We develop an optimal growth model that includes several important new features. First, technological change is endogenously related to the growth of 'knowledge.' Investment may be directed either towards physical capital or knowledge (or both). Knowledge becomes an effective substitute for scarce resources by increasing the technical efficiency of resource utilization both for consumption and in capital. Nevertheless, a finite quantity resource must be embodied in capital and a finite flow is required for depreciation. Thus, there is an upper limit to technical efficiency and economic growth is thus ultimately limited by the availability of renewable resources. For a simple aggregate production function it is shown that technical efficiency never approaches unity on an optimal path.