I'm adding some more intuition to our paper on the Industrial Revolution. I have a sketch of the math but still need to work out the details. Here is the argument:
"In this section, we show that both Malthusian Sluggishness and Modern Economic Growth are characterized by a strong equilibrium bias of technical change (Acemoglu, 2009). This means that in both regimes the long-run demand curve for the resource is upward sloping – higher relative prices are associated with higher demand. Under Malthusian Sluggishness the price of wood is rising relative to coal and technical change is relatively wood-augmenting. At the same time, wood use is rising relative to coal use. Because when the elasticity of substitution is greater than one the market size effect dominates the price effect, technical change becomes increasingly wood-augmenting. As a result, the economy increasingly diverges from the region where an industrial revolution is possible or inevitable. Modern Economic Growth is the mirror image. The price of coal rises relative to the price of wood, but coal use increases relative to wood use and technical change is increasingly coal-augmenting."
"In this section, we show that both Malthusian Sluggishness and Modern Economic Growth are characterized by a strong equilibrium bias of technical change (Acemoglu, 2009). This means that in both regimes the long-run demand curve for the resource is upward sloping – higher relative prices are associated with higher demand. Under Malthusian Sluggishness the price of wood is rising relative to coal and technical change is relatively wood-augmenting. At the same time, wood use is rising relative to coal use. Because when the elasticity of substitution is greater than one the market size effect dominates the price effect, technical change becomes increasingly wood-augmenting. As a result, the economy increasingly diverges from the region where an industrial revolution is possible or inevitable. Modern Economic Growth is the mirror image. The price of coal rises relative to the price of wood, but coal use increases relative to wood use and technical change is increasingly coal-augmenting."
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