where Ko is the initial capital supplied from Earth. Evidently, separating the production of K and Q requires that the capital stock grow exponentially (13). Implicit in the integration is the assumption that the capital stock is infinitely divisible and compounds continuously. This approximation might be approached in practice since most space equipment is expected to be relatively small. Increased production can be achieved in many cases by building additional similar sized parallel units. The Earth launch requirement can be reduced similarly to where 6 is the annual import mass per unit mass of capital. Assuming a fixed fleet during capital production, UP may never exceed the transport capacity, M tons/year. Therfore M/0 is an upper bound on the capital operating during its formation period. More machinery may be accumulated, but the additional capital cannot function until manufacturing of the final product has begun. The transport fleet also affects the onset of exponential growth. If the vehicles are used to capacity, installation of the initial equipment will take KJM years. In this way, the entire production path for a given technology can be specified by just two parameters — Ko and Af. These same factors also uniquely determine the cost of developing a given capital mass. The initial capital nominally costs G $/ton, with the payment schedule fixed by M. Once all of this equipment is in place, the cash flow required to finance production of machinery in space is where ip is the annual cost per unit mass of capital. If K is defined as the equipment in actual operation at any given time, Eq. 8 holds whether the capital grows linearly, as when constrained by fleet size, or exponentially. The costs at all points during SMF formation, (and consequently the PDV costs) are therefore fixed by the same two variables which determine K. The dependence of PDV costs on Ko and A/ for the base case technology described in Appendix 2 is illustrated in Fig. 3. The lowest isocost contours are at the origin, indicating a preference for the maximum amount of bootstrapping (smallest Ko) and the smallest transport fleet. The reason for this bias is readily explained. By starting with a minimum of capital from Earth, capital costs are deferred to the discounted future. Similarly, a small transport capability forces expenses to be spread out over a long period so that costs are discounted heavily. However, even though this strategy minimizes the cost of establishing an SMF, it also delays receipt of revenues from the final product.
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