K is not the only function that links the production functions. Additionally, the final space-production ratios depend on how early the inflection point is reached. Such correlations seriously complicate the study of bootstrapping. Variation of productivity over time poses another major problem. Although p tends to increase, like the space-production ratios, due to technological change and returns to scale, there are other considerations which counter this influence. First, the items which are initially produced in space will be those requiring the least capital, so that the mass of output per (year-mass) of machinery should decrease. In addition, as the output from bootstrapping shifts from K to Q, any equipment which is unique to the production of capital will fall into disuse, decreasing the productivity of the total capital stock. (Of course multipurpose systems will have the opposite effect.) Finally, there is the effect of equipment wear. Without adequate information regarding the relative weight of these opposing influences, the net change in productivity is ambiguous. Similar arguments interfere with evaluation of the functions A through E, Z, and Z,, as defined for Eqs. 1 and 2. Even with these factors constant, one would expect costs to change as the nature of the items brought up from Earth changes. Since the first goods to be produced in space will be those which require the least processing, the intrinsic value (cost per ton) of the average import will increase over time. Simultaneously, however, the proportion of imports which are less processed, but which contain lunar deficient elements, will also increase. Only the source of medium cost imputs will change, so the overall effect is again unclear. Apparently, bootstrapping permits so many degrees of freedom that modeling is extremely difficult. In addition, this strategy necessarily introduces complex interdependencies among the various physical and economic functions. In the absence of any significant experience or information to indicate the nature of the correlations, rather than attempting to formulate a general bootstrapping model, we consider a restricted case which should suffice for our exploratory purposes. SIMPLIFIED BOOTSTRAPPING MODEL One way to make the analysis mathematically tractable is to assume that manufacture of the final output is delayed until all of the capital — whether produced in space or merely transported there (as in 11 and 12) is operational. This restriction has the effect of separating both the mass and cash flows into two simpler equations, corresponding to the two stages of processing. During the capital production phase, lunar soil is used only to form expendables and machinerv. Thus. Since no benefits can be derived until some Q is produced, this initial period will probably be quite short — a few years at the most (12). As a result, the technology, as embodied in the scaling, productivity, expendable requirements, and prices, is nearly constant. Equation 4' then reduces to
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