Technical Report A Macro Model of Heterogeneous Growth

DOHTANI, Akitaka

Developing the AK model, we construct an endogenous growth model with many industries. Unlike the original AK model, our model generates endogenous growth accompanied by the change of relative price. The growth rate of each industry is determined by such fundamental parameters as the rate of technological progress of the industry, the elasticity of marginal productivity of the industry and the elasticity of marginal utility of the goods produced by the industry. In our model, the persistent change of relative prices admits of consistent growths of heterogeneous industries. Therefore, our model gives a theoretical explanation of the persistent transition of industrial structure accompanied by a change of relative prices. The transition of industrial structure depends on the fundamental parameters. We derive an equation that relates the growth rate of relative price of an industry to the growth rates of capital stock and production of the industry. By using our model, we unifiedly explain many empirical facts that have been known so far. We also give a new theoretical viewpoint about the empirical fact that the relative price of investment is higher in poor countries relative to rich countries. We demonstrate that the empirical fact results from the myopia concerning consumption in the poor countries. Moreover, in the case where the number of consumption-goods industry is one, we incorporate population growth. In the modified model, we derive an equation which relates the growth rate of relative wage to the growth rates of capital stock and relative price.

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