Capital Substitution in an Industrial Revolution
A unified growth model is presented in which productivity growth is driven by learning-by-doing. We show that the growth rate of productivity is an increasing function of the share of capital. It is assumed that the industrial sector has a higher capital share than the agricultural sector and that the ability to substitute one output for the other slowly rises over time. Two distinct regimes of constant growth emerge, connected by a rapid transition in which the growth rates of population and income increase by an order of magnitude, indicative of simultaneous agricultural and industrial revolutions.
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