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Introduction to Modern Economic Growth Although this question has some descriptive merit (in the sense that describing the discovery of new technologies with a production function obscures some important details of the innovation process), the concern is largely irrelevant There is no reason to assume that the meta production function for technology is deterministic For example, we can assume that when a researcher puts l hours and x units of the final good into a research project, then there will be some probability p (l, x) that any innovation will be made Conditional on an innovation, the quality of the good will have a distribution F (q | l, x) In this particular formulation, both the success of the research project and the quality of the research output conditional on success are uncertain Nevertheless, all this can be formulated as part of the meta production function with stochastic output Therefore, the production function approach to technology is not particularly restrictive, as long as uncertain outcomes are allowed and we are willing to assume that individuals can make calculations about the effect of their actions on the probability of success and quality of the research project Naturally, some may argue that such calculations are not possible But, without such calculations we would have little hope of modeling the process of technological change (or technology adoption) Since our objective is to model purposeful innovations, to assume that individuals and firms can make such calculations is entirely natural, and the existence of individuals and firms making such calculations is equivalent to assuming the existence of a meta production function for technologies 12.1.3 Non-Rivalry of Ideas Another important aspect of technology is emphasized in Paul Romer’s work As we already discussed in the previous chapter, Romer’s first model of endogenous growth, Romer (1986), introduced increasing returns to scale to physical capital accumulation The justification for this was that the accumulation of knowledge could be considered a byproduct of the economic activities of firms Later work by Romer, which we will study in the next chapter, took a very different approach to modeling the process of economic growth, but the same key idea is present in both his early and later work: the non-rivalry of ideas matters 540