Now, if we assume that CL is equal to DC, it is easy to show that aL must equal a. This assumption is simply that if a lunar product of a particular type requires D times the manhours required on Earth, hen the least value lunar product will require D times the manhours of the least value Earth product, or in other words, the least value products are similar. This seems as good an assumption as any at the present state of knowledge. We can then quickly solve for R: The lunar economy is thus characterized by analogy with the Earth economy and the factors f and D. Given these factors we can calculate the number of lunar manhours per worker to produce all the goods needed by the lunar economy. If that number of manhours are not available, the balance to sustain the economy must be imported from Earth. Since Earth imports are inflated in value by transport costs, it makes sense to allocate production of goods on the Moon beginning with the least cost (i.e. most mass per lunar manhour expended) and work up the distribution curve until the lunar manhours resource is exhausted, as shown in Fig. 6. The balance is import, and the mass can be readily calculated. The equation used to calculate import mass requirements is readily derived from the above equations, and is: The point at which import from Earth must begin is (not surprisingly) about at D=MA/(ME*f), where ME is the average annual worker manhours on Earth, 1800 in this paper. Above this point, the per capita mass increases rapidly, soon to exceed typical values assumed for base resupply (2 to 5 kg/manday). This may indicate that base resupply assumptions are too low, and certainly indicates that unless a lunar settlement is fully self-sufficient, it will probably present a resupply burden not where the lunar cutoff value (most costly product produced on the Moon) is given by: where AM is available manhours per lunar worker. Results are given in Table III and Fig. 7.
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