This paper provides microfoundations for the knowledge production function in an idea-based growth model. It argues that the ultimate limits to growth are not in our ability to generate new ideas, but in our ability to process an abundance of potentially new ideas into usable form. The paper introduces a production function for new knowledge that depends on new recombinations of old knowledge, drawing an analogy with the development of new cultivated varieties by an agricultural research station. The core of the analytical structure is a theory of innovation based on this recombinant innovation metaphor. The paper uses the example of Edison's electric candle to illustrate the innovation process as a hybridization of ideas. It argues that innovation is a process of combining ideas, and that this combinatoric process is central to endogenous growth. The paper then presents a binary recombinant expansion process, which is shown to be more powerful than exponential growth. It then applies this model to a simplified "recombinant-growth economy" called Station Sci-Fi, where the productivity of the economy is proportional to the number of idea-cultivars. The paper then generalizes this model to a more comprehensive theory of recombinant growth, where the aggregate production function is defined as the total output from various amounts of capital and knowledge. It argues that knowledge plays two roles: as a productive factor and as a recombining factor. The paper then introduces an ultimate-limiting cost-of-R&D index, which is used to analyze long-run growth prospects. The main result of the paper is a theorem that shows that the long-run growth rate of an economy is a linearly homogeneous function of the two savings rates, expressed in a straightforward form that reveals the influence of the aggregate production function and the ultimate-limiting R&D cost on steady-state growth. The paper then analyzes the implications of this result for three special cases: when the ultimate-limiting R&D cost is infinite, zero, or positive.This paper provides microfoundations for the knowledge production function in an idea-based growth model. It argues that the ultimate limits to growth are not in our ability to generate new ideas, but in our ability to process an abundance of potentially new ideas into usable form. The paper introduces a production function for new knowledge that depends on new recombinations of old knowledge, drawing an analogy with the development of new cultivated varieties by an agricultural research station. The core of the analytical structure is a theory of innovation based on this recombinant innovation metaphor. The paper uses the example of Edison's electric candle to illustrate the innovation process as a hybridization of ideas. It argues that innovation is a process of combining ideas, and that this combinatoric process is central to endogenous growth. The paper then presents a binary recombinant expansion process, which is shown to be more powerful than exponential growth. It then applies this model to a simplified "recombinant-growth economy" called Station Sci-Fi, where the productivity of the economy is proportional to the number of idea-cultivars. The paper then generalizes this model to a more comprehensive theory of recombinant growth, where the aggregate production function is defined as the total output from various amounts of capital and knowledge. It argues that knowledge plays two roles: as a productive factor and as a recombining factor. The paper then introduces an ultimate-limiting cost-of-R&D index, which is used to analyze long-run growth prospects. The main result of the paper is a theorem that shows that the long-run growth rate of an economy is a linearly homogeneous function of the two savings rates, expressed in a straightforward form that reveals the influence of the aggregate production function and the ultimate-limiting R&D cost on steady-state growth. The paper then analyzes the implications of this result for three special cases: when the ultimate-limiting R&D cost is infinite, zero, or positive.