The analytical solution of balanced growth of non-linear dynamic multi-sector economic model

In a one-sector neoclassical dynamic economic growth model, a reasonable ratio of investment to consumption exists, i.e., the “Golden Rule of Consumption”. This study is to extend one-sector neoclassical growth model to a multi-sector one. It is assumed that both the production function and the utility function are of Cobb–Douglas type, and the analytical expression of the balanced growth solution of the multi-sector model is provided, mainly including analytical expressions of the optimal distribution coefficient of fixed capital investment, the optimal distribution coefficient of labor hour, the proportion of production, the economic growth rate, the rate of change of the price index, and rental rates of different fixed capital.