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There is a nice review from Petra Moser (NYU) on Patents and Innovation: Evidence from Economic History in the Journal of Economic Perspectives (2013). There is another paper on The Choice between Formal and Informal Intellectual Property: A Review, in the Journal of Economic Literature (2014), where the role of innovation is central.

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There are two main theories of economic growth, the Solow-Swan growth model and Romer endogenous growth model. Both of these models allow for exponential growth. The economic output (GDP) can be modeled through standard Cobb-Douglas production function. For example, a classical production function is given by: $$F(K,L) = AK^{\alpha}L ^{(1-\alpha)},$$ where,...

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Business cycle fluctuations can be studied in many ways including also growth models. An example of using growth model to study business cycle would be this 1995 paper by Cho & Cooley. This being said growth models are not as common for examining business cycles as for example DSGE models so saying they are usually used for that purpose is correct. To my ...

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