulations as reflecting what actually occurred, some interesting insights and interpretations emerge.

	The experience of York Factory, in particular, illustrates the central role of the French in the depletion 
	of beaver stocks.  Trading began in 1715, but it was not until 1741 that the French built a post in the 
	hinterland, although they had begun trading several years earlier.  According to the qualitative literature, 
	French competition increased in the 1740s and the 1750s until it was suspended in the late 1750s by war.  
	Based on the historical accounts and applying our methodology, we have derived a population series and a 
	pattern of French harvest consistent with the observed trade at York Factory.  Our simulations highlight 
	the impact of French competition on depletion.  The trade at York Factory was consistent with maximum 
	sustained-yield management until 1739 when we estimate the beaver population at 116 thousand.  Starting in 
	1739, however, the population fell sharply.  The decline was due in part to exploitation by the French but 
	even more important was the apparent change in strategy by the Hudson's Bay Company in response to the 
	competition.  After receiving about 30 thousand furs per year over the period 1732-8, which stabilized the 
	beaver population, York Factory took in an average of 38 thousand furs over the years 1739-42, reducing the 
	beaver population to 75 thousand by 1743, and substantially lowered future returns from the region.

	The third post, Fort Churchill, was furthest along the Hudson Bay coast and the least open to competition 
	from the French.  Here, we estimate the beaver population to have been much more stable through the period 
	examined.  In fact, prior to 1750, the population never fell below 80 percent of the level consistent with 
	maximum sustained yield.  This is very similar to the York Factory experience before it faced French 
	competition in the 1740s.  The trade at Fort Churchill provides further evidence that French competition 
	was a major factor in the over-exploitation of the beaver population.  As long as the Hudson's Bay Company 
	had a monopoly, the harvest was at a rate approximately consistent with a maximum sustained yield.  This 
	was true at York Factory and Fort Churchill.  It was only when the French began trading in a region that 
	excessive harvests were observed.  Also significant is the fact that these excessive harvests were due not 
	to large numbers of furs being taken by the French, but rather to a shift in Hudson's Bay Company policy.  
	In response to the French trade, the Company began to receive furs at much higher rates, rates that led to 
	severe depletion of the beaver stocks.  Only at Fort Churchill, which was insulated by distance from 
	significant competition did Company policy not change.

	In the above analysis, we assume that the Hudson's Bay Company could control the number of furs traded 
	at each post, but given the nature of its relationship with the Indian trappers and middlemen, it could 
	do so only indirectly.  After all it was the Indians who did the actual trapping.  The Hudson's Bay Company, 
	however, could set fur prices through its post managers and it was pricing policy that ultimately determined, 
	or at least strongly affected, the size of the fur harvest.  To derive a relationship between fur prices 
	and the harvest, we relate the (Indians') level of harvesting effort to the price of furs and the size of 
	the resource stock.  This allows us to relate price changes at the three trading posts in our study to 
	changes in our estimated beaver population.  Throughout the period 1701-63, although the Company's Official 
	Standards, which remained constant over time and was the same across posts, actual prices received rarely 
	equalled that standard because post managers were permitted to offer the Indians lower prices, and record an 
	overplus in the accounts.  At the same time, managers incurred "expenses" in addition to the value of goods 
	traded directly for furs.  These expenses represented the cost of gifts given to the Indians, and were an 
	important feature of the trade.  When the overplus exceeded expenses, Indians received less than the official 
	standard for their furs, and when the reverse was true they received more.  Since both the overplus and the 
	expenses are reported in the annual accounts for each post, it is possible to derive price series for each area.

	A comparison of the Fort Albany and York Factory price series with the population estimates suggests a 
	connection between the prices Indians received for their furs and the rate of depletion.  In the Fort Albany 
	region we estimate that from 1720 to 1730, when the beaver population was stable, there was almost no change 
	in fur prices; whereas during the 1730s, when fur prices were raised by about 20 percent, the beaver population 
	declined from 60 to 50 thousand, or by about 15 percent.  There was another large price increase starting in 
	the late 1740s which saw the price of furs move from .9 to 1.25 MB by 1755, and the beaver population fell 
	by more than 50 percent.  This negative relationship is also observed in the York Factory data.  In that 
	region the population fell from 115 thousand in the late 1730s to 50 thousand by 1750, with fur prices 
	increasing from .68 to .99 MB.  Equally suggestive is the evidence from Fort Churchill, where we estimate 
	the beaver population remained fairly stable throughout the period, and the price series for Fort Churchill 
	is consistent with that stability.

        Our analysis highlights the role played by competition in the over-exploitation of the beaver population.  
	As we point out, what was important was not the size of the French harvest by rather the fact of the 
	French presence and the Company's reaction to that presence.