We have an innovation-based Schumpeterian model in which productivity and aggregate output growth are driven by product improvements, which are driven in turn by spending on Research and Development (R&D). However, as the economy becomes larger, and more technologically advanced, it becomes more complex.

The final equation of the model is explained and shown as follows: the "flow" probability of an innovation in any sector (p) is proportional to the current flow of "productivity-adjusted" R&D spending as a share of GDP, such that: 1) (p) = OR/A Where Ris R&D spending as a share of Y, and A is a proxy for how specialized - and this how complex the economy is, and o is the proportion in which R&D spending and complexity generate productivity-enhancing innovation, p. And the probability of such innovation is o. If output, Y, is driven by capital and labour, and by innovation, and innovation is driven by R&D spending as a share of GDP, and the degree of specialization of the economy and its complexity, A, help to drive growth and make society more complex (which could so slow growth down), such that: 2) Y = f {0 (R/A), A, K, L}, where K and L are constant Then what must happen to R as the complexity of the economy (and wider society) tends towards infinity (as A )? The final equation of the model is explained and shown as follows: the "flow" probability of an innovation in any sector (p) is proportional to the current flow of "productivity-adjusted" R&D spending as a share of GDP, such that: 1) (p) = OR/A Where Ris R&D spending as a share of Y, and A is a proxy for how specialized - and this how complex the economy is, and o is the proportion in which R&D spending and complexity generate productivity-enhancing innovation, p. And the probability of such innovation is o. If output, Y, is driven by capital and labour, and by innovation, and innovation is driven by R&D spending as a share of GDP, and the degree of specialization of the economy and its complexity, A, help to drive growth and make society more complex (which could so slow growth down), such that: 2) Y = f {0 (R/A), A, K, L}, where K and L are constant Then what must happen to R as the complexity of the economy (and wider society) tends towards infinity (as A )