High School

Consider the simple Solow growth model without technological progress and without population growth. Assume that the production function has the same properties as we assumed in class.

a) Capital per worker: The steady-state capital per worker is positively related to the saving rate.

b) Output per worker: The steady-state output per worker is positively related to the saving rate.

c) Capital per worker: The steady-state capital per worker is negatively related to the saving rate.

d) Output per worker: The steady-state output per worker is negatively related to the saving rate.

Answer :

Final answer:

In the Solow growth model without technological progress and population growth, both steady-state capital per worker and steady-state output per worker are positively related to the saving rate, leading to higher investment in capital and thereby higher output, albeit with diminishing returns. The correct option is a) capital per worker, the steady-state capital per worker is positively related to the saving rate.

Explanation:

In the Solow growth model without technological progress and population growth, two main components come into play: capital accumulation and saving. The model posits that saving per capita (St) is proportionate to the output per capita (Yt), with the savings rate (s) being a constant fraction of total output. The savings lead to investment, which in turn affects the level of capital.

In such a model, the steady-state capital per worker is positively related to the saving rate, because higher savings allow for greater investment in capital stock. Furthermore, since the production function assumes a diminishing marginal product of capital, the steady-state output per worker is also positively related to the saving rate, but with diminishing returns. In other words, increases in the saving rate lead to higher steady-state values of both capital and output per worker, but the effect diminishes as capital per worker increases.