Question

In the Solow model, suppose the per worker production function is y = 5K^ 0.5. Suppose s = 0.12, n = 0.04, and d = 0.10.

Calculate the steady-state equilibrium capital-labor ratio.
k =___ (Round to two decimal places.)

Answer 1

The steady-state equilibrium capital-labor ratio (k) can be calculated using the Solow model with the given values of savings rate (s), population growth (n), and depreciation rate (d). Plugging these values into the formula, we find that k is approximately 0.7353.

Step-by-step explanation:

The steady-state equilibrium capital-labor ratio (k) can be calculated using the Solow model. The formula for calculating the steady-state capital-labor ratio is:

k = (s / (n+g+d))^(1/ (1-a))

where:

• s is the savings rate (0.12)
• n is the population growth rate (0.04)
• g is the technological progress rate (0 as it is not given)
• d is the depreciation rate (0.10)
• a is the output elasticity of capital (0.5)

Plugging in the values, we get:

k = (0.12 / (0.04+0+0.10))^(1/ (1-0.5))

k = (0.12 / 0.14)^(1/0.5)

k = 0.857^(2)

k ≈ 0.7353