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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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