In this paper, we formulate the optimal growth model of a dual economy. In our model, the production and consumption in traditional sector are more explicitly taken into consideration. For instance, the average product of labour in traditional sector diminishes with increment of labour input. The value of it is equal to the income
per capita in traditional sector and the supply price of labour to modern sector.
We obtain the following. On the optimal path, capital accumulation and the enlargement of consumption make progress simultaneously. And, in one case, income difference between two sectors occur after the lapse of sufficient time and the relation lasts long. The value of product of labour in traditional sector becomes larger than that in modern sector. In the other case, even after the lapse of sufficient time, the imputed price of investment is larger than the marginal social value of consumption of product of modern sector. Whether one of two cases occurs depends on the production technologies of two sectors, the depreciation rate of capital stock and the social discount rate. These are the characteristics which the Marglin-Dixit-Stern model fails to take into account.
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