# (p.383) Appendix I Metropolitan Provisioning: Economic and Administrative Maxima

# (p.383) Appendix I Metropolitan Provisioning: Economic and Administrative Maxima

THE PRINCIPAL TECHNICAL obstacles to metropolitan provisioning lay in the physical limitations of muscle-powered transport over land. At the root of the problem was the relationship, analysed by Von Thünen, between the daily fodder requirements of working animals and the capacity of the load which they could carry or draw. Some simple calculations should suffice to demonstrate the implications that this relationship had for the provisioning of a large population concentrated at a point. For simplicity’s sake we shall assume that each city dweller requires 3 daily pounds of ‘grain’ and that transport animals need 20 pounds each and can move 10 miles in a day. Three pounds is rather more than normal daily grain consumption, but is likely to have been somewhat below the total requirement for agricultural products overall. The figures for transport animals probably approximate to a realistic norm. In order to show the range of plausible outcomes we make two sets of assumptions for the energetic efficiency of transport and the availability of grain surpluses in the hinterland. These are as follows:

*Surplus*:

Case I—we assume that the rural population has a density of 80 per square mile and that agriculture can support a further ‘urban’ population equal to 20 per cent of the rural total.

Case II—assumptions as I, but we assume figures of 40 per square mile and 10 per cent.

In each case it is assumed that 3 pounds of provisions must be transported per day to support one urban dweller

*Transport*:

Case A—assumes a load capacity of 600 lb per animal.

Case B—assumes a load capacity of 300 lb per animal

In each case we assume a sustainable rate of 10 miles’ transport per day and that animals require the equivalent of 20 pounds of grain daily.

The figures in the table results show the size of the population that can be supported as the provisioning radius moves out an increasing number of days’ journey from the point.1 We assume that, on average, each wagon travels from a point in the middle of the daily ‘ring’ and measure the costs of transport entirely in terms of grain consumed by animals. This ignores labour and capital costs, and so in this respect is over-optimistic, but it also discounts the possibility of back-hauls and so loads total metropolitan transport costs onto (p.384) food supply more than is entirely justiWed. The size of the animal herd required is calculated, in the first instance, from the number of animals required in the ‘pipeline’ to supply the point population. We also need to take account of the arrangements required to provision the draught animals. In practice these could not be fed from their own loads, but if they were all provisioned along the wayside the inner rings would be stripped clean by teams travelling further aWeld. We therefore assume that further draught animals are required sufficient to move half the grain ‘fuel’ one daily journey.

The ‘administrative maximum’ (or Max(admin))—that is the absolute maximum that the technology will support, once economic logic is set aside and costs ignored—can be determined directly from the calculations. It is the geographical radius beyond which the animals’ fodder requirements exceed their load capacity. It is more difficult to determine the economically sustainable maximum (or Max(econ) ). In a free market, provisioning would expand geographically until the costs of procuring the marginal unit of subsistence exceeded the price premium urban consumers were prepared to pay. But this is not a realistic model criterion in the context of provisioning large towns or cities before the nineteenth century. In these cases provisioning was regulated, if not subsidized, by the authorities. Where subsidies are paid the maximum population may be anywhere up to Max(admin), but we can construct a simple model on the basis that the authorities purchase grain from middlemen, paying them their transport costs, and resell it on the urban market at a standard price. On the basis of such ‘cross-subsidy’, and ignoring other costs, provisioning will expand until the average transport cost equals the urban premium. This extent of this premium cannot be determined, but it seems unlikely to have been more than 20 per cent. Hence the maximum economic size for ‘point’ populations provisioned on this basis will be as in the table below (Max(admin) values bracketed):

16,60 |
|||

A |
66,400 (370,780) |
IA |
(90,450) |

4,200 |
|||

IA |
16,800 (90,380) |
IB |
(20,350) |

These calculations are too schematic, and the underlying assumptions too arbitrary, for the results to be worth much consideration in terms of their absolute values, but they should serve as reasonable indicators of orders of magnitude. As such they suggest that, under intermediate assumptions, centres of 10,000 to 20,000 people could be supported from local resources on an ‘economic’ basis, but this ceased to be possible as population grew much over 60,000, even on the most optimistic assumptions. Moreover on the most pessimistic assumptions, which are probably quite realistic for many times and places in pre-industrial Europe, ‘extra-economic’ means may be needed to provision centres in the 5,000 range. Of equal signiWcance, however, is the range of values resulting from variant assumptions. The differences between cases (I) and (II), high and low volumes of agricultural surplus, are just what we would expect, but changes in the energetic efficiency of transport have disproportionate effects. Doubling the animals’ load capacity quadruples the size of the population that can be supported. This is because the additional resources made available are proportional to the square of the extra distance travelled. The value for population at the Max(admin) point is in each case some Wve times (p.385) the ‘economic’ maximum and exceeds 20,000 even under the most pessimistic assumptions (IIB), a divergence which indicates the scope of politically driven resources mobilization.