Question

Consider how unemployment would affect the Solow growth model. Suppose that output is produced according to the production function Y = Kα(1-U)L¹⁻α , where K is capital, L is the labor force, and u is the natural rate of unemployment. The national saving rate is s, the labor force grows at rate n, and capital depreciates at rate α.

Express output per worker (y=Y/L) as a function of capital per worker(k=K/L) and the natural rate of
unemployment(u).

Answer 1

The Solow growth model is affected by unemployment, with output per worker decreasing as the natural rate of unemployment increases.

Step-by-step explanation:

The Solow growth model can be affected by unemployment. In the production function Y = Kα(1-U)L¹⁻α, where Y is output, K is capital, L is the labor force, and U is the natural rate of unemployment, we can express output per worker (y=Y/L) as a function of capital per worker (k=K/L) and the natural rate of unemployment (u).

Substituting the values in the production function, we get y = kα(1-u). This equation shows that output per worker is a decreasing function of the natural rate of unemployment.

In other words, when the natural rate of unemployment increases, output per worker decreases. Conversely, when the natural rate of unemployment decreases, output per worker increases.