Fig. 2. Strategies for space industrialization. Indeed, if the project horizon is finite, K will stop growing altogether since production of machinery in the last period yields no benefits. Taken together, these arguments suggest that K is S-shaped, like a learning curve. There are many mathematical equations (e.g., logistic or the Gompertz curves) which fit this general form, all requiring at least three parameters. In general, these functions are sufficiently complicated to make numerical analysis a necessity. The computations become especially burdensome since production must be optimized with respect to all three variables for every set of engineering specifications considered. (Additional complications arise from the need to specify the transport capacity function.) Since the capital stock grows over time, the space-production proportions will not be constant. Instead, just like in underdeveloped countries, the portion of goods which are produced locally will increase as an industrial base is established. Other reasons for augmented ratios include technological improvements and increasing returns to scale, which overtake the impracticality of producing certain items in the small quantities demanded at the beginning of industrialization. The output of a fixed capital stock could be increased by changing the number or types of inputs. However, any large increase in production would require more machinery. Ayres et al. (16) have discussed formalisms for analyzing the growth of flexibility in production systems. Unfortunately, the growth of the space production ratios cannot be fixed without regard to K. Any substantial increase in the number of items produced in space also requires enlargement of the capital stock. Consequently, the inflection points of m, n, I, and must occur close to that of K.
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