The premise that man resides within a bounded and closed natural environment, an environment with relatively fixed dimensions, has been discussed in many forms for at least three centuries. The idea of a "spaceship earth" has recently caught the imagination and interest of both economists and environmentalists in particular, and the public in general. A basic tenet of this viewpoint is that whatever has been produced, consumed, not recycled and discarded within the sealed" spaceship earth" is still here and will continue to be. Of course, energy dispersion may be offset by nuclear fusion or breeder reactors so that what was previously discarded may be completely reused without seriously impinging on the earth's natural energy reservoirs. Economically and technically-feasible extraterrestrial transportation systems, destruction of wastes by symmetrical anti-wastes, or increased efficiencies in solar energy conversion also may become realities. However, such energy-augmenting technological changes, at least at this time, appear to be in the very distant future. What is of pressing current importance, if we accept the premise of a nearly sealed capsule earth with relatively fixed dimensions in terms of mass-energy and waste assimilative capability, is how rapidly economic growth should proceed. Rather than attempting to dissect the "spaceship earth" premises regarding limited energy reserves and assimilative capability, we take these as given in this paper. We then construct several simple paradigms of an economy confronted with a bounded, closed natural environment and then we analyze how such an economy should optimally produce and consume over time. The next section of the paper deals with an extremely simple model of waste generation, based on the conservation of matter-energy principle, and with the consumption behaviour of the economy's inhabitants assumed to be predetermined. In subsequent sections, the model is generalized to an optimal control problem where consumption and waste generation are allowed to be regulated, and an attempt is made to integrate the non-mutually exclusive processes of resource extraction and waste generation. [ABSTRACT FROM AUTHOR]