Brief introduction of traditional Solow model

Population growth has changed the basic Solow model in three aspects. First, it brings us closer to explaining the sustained economic growth. In the stable state of population growth, per capita capital and per capita output remain unchanged. However, as the number of workers increases at the speed of N, the total capital and total output must also increase at the speed of N. Therefore, population growth can not explain the sustained growth of living standards (because the steady-state per capita output remains unchanged), but it helps to explain the sustained growth of total output.

1. Solow growth model assumes that the labor force growth rate is n (assuming that the whole population is labor force); The savings rate remains unchanged;

Per capita capital k remains stable; The increase of k will lead to the increase of per capita labor output y; The marginal return of capital to output decreases.

The model assumes that people save a fixed part of their income and use the rest for consumption. The composition of total capital (public and private) is the unconsumed part of output (public and private).

2. Solow growth model: In order to keep the per capita labor capital K stable, while the labor growth rate N increases, more per capita investment is needed. The faster the labor force growth rate n is, the more per capita capital we need to provide. When the steady state is reached, the per capita capital K remains unchanged, so the per capita investment sy must be equal to NK. Per capita investment needs to keep K constant by keeping the growth of capital and labor consistent. Capital, labor and output all grow at the same speed along a stable path.

3, the higher savings rate, the initial steady-state point at point E, assuming that people permanently increase the part used for savings, the savings rate increases. With higher savings rate, per capita savings and per capita investment, point F becomes a new steady-state point. Higher savings rate increases per capita labor output and capital, but does not affect the growth rate n.

4. Technological progress and growth, the conflict between theory and reality: So far, according to the growth theory, capital, labor and output all grow at the same speed N along a stable path, but in fact, the growth rate of capital and output here is much faster than that of labor. This may be due to technological progress. Under the condition of the same labor force, technological progress may make the same workers do twice as much work, just like population growth. Assuming that the rate of technological progress is t and the growth rate of labor force is (T+n), the growth rate of output and capital is also (T+n).