Defining Z as the mass of expendables required per (year-mass of machinery), and ZQ as the corresponding expendable requirement for Q, In this way, then, Q is functionally related to K once the scaling, productivity, expendable requirements, and space-manufacturing proportions are specified. There could, in more complex models, be complicated interdependences among the bracketed expressions, as well as between them and the functions Q and K. Besides being limited by the productivity of capital in space, extraterrestrial operations may also be constrained by the ability to transport support material from Earth. The mass which must be imported to space any given year is Thus, UP is a function of Q and K. Since Q is a function of K in Eq. 4, the mass which must be supplied from Earth depends simply on how the capital stock varies ovei time. The value of UP must never exceed the transport capacity, M tons/year. The converse, however, does not hold. Indeed, in the long run, even with a fixed launch fleet, UP will decrease as the space industry becomes less dependent on Earth. Since UP depends only on K, the transport constraint M effectively limits the potential capital growth. In addition to modeling the physical flows, it is important to describe the cash flows mathematically. The net cash flow CF in any given year is simply the revenue obtained during that year less expenditures. As in national income accounting, costs of goods produced and used within the manufacturing complex are internal transfers which do not contribute to the balance of payments. Consequently, the cash flow can be expressed as follows: where the new terms are the revenue per year derived from each unit of output (P), and the costs per mass of process expendable (F), capital (G), output (H), and output-related expendable (I) brought up from Earth. The functions F, G, H, and / must be adjusted for any deviation of A through E from unity. Simplifying as before,
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