The core of economic study lies in quantification, but for Egypt no number or measure is absolutely accurate. Population size depended on the area of land cultivated and its carrying capacity (Baer 1962; Butzer 1976: 76-98; Grandet 1994, I: 128). The ancient flood-plain is estimated at just over 8,000 sq. km for Upper Egypt, and about 22,000 sq. km to include the Delta and Fayum (Butzer 1976: 83). A square kilometre equates to roughly 400 aroura. In practice nowhere near the entire flood-plain can have been under arable cultivation. Papyrus Harris, of the reign of Ramesses III, records national temple endowments of 1,071,780 arouras - approximately 2680 sq km - and 107,615 persons (Grandet 1994, I: 91-101). This figure represents about 12 percent of the notional floodplain for the whole country but in practice might represent as much as half the land under arable cultivation in Upper Egypt. Papyrus Harris also records donations of 3,000,000 khar of grain to the temple of Karnak, and 309,950 khar to Medinet Habu and the minor temples of (Haring 1997, 412-14). Papyrus Wilbour, of the reign of Ramesses V, shows Karnak administering 17,324 arouras in Middle Egypt (Janssen 1975b: 148). The assessments on different plots vary between 5, 7.5, and 10 khar per aroura, suggesting an income in the region of 100,000 khar per year. At Deir el-Medina wage-rates this would provide for about 1,000 non-agricultural workers on top of the entire agriculturally productive workforce of the temple, and Papyrus Wilbour does not cover all the land managed by Karnak temple.
The calorific value of ancient grain is difficult to evaluate against modern grain (Kemp 1986; Miller 1991; Foxhall and Forbes 1982), but the best estimate suggests that one aroura under grain would suffice to feed an adult male (Miller 1991); the estimate that 2 arouras of actual flood-plain could support each person suggests a population for Upper Egypt of around 1.5 million (Baer 1962); the occupation of the Delta and Fayum will be much lower before the Graeco-Roman Period. This corresponds to the practical calculation that a plot of 5 arouras provided for a nuclear family and compares well with the more modern calculation that 3 feddan provided minimum family subsistence. The most reasonable guess is perhaps a population of about 1 million in the early Old Kingdom, rising to about 3 million in the New Kingdom, but the margin of error is very high. These estimates leave no margin between production and consumption, and even a small drop in cultivable area or yield would mean hunger. The population is likely to have fluctuated considerably with economic and ecological cycles. Population density is also poorly documented (Hassan 1993); census information of any sort is very scanty (Valbelle 1987). A population of 25,000 has been estimated for late Eighteenth Dynasty Amarna, from the extent of the archaeological site (Kemp 1981), and roughly similar figures for New Kingdom Memphis and Thebes (Strudwick 1995). The Middle Kingdom pyramid town of Kahun contained an estimated 450 houses, so that one might guess a population in the region of 2,000 using an average family size of 4.3 based on demographic data from the Graeco-Roman Period (Clarysse and Thompson 2006, II: 240-1), but figures as high as 10,000 have been suggested. At Ramesside Deir el-Medina, a norm of 60 men employed suggests a population of around 250.
Although they are special foundations, Kahun perhaps models the size of a regional town and Deir el Medina the size of a rural community within immediate walking distance of their fields.
Immigration posed special difficulties. When a Fourth Dynasty text claims 17,000 Nubians were brought captive, the figures have to be treated with care. The Old Kingdom does, however, seem to be a period of major economic expansion through deliberate rural colonization to expand the agricultural base by the development of new settlements and the creation of estates in the provinces (Eyre 2004: 161-3), at least partly using immigrant population. Similarly prisoners in large numbers - the profits of empire - underpinned the temple wealth of the New Kingdom, both as building labor and to expand the supporting base of agricultural production. This particular model of internal colonization is, however, an ideological one. In the aftermath of the great population movements of Libyans in the Nineteenth and early Twentieth Dynasties Ramesses III settled huge numbers of ‘‘captives’’ in new settlements in the (actually devastated) areas of the western Delta. In practice this represents acceptance of a status quo, resulting from their violent and disruptive mass migration. At a much lower level Upper Egyptian magnates of the First Intermediate Period and early Middle Kingdom talk of acquiring people and flocks as populations migrated from neighboring nomes in search of food in times of famine. The context in both cases is one of serious violence and economic disorder.
Other forms of quantification are even less reliable. Estimates of the numbers employed to build the great pyramid are pure guesswork, so provide no sound basis for estimating the levels of economic reserve - agricultural surplus - available in the Old Kingdom. The Eighteenth Dynasty was evidently the richest period for pure bullion. Gold donations to Karnak temple in the reign of Thutmose III come to about 15,000 kg, although this includes booty from the wars: production in the Nubian mines - not the most productive - was rated at only 265 kg a year. In contrast, Papyrus Harris, of the reign of Ramesses III, records only 51.8 kg gold delivered annually to Karnak, and other donations to temples at only 232.7 kg (Janssen 1975b: 153-8). The gold mines were at their most productive in the Eighteenth Dynasty, but Ramesses II already had difficulty keeping the Nubian mines in production, and by the Twentieth Dynasty supply had declined to lower levels seen in the Middle Kingdom. The gold from the tomb of Tutankhamun does not represent a norm for royal burials but something close to a peak.