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Why is the steady-state growth rate of per capita output and per capita capital G in Solow model, and what is the derivation process?
Solow growth model sf(k)=k*+nk.

The change rate of per capita capital possession k* depends on the difference between the per capita savings rate sf(k) and the capital required to equip each new population according to the established capital-labor ratio N K.

One is to increase the per capita capital, that is, to equip everyone with more capital equipment, which is called "capital deepening".

The second is to provide average capital equipment nk for each new population, which is called "capital popularization". In other words, after all the savings in the economy are converted into investment, some of them are used to improve the per capita capital possession (capital deepening), and the other part is used to provide an average amount of capital equipment for the new population (capital expansion).

Mainly in the following aspects:

1, he adopted continuous production function in the process of analyzing economic growth, and people called it neoclassical production function from now on.

2. The hypothesis that labor and capital can be substituted for each other makes the process of economic growth have the ability to adjust, so the theoretical model is closer to reality.

The long-term growth rate is determined by the increase of labor force and technological progress. The former not only refers to the increase of labor force, but also includes the improvement of labor quality and technical ability.

Therefore, Solow's long-term growth model breaks the theory that "capital accumulation is the most important factor of economic growth" and shows people that long-term economic growth depends on technological progress, education and training besides capital.