Any errors or omissions are the sole responsibility of the author and do not represent the opinion of any other individual or institution.

This paper will compare the productivity of slave labor in the West Indies and free agricultural laborers in West Africa between the late seventeenth century and the early nineteenth century using data, taken from secondary sources, on hire rates and subsistence costs for slaves in the West Indies as well as surplus to subsistence ratios in pre-colonial-West Africa. The results of this comparison, between upper-bound estimates of labor productivity in the West Indies and lower-bound estimates of labor productivity in Africa, are that the intercontinental labor productivity differential was not large enough to have made the forced mass migration of African labor to the Americas economically efficient. This paper finds that the cost of transporting slaves to the Americas and the high mortality rate of slaves, en-route, erase any increase in world output that can be attributed to the transatlantic slave trade. An alternative explanation for the transatlantic slave trade is proposed. The export of slaves allowed the West African elite to consume imported goods for which, given extremely high intercontinental transport costs, they had no alternative means of payment. Hence, West Africa exported slaves because slaves were uniquely mobile and, given West Africa’s paucity of exportable commodities and high intercontinental transport costs, there was no other way to bridge the balance of payments.

Past work by economic historians on the origins of the transatlantic slave trade attempt, but fail to explain one stylized fact: the low price of slaves on the African coast. The explanations offered fall into one of two general categories: low labor productivity in Africa or market failure in Africa. The former explanation is generally favored by the ‘americanist’ school; it is most often forwarded by scholars whose specialty is American Economic History. The latter explanation, based on market failure in Africa, is more often forwarded by ‘africanist’ scholars – those specializing in African economic history. According to thirty years of scholarship by americanists, the transatlantic slave trade was caused by the intercontinental labor productivity differential between Africa and the Americas. Stanley Engerman (1973), Richard Bean (1975), and Herbert Klein (1978), for instance, all argue that labor productivity was low in Africa, but high in the Americas, hence these scholars conclude that the transatlantic slave trade was driven by American demand for African labor. Herbert Klein (1978, 3) argues that the "forced migration of peoples of sub-Saharan Africa to the New World was the direct outgrowth of a seemingly inexhaustible demand for labor on the part of European colonizing powers." Richard Bean claims that

[t]he reason Africa provided so much of the un-free labor shipped to America was

because Africans were available cheaply, and were more efficient than were most

other types of labor. The choice between African, European, Asian, or Amerindian labor was a function of their relative costs and relative efficiencies (Bean 1975, 120).

Africanist scholars such as Philip Curtin, Robert Harms, and Patrick Manning have explained the origins of the transatlantic slave trade differently from Americanist scholars. In the Africanist literature, the slave trade is explained as a response to a differential in the exploitability of slave labor between the Americas and Africa. Philip Curtin (1979) and Robert Harms (1981) have both argued that slaves were less exploitable in Africa because proximity to the point of capture made it difficult to prevent escape or revolt. The further slaves were taken, the more valuable they became because the chances of their escaping or revolting declined the further they moved from home. Low African slave prices result from the uncertainty of property rights in slave captives within Africa. Curtin (1979, 116) compares the cost of raising a child to a productive age of fourteen and finds the cost to be significantly higher than the nominal cost of a fully grown slave captive.

The major weakness in Curtin’s diagnosis is that the food price data that he uses, for food purchased in Africa by Europeans for use as provisions during the middle passage, included the high costs of hauling and loading the food aboard European ships. Since loading costs for food were likely to be higher than the loading costs for slaves, high food prices relative to low slave slave prices originate in differences in their relative mobility. Subtracting loading costs from final food and slave prices would probably reduce the high food to slave price ratio significantly and thus undermine Curtin’s contention that, in Africa, it cost more to raise a child to the age of fourteen than it cost to purchase a fully grown slave captive.

A second weakness in the relative exploitability model found in work by Africanists is that if relative exploitability were a simple function of distance from the point of capture, exploitability would increase with distance going in any direction away from the point of capture, but in fact prices rose only in the direction of the slave exporting coast. Furthermore, if the percentage of surplus that an owner could appropriate from his labor force was higher given a lower risk of slave rebellion or escape, the greater the exploitability and hence value of women and child slaves in Africa, nevertheless women and children wee a clear majority in the Indian Ocean and trans-Saharan trades. If relative exploitability were the primary concern, then the slaves that were exported should have been those most likely to escape or rebel – the men rather than the women and children.

Patrick Manning was the first to note that slave prices were not equivalent, as is the case when markets function well, to the marginal physical product of labor or ‘African labor productivity.’

The level of productivity – the value of the output of an African man or woman – was the most basic determinant of slave prices. But when we note, for instance, that the average price of slaves rose by a factor of from five to six over the course of a century, we can be sure that this does not mean the productivity of African workers increased by a similar factor (Manning 1990, p. 93).

Manning attributes the disjuncture between low slave prices and high African levels of labor-productivity to a local inability to efficiently exploit slave labor. Most captives were destined for slavery in the Americas, rather than in Africa, because of the continent’s pervasive levels of insecurity, violence, theft and kidnapping. Manning (1990, 34) claims that "prices of slaves in Africa were also held down by the limited demand for slave labor or for slave produced produce: while monarchs relied on slaves to produce for the palace entourage, few other Africans had the wealth to sustain many slaves, nor could they find purchasers for goods the slaves might produce."

II. An Empirical Examination of the Labor Productivity Differential between Africa and the Americas.

 

Because there is no data on the hourly productivity of labor in Africa or the Americas in the era of the transatlantic slave trade, this paper compares the net lifetime output of individual laborers in Africa and the West Indies. The vast majority of production, investment, and savings in Africa was devoted to reproducing the population, the ratio of surplus product to subsistence needs can be estimated based on the number of children Africans, on average, must have had for the population there to have remained stable or to have grown at a slightly positive rate – Patrick Manning (1990, 196) estimates Africa’s population growth rate to have been 0.3 to 0.5 percent throughout the era of the transatlantic slave trade.

In the Americas, with few exceptions, the slave population had a negative natural rate of growth and, until the end of the eighteenth century, most slaves had a few or no children. Thus, the proportion of output that constituted a surplus must be estimated differently. Slave-labor productivity can be calculated using daily hire rates for slaves on Caribbean sugar plantations. Slaves were hired for periods of acute labor need, during planting or harvest periods, when slave-labor productivity per day was likely to be especially high. Hire rates are used to measure labor-productivity because data on subsistence costs, to be paired with hire rates, come from the same West Indian sugar plantations and for the same dates for which hire rates exist.

Comparing the ratio of surplus to subsistence levels in Africa and the Americas bypasses the problems of converting other nominal labor-productivity measures into comparable units of real value. If the surplus to subsistence ratio increased by more than the transportation and mortality costs of the slave trade, then the forced slave migration produced more value than it erased via mortality and expensive transportation.

Price data in this study are quoted in pounds sterling for reasons of convenience and accuracy. The pound’s value in terms of gold was constant throughout the era of the slave trade (Jastram 1977, 26). Data on wholesale commodity prices in England between the 1640s and 1795, when the English were heavily involved in trading and using slaves, point to negligible levels of inflation. The pound’s ubiquity in source material, its stable purchasing power, and its constant value in terms of gold combine to make it the ideal unit of account for this study.

A. Labor Productivity in Africa

Scholars generally agree that Africa, relative to Europe and even the Americas, was sparsely populated. According to Ester Boserup (1981), food production techniques evolve in response to the relative abundance or scarcity of land and labor. Where population densities are low, food is produced in ways that take advantage of land, yet economize on scarce labor. Hunting and gathering or long fallow systems of cultivation are almost never found in places where land is scarce relative to labor. As larger populations come to depend on a fixed amount of land for sustenance, cultivation techniques become more intensive: fallow periods are shortened, the number of crops grown each season is increased, irrigation systems are built, fertilizer is produced, and more sophisticated systems of land tenure evolve. In Africa, low population densities created an economy where most food was produced by hunting, gathering, or in areas of greater population, by ‘extensive’ rather than ‘intensive’ systems of cultivation. In Boserup’s schema, areas of ‘bush fallow’ or ‘forest fallow’ agriculture, capable of sustaining a population density similar to Africa’s, produce (at most) one or two crops a year for one or two years followed by an eight-to-ten-year-fallow period. Despite their use of primitive technology, extensive systems of cultivation are characterized by high labor-productivity (Hayami and Ruttan 1971, 732). Cultivators in Africa worked fewer hours, on average, and were able to support a larger number of non-productive dependents, per hour worked, than farmers in more densely populated Europe or Asia (Boserup 1981, 147).

Given the close link between land-to-labor ratios and labor-productivity found by Boserup (1981), comparisons of population density between pre-colonial Africa and slave using economies in the Americas will, at the very least, prove how labor scarce Africa was in absolute and relative terms. According to Joseph Miller (1988, 7), the slave catchment area in West Central Africa including Angola was approximately 2.5 million square kilometers. Miller estimates that before 1830, the area had 12.5 million inhabitants and a population density of 1.54 persons per square mile. Ester Boserup (1981, 11) concurs and gives a population density range for tropical Africa between 1500 and 1750 of 0.386 to 1.54 persons per square mile. At the upper limit, according to Boserup (1981), food production in African, long-fallow agricultural systems would support densities of 5.8 persons per square mile, but no higher. There were, of course, pockets of high density populations in Africa including some urban areas. Population densities in certain humid forest regions such as the Pende area in West Central Africa’s forest were quite high. Curtin (1975, 28) finds that Sereer regions in mid twentieth century Senegambia had a population density approaching 28.95 persons per square mile; Curtin credits the use of cattle manure for fertilizer and millet for cattle fodder with generating the surplus that enabled the high Sereer population density. Generally speaking, however, the few urbanized areas along the Gold Coast and in colonial enclaves were exceptions to the rule of low population density in Africa during the slave trade.

Before Europeans arrived, population density in the Americas was 0.386 to 1.54 persons per square mile – similar to population densities in tropical Africa (Boserup 1981, 11). The immigration of 10 million Africans and, by 1920, 60 million Europeans increased population densities in the Americas to levels far higher than in Africa. During the slave trade, however, all available data indicate that population density in the Americas was higher than in Africa. In the West Indian sugar colonies, the general rule of thumb was one acre of land per slave could produce one ton of unrefined sugar (Curtin 1990, 197). Even as output of sugar per acre rose, planters kept their slave-to-land ratio constant at one slave per acre. With one slave per acre or about 95 acres in a square mile, the population density of sugar plantation land would have been 95 slaves per square mile – far higher than any parcel of land in even the most densely populated regions of pre-colonial Africa. Between 1771-1778 population and sugar production in Barbados peaked – a 166 square mile island supported a population of 89,000, meaning that Barbados had a population density of 79.53 persons per square mile. Jamaica had 276 times the land area of Barbados and, in 1771, still possessed much unused frontier land; its total population density was 7.72 persons per square mile (Sheridan 1973, 123). Data on population density for Africa and the Americas are enumerated in the tables below.

We conclude that Africa was scarce in labor relative to the Americas in the eighteenth century. To the extent that high land-to-labor ratios suggest that labor was highly productive, then Africa, where labor was scarce and productive, was exporting its people to the Americas, where labor was less scarce.

Before moving on with the discussion of labor-productivity in Africa, the term ‘surplus output’ must be defined. Total output consists of subsistence output and surplus output; surplus output is that portion of total output which is not needed for the subsistence of the producer alone. Resources used to raise children and care for the elderly are here defined as surplus output because they are not consumed by the producer themselves. This way of defining surplus, as being equal to the maintenance cost of non-productive dependents, is unusual. In Meillassoux (1981, 55), subsistence is defined as total maintenance costs including food, clothing, health, shelter, education of non-productive dependents – children under 15 and elderly over age 45 – as well as productive members of a family. Ensuring that slaves did not have their own children allowed the slave’s owner to maximize the appropriable surplus of a slave’s output – the less used to care for the children of slaves, the more that owners could appropriate for themselves. Since labor productivity in the Americas (where slaves were childless) cannot be measured by counting the average number of offspring for slave couples, I compare the number of non-productive dependent producers in Africa could support with the hire rates divided by the subsistence costs of slaves in the West Indies in order to arrive at African and American surplus to subsistence ratios that allow a transcontinental comparison of labor productivity. This method bypasses unit and price conversion problems; also, there is virtually no data on surplus product from precolonial Africa. A conjecture on the minimum number of children necessary to maintain population levels will serve as an adequate lower bound measure for surplus output in Africa.

Demographic historians and anthropologists believe that Africa’s population grew at an annual rate of 0.3 to 0.5 percent (Manning 1990, 196). According to Meillassoux (1983, 53), men and women supported large families. In the Sahel, a male adult produced enough during his active life (between the ages of fifteen and forty-five) to bring up to the age of seventeen years about nine children (Meillassoux 1983, 53). The high African mortality rate made it necessary for women to have an average of about 4 surviving children for the population to continue to increase (Retel-Laurentin 1974). In addition to non-productive children, African producers generally had to support elderly non-productive dependents – mostly those surviving past age forty-five. If, as is the case for peoples living in difficult subsistence environments, most production, savings, and investment were devoted to reproduction and maintenance of the population then it is possible, from population growth rates, to estimate a lower bound figure for the proportion of output which constituted the surplus. Though it is quite likely that some of the surplus generated in African subsistence agricultural societies was expended on items such as clothing, housing, ritual, war, and culture, at a minimum a couple in Africa supported two children and one elderly dependent if the population were to reproduce itself. If a couple had three non-productive dependents, then in addition to their own subsistence needs, the couple produced a surplus that was three times larger than their own subsistence requirement. If the number of children increased to four and there were no elderly dependents, the surplus would have been roughly four times the value of subsistence. At the upper limit, a couple with nine children, as Meillassoux claims was common in Africa during the slave trade, produced a surplus nine times as large as their own subsistence needs.

In order to apportion the surplus produced by the man versus that produced by the woman, data or estimates of gender specific production is required. Based on data gleaned from field work done among sorghum eaters in the Sahel, Claude Meillassoux (1986, 96) reports that an adult male consumes approximately 300 kilograms of sorghum per year. He produces at least 1000 kilograms a year while a woman in the same group produces 500 kilograms a year and consumes at least 180 kilograms. Together they support at least 3 non-productive dependents (each non-productive member consuming the annual average of 180 kilograms) for fifteen years if the man and woman remain productive between the ages of fifteen and forty five. While men produce 67 percent of the surplus product, double the amount of women, they would have to produce an even larger proportion of the surplus if women had more children, since pregnant and/or lactating women have less time to work the more children they bear. It is difficult to be precise about the percentage of the surplus product men produce, but it would most likely rise above 67 percent with the birth of each extra child so that a couple with nine children would be twice as dependent on the surplus produced by the male as a family with only four non-productive dependents. The ratio of surplus over subsistence and the estimated proportion of the surplus generated by the male family member will vary with the number of non-productive members in a family unit as follows:

The reason for focusing on the labor productivity of a male with dependents is that African males made up a majority of African slave exports.

B. Labor-productivity in the Americas

Whereas Africa’s population had a slightly positive rate of growth, most slave populations in the Americas, especially those where first generation arrivals from Africa were a majority, had negative rates of growth. The situation in Barbados was typical of many American sugar economies. Between 1712 and 1734, 75,898 slaves were shipped there, yet the island’s slave population rose by less than 5,000. Barbadian plantation records indicate that there was only one slave birth for every six slave deaths (Blackburn 1997, 423). Birth rates generally rose as the proportion of American-born slaves in a slave population increased. Slave population growth rates were positive only for slaves in temperate climates such as North America and Minas Gerais in Brazil. Until the end of the eighteenth century, African born slaves comprised the majority of all American slaves and slaves in temperate climate zones were too small a part of the total to accurately reflect the average level of slave-labor-productivity in the Americas. Consequently, slave labor-productivity cannot be measured in the Americas in the way it was determined in Africa, based on the number of children families raised to adulthood.

This paper’s null hypothesis is that the labor-productity differential between Africa and the Americas was high enough to support the high mortality and resource cost of the trade. As such, upper-bound estimates of American slave labor productivity, based on data from the most productive sugar growing regions such as Barbados (Eltis 1995), will be considered representative and used for comparison with Africa. A lower-bound estimate of American subsistence costs will be juxtaposed with an upper bound estimate of surplus product to provide a ratio of surplus to subsistence that, if anything, errs on the side of exaggerating the productivity of slave labor in the Americas.

Since the focus of this paper on comparing the ratio of surplus output to subsistence output between Africa and the Americas, all that is needed are two ratios. Nominal-unit-conversion problems are bypassed; the units cancel out when surplus to subsistence values are divided and then changes in this ratio are compared to a measure of the transport and mortality costs of the slave trade. Because the longer one works, the greater the portion of output considered as ‘surplus’ grows relative to that which is considered ‘subsistence,’ more hours worked leads to higher gross output, higher surplus, but this does not also mean that labor productivity per hour is any different because a very high surplus to subsistence ratio can also simply mean that many more hours of labor were expended, but not at higher per-hour productivity.

There were two important differences between slave subsistence diets in the Americas and in Africa. Slaves had more food to eat in the Americas and this food was more costly than the food African captives were given before boarding transatlantic ships. Until the mid eighteenth century, most food for slaves in the British West Indies was imported because the islands only produced sugar and had little land left for anything else including food (Ward 1991). In Africa, on the other hand, slave captives consumed food that was locally produced. Slave diets in the Americas tended to be higher in calories required by their intense labor regimen, while the diet of captives in Africa was simply meant to keep individuals healthy enough to survive the middle passage. The average daily caloric intake for slave captives in Africa was 2,700 calories (Watts 1987, 64). A young male slave laboring during the most trying period of a sugar harvest consumed between 3,200 and 4,000 calories per day (Kiple and Kiple 1991, 124).

Information about the cost to owners of feeding slaves on sugar plantations in the Americas came from a variety of secondary sources in the literature on Caribbean economic history. For the earliest period of slave use in the British West Indies, the 1680s in Barbados, planation owners spent less than two pounds sterling per annum to feed and clothe each slave according to Richard Dunn (1972, 248). A hundred years later in the British West Indies, the annual cost of maintaining a slave, from 1763 to 1788, averaged between four and five pounds sterling according to Robin Blackburn (1997, 425). J.R. Ward examined the expense records of several plantations in Jamaica and Barbados for annual maintenance costs including food, medicine, and clothing for slaves. From 1799 to 1807, annual maintenance costs totaled 4.45 pounds per slave; for the period 1808 to 1819, annual maintenance per slave equaled 5.5 pounds and for 1820 to 1834, these costs totaled 3.170 pounds. The final observations for Cuba and Brazil from 1821 to 1860 near the end of slaving in the Americas, yield a yearly maintenance cost per slave of fifty dollars (Le Veen 1977, 53). When converted into pounds sterling, at the approximate exchange rate of five dollars per pound, the total annual maintenance cost per slave in pound sterling was ten pounds for Cuba and Brazil in the final days of American slavery. Over a two hundred year period, yearly maintenance costs ranged from a low of two pounds and a high of ten pounds, but the median was closer to four pounds.

One way of estimating the value of the surplus product obtainable from slave labor is to examine hire rates for slaves on sugar plantations during certain short periods when intense labor inputs are needed. Slaves were routinely hired out for particularly onerous tasks such as the holing of fields before new sugar cane was planted and harvested – both times when extreme effort was required for a limited amount of time. The daily price charged for hired slave labor approximates, in a competitive market, an upper-bound figure for the value and productivity of slave labor. Slaves were hired on a day-to-day basis, so an upper bound yearly rate is computed by multiplying the daily rate by 365. An upward bias is created because daily hire rates are multiplied by 365 – though slaves never worked every day of the year. Ignoring the many days where work was not done, ensures that the resulting measure for slave-labor productivity in the Americas is a maximum-upper-bound measure.

The data accumulated now allow some interesting comparisons. Please note that the data on subsistence expenses for slaves in the Americas, though more complete than similar data for Africa, does not match up exactly for every observation on slave hire rates. In Brazil and Maryland from 1783 to 1818, for example, I do not have good data on subsistence expenses. There is reason to believe that expenses in Brazil and Maryland were different from subsistence costs in the West Indies; Brazil and Maryland were self sufficient in food production while the West Indies were dependent on imports. Consequently, I have excluded Brazil and Maryland from the tabulations giving surplus to subsistence ratios in the Americas. I also have not included Brazil and Maryland in calculating productivity differentials between Africa and the Americas. The omission is excusable since the original intent of this paper was to compare the most productive regions in the Americas with areas in Africa. On average, slave labor in Barbados and the other West Indian sugar colonies, not in Brazil or North America, were the most productive (Eltis, 1995).

A few large numbers stand out in slave hire rates; they are generally for dates near the end of the legal trade in 1808. In newly cultivated and highly productive sugar colonies such as Jamaica and Trinidad from 1783 onwards, planters expected the legal import of slaves to cease; the fear of future shortage led to speculation and a huge rise in slave prices that, as the figures below confirm, also greatly increased slave hire rates. These rates do stand out from the rest and must be considered aberrations from the trend in slave hire rates. Barbados did not experience an equivalent rise in rates since its economy was already in steep decline as a sugar economy and would not have had many planters interested or capable of paying high prices to buy or hire slave labor. The surplus-to-subsistence ratios and productivity differentials quoted for Jamaica and Trinidad after 1783 must therefore be interpreted with caution.

The productivity differential tabulated in the last column of Table 6 tells us how much more or less productive an American slave was than a free African worker. The differentials are positive, indicating a higher labor-productivity in the Americas.

Since most of the data on subsistence costs and surplus values for Africa come from the late seventeenth century, it is best to compare that time period with the seventeenth century in the West Indies. Fortunately, the data presented above allow such a comparison. The Slave Coast, especially Whydah and Allada furnished a disproportionately high number of slaves who ended up in Barbados (Eltis 2000, 245). As a result, any productivity differential estimates between the Slave Coast and Barbados are meaningful indicators of change in labor productivity brought about by the forced migration between these areas.

In Barbados, the per-annum-hire rate for slaves was 9.125 pounds from 1670 to 1725. The per annum subsistence needs of slaves in Barbados at the same time cost 2 pounds. The ratio of surplus to subsistence therefore equaled 4.56. If this is an accurate description of labor-productivity in the Americas and if I have correctly measured the lower-bound of African labor-productivity, then American slaves were 3.62 times as productive as free men in Africa in the 1680s. Note that the productivity differential between the two continents declines as the average number of non-productive dependents an African male supported increased. For instance, if Slave Coast residents had, on average, nine children per couple instead of just four, the productivity differential declines from 3.62 to 1.3. The latter estimate, a productivity differential of just 30 percent leads to the opposite conclusion, that the forced migration of Africans reduced world surplus output because the costs of the forced migration were greater than the increase in world surplus output which the migration enabled.

C. The Costs of the Trade

The information and data on mortality as well as transportation costs presented in

Table 7 and 8 indicate that the forced transatlantic migration of Africans was very costly. As is the case with many other variables in this study, mortality and transport costs fell within a broad range.

Slaves were procured in a variety of ways, both peaceful and violent, and the challenge in finding mortality rates for the African segment of the trade is to judiciously estimate the percentage gathered in each of the two ways. Some slaves were prisoners of war sold by victors for profit. Others were victims of organized raiding parties that preyed on the many acephalous populations in the African interior. Still others were debtors in default who were sold by their creditors or hapless individuals intended for ritual sacrifice, but spared death only to be sold into slavery. For those who were captured violently and then marched long distances to coastal embarkation points, mortality was extremely high. The English abolitionist, Thomas Fowell Buxton, claimed that 71 percent of the total mortality of the slave trade occurred in Africa during capture and travel to the coast and only 18 percent occurred during the middle passage during which mortality was well documented. While the transatlantic journey from Africa to Brazil took a month to complete and the journey from West Africa to other areas in the Americas, including the Caribbean, took two months, slaves spent at least triple that amount of time after their capture in Africa. According to Klein (1999, 130), most slaves spent at a minimum six months from their capture to embarkation with time waiting in coastal barracoons averaging about three months.

Given the duration of the African segment of their journey from freedom to slavery, the distance from the point of capture to the coast, and the incidence of sickness, hunger, thirst and violence throughout the journey, high estimates of mortality in Africa are quite credible. According to Joseph Miller (1988, 384), "one experienced Luanda merchant reported that slavers toward the second half of the eighteenth century expected to lose about 40 percent of their captives to flight and death between the time they purchased them in the interior and the time they put them aboard the ships in Luanda." Miller’s own final estimate, based on a careful distinction between cases of peaceful and violent enslavement, separates slavery-induced mortality rates into three components. The violent capture of slaves killed 10 percent of the potential captives; the march to the coast killed 25 percent and the sometimes lengthy stay in coastal barracoons killed another 15 percent so that, on average, 50 percent of all those intended for sale in Angola and Central Africa died before they could be loaded onto America-bound ships (Miller 1986, 64).

After embarkation, it took Africans one to two months of sailing to reach destinations in the Americas. Mortality during the middle passage ranged between 9 and 20 percent. The variance in mortality rates was quite high and there were many ships with mortality rates far below 9 percent and a few with mortality rates over 20 percent. Middle passage mortality rates fell steadily from the seventeenth century, when they were routinely in the 20 percent range, until the late eighteenth century, but then they rose once again in the early nineteenth century.

The nineteenth century rise in mortality rates is blamed on the practices of smugglers who dominated the trade after the 1830s when Britain began to capture and confiscate transatlantic slavers. Rising mortality is also blamed on the fact that African captives in the nineteenth century originated from further inland since African coastal populations were depleted of potential captives. The greater the distance from the point of capture to the coast, the sicker slaves were likely to be on boarding transatlantic ships and the higher their middle passage mortality rates.

Finally on arrival in the Americas, African slaves died from sickness and disease contracted during the ocean crossing. These sick slaves, unwanted by any potential buyers, were left to die. Miller (1988, 440) estimates that 5 percent of the slaves who made it alive to the Americas died after landing and before sale. Klein (1999, 157) says that mortality after landing and before sale was lower – in the range of 0.4 to 0.6 percent. This study will accept Klein’s lower estimate. If the productivity differential can sustain a lower-bound estimate of the trade’s mortality costs, then the trade did increase world surplus output. Because a lower-bound estimate of the slave trade’s costs is greater than an upper bound measure for the productivity differential between Africa an the Americas, the slave trade could not have increased world surplus output.

The last hurdle to survival was the two to three year ‘seasoning’ period after sale in the Americas. Miller (1988, 440) estimates that 15 percent of all African arrivals died within a year either from new diseases for which they lacked immunity or from exhaustion as a result of inability to adjust to the harsh new regimen, especially on sugar plantations in the Americas. Bean (1975, 223) finds that in Jamaica, 33 percent of all African born slaves died within 2.5 years of their arrival. J.R. Ward’s (1988) research indicates that from 1700 to 1750, 40 to 50 percent of African slaves died within three years of coming to the West Indies.

Enumerating all the information on mortality above, we can calculate that out of an initial group of one hundred Africans were are set upon by raiders, captured, and marched to the coast, only fifty will survive to board ships for the Americas. Of these, 15 percent or eight will die during the middle passage leaving forty-two who disembark in the Americas. A further 5 percent will die in the Americas before sale leaving forty for the three year ‘seasoning’ period. After three years ‘seasoning,’ only twenty to twenty-four of the original one hundred slaves remained. In other words, for every slave that survived to become a productive laborer in the Americas, three or four perished along the way. Without factoring in transport costs, each surviving slave would have to be four times as productive (in terms of the African surplus to subsistence ratio) as a unit of labor in Africa in order for this trade to have increased world output.

To complete the description of the cost of the slave trade, data on transportation in the African interior and shipping costs to the Americas are presented and discussed. Before reaching coastal embarkation points, slaves were brought great distances from the interior. Inland transport costs rose over time as slave exports led to the depletion of coastal populations and new captives were brought to embarkation points from further and further inland. The absence of pack animals (attributed to the prevalence of the tse-tse fly), the inhospitable bush that separated the coast from slave catchment zones, and the need to pay frequent tolls to local power brokers made overland transport far more expensive than the transoceanic movement of captives. Fisher and Fisher (1971) claim that transport to the coast increased a slave’s price by 500 percent. Le Veen (1971, 136) points out that high transport costs to the coast made slaves in the African interior extremely cheap: "Slaves might be bought for as little as a few old buttons in some areas. One observer noted that slaves were initially selling for the cost of an old musket; another states that, when the coastal price of a slave was eight pounds, the interior price was 1.5 pounds." The transport cost for slaves varied with time. Slave prices more than doubled in the eighteenth century because captives were brought from further inland. Phillip Curtin (1975, 174) notes that while goods brought to Africa from England in 1733 increased in cost by 45.8 percent as a result of shipping charges, slaves brought from the interior of Africa to coastal European forts such as James Island, at the mouth of the Gambia River, increased in cost by 280 percent. The equivalent price differential, between coastal and inland prices , was 360 percent for ivory, and 230 percent for wax. The average increase in price the large majority of slaves taken from their homes in the interior to coastal loading points was over 400 percent.

The charge for the transatlantic shipping of slaves did not have any particular time trend; with the exception of periods of inter-European war or nineteenth century British attempts to suppress the trade, the cost of shipping slaves for most of the trade’s 400 year history is best described as a ‘random walk.’ Constancy in freight rates is attributed to the competitive organization of the slave shipping industry and the fact that there were only minor increases in slave shipping productivity over time (Eltis and Richardson, 1995). Unlike other shipping activity that benefited from a drastic decline in the number of crew per ton of cargo due to a reduction in piracy (North 1968), slavers remained heavily manned because of the constant threat of on-board-slave revolts.

Ships not only brought slaves to the Americas, they also brought the goods that were traded for slaves from Europe and the Americas to Africa, thereby doubling the value of the trade goods and increasing the portion of final slave prices that went to shipping. Shipping costs made up, with some variation, approximately 75 percent of the final selling price of slaves in the Americas (Eltis 2000, 115). On average, transatlantic freight charges doubled the African coastal price of slaves, just as shipping trade goods from Europe to Africa doubled the value of those trade goods from their ‘f.o.b.’ (free on board) values in Europe (Richardson 1991, 29).

According to Bean (1975, 177), "no series of per capita freight rates for slaves from Africa to Americas seems to have come down to us." Instead, scattered observations from merchants’ correspondence, business contracts with private shippers, and various estimates based on geographic price differences provide a general range for transatlantic freight rates. The freight rates charged in the Americas for each slave delivered alive, included the cost of transportation for the entire voyage, for trade goods from Europe to Africa and then slaves to the Americas. Ships generally returned to Europe in ballast so that freight rates for slaves paid for the entire-round-trip voyage. Note that slave prices in the fifth column of Table 8 below are ‘f.o.b.’ (free-on-board) prices, meaning that the prices represent the prime cost in Europe, before customs, insurance, and freight charges are added, of a bundle of goods to be traded for each slave in Africa. Due to transport costs in the course of traveling between Europe, Africa and the Americas, ‘f.o.b.’ values usually increased several times over (Eltis 2000, 115).

Because profits were made by successful voyages, the marginal cost of transportation was lower than actual freight rates by the rate of profit for successful voyages – a deduction of 7 to 27 percent. At a minimum then, shipping costs would have doubled the cost of slaves from their value in terms of the prime cost of the goods they were traded for in Europe. In addition, overland transport costs raised slave prices by more than 400 percent between the interior and the coast.

Taking the four-fold increase in slave prices from the African inland to the coast, and the further two-fold increase due to the transatlantic crossing, the transportation to the Americas (at a minimum) raised a slave’s price eight times. If mortality is included in this analysis of costs, then for the trade to have increased world surplus output, each slave arriving in the Americas would have to cover the total costs of their own output and the output of others who were killed (for every slave who survived, at least three died en-route) plus the transportation cost of all captives who did not complete their forced migrations from the inland of Africa to the Americas (this unknowable variable is excluded from my lower-bound estimate). Captives who did not survive to the end of the journey died at different points and the surplus lost as a result of their death (transportation costs to point of death plus their lost lifetime surplus output) varies with the location of their death. Incorporating mortality rates into the calculation raises the productivity differential necessary to ensure that world output increased to twelve. At a lower bound, each slave surviving past seasoning in the Americas would have to produce a surplus to subsistence ratio that was twelve times larger in the Americas than it had been in Africa if the slave trade were to have increased world surplus output – this is much higher than any upper-bound estimate (presented in Table 6) of the productivity differential between Africa and the Americas.

D. A Dynamic View of the Labor-Productivity Differential

The data provided above and the conclusion that the labor-productivity differential between Africa and the Americas was dwarfed by the costs of the trade is a static view of the trade. Looking at the whole trade over its four hundred year long evolution, one finds that the labor-productivity differential between Africa and the Americas was increasing. As new land was opened to cultivation and the American frontier expanded to make way for more plantations, land to labor ratios increased and production, from cultivation to processing, became more capital intensive and technologically sophisticated (Findlay 1995). By the eighteenth century, African-born slaves were no longer a majority of American slaves. Since birth rates, life expectancy, and productivity were higher for American-born slaves, average slave-labor productivity in the Americas also rose. Secondly, the costs of the trade were falling. Mortality rates during the middle passage decreased from a high of 20 percent in the late sixteenth century and early seventeenth to less than 10 percent by the late eighteenth century (Klein 1999, 136).

Though the slave trade led to an extremely high death rate among Africans and Europeans, most long distance migration in the pre-modern era was characterized by high mortality. Increasing intercommunication during the last half millennia made disease environments much less diverse than they had been in previous epochs. Each breach of previous isolation brought higher death rates, as unfamiliar diseases attacked populations whose environment provided no source of immunity. The Atlantic basin on the eve of the great European discoveries was especially open to this pattern of high death rates from new diseases. All the shores of the Atlantic were relatively isolated from one aother. As people moved from one disease environment to another their, death rates rose. As diseases moved with them from one previously isolated environment to another, they spread to non-immune host populations, who then experienced the increased mortality of disease migration (Curtin 1968, 114). Thus, the very nature of long distance labor migrations (convergence in disease environments) led to falling mortality rates and a reduction in the costs of migration.

Nineteenth century slave shipments contained proportionately more children and fewer adults than in earlier times; this lowered the opportunity costs to Africa of surplus foregone since more non-productive children were being taken and fewer productive prime aged men. During the seventeenth and eighteenth centuries, adult men were 51 percent of slave arrivals. By the nineteenth century, the proportion of adult men declined to 42 percent. The proportion of boys rose from 8 percent in the seventeenth century to 25 percent in the nineteenth. The proportion of young girls in slave cargoes tripled from 4 percent in the seventeenth century to 12 percent by the nineteenth. Adult women were 37 percent in the seventeenth century and declined to just 17 percent in the nineteenth century (Klein 1999, 163).

The increase in the proportion of children in slave shipments was either the result of falling freight rates or rising slave prices; less valuable non-adult slaves were cost effective to ship only if freight rates fell or if prices for non-adult slaves rose in the Americas. According to Galenson (1986, 114), the share of children in cargoes decreased during King William’s 1689 war and Queen Anne’s War from 1702 to 1714. These wars doubled transatlantic freight rates and made it unprofitable to ship lower priced child slaves. The share of children in cargoes increased as freight rates fell during periods of peace.

Toward the very end of the trade, steam ships lowered voyage times by a factor of four. Had the productivity differential between Africa and the Americas continued to rise and the costs of the trade continued to fall, the net loss in world surplus output, induced by the mortality and resource costs of the slave trade, might have been reversed. A slave trade, born from low cost transportation, reduced mortality, and highly productive American slave labor, would have led to a net gain in surplus world output.

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