Question

The economy of Solovia is described by the Solow model with population growth and technological progress. The production function is Y=K ^1/2 (EL) ^1/2 . The saving rate s is 30 percent, the rate of population growth n is 3 percent, the rate of technological orogress g is 2 percent, and the rate of depreciation δ is 5 percent. Calculate the steady-state values of the capital-output ratio K/Y.

Answer 1

In the Solow model, the steady-state value of the capital-output ratio (K/Y) can be calculated using the saving rate, population growth rate, technological progress rate, and depreciation rate. The steady-state capital-output ratio in this case is 6.

Step-by-step explanation:

The Solow model with population growth and technological progress can be used to calculate the steady-state values of the capital-output ratio (K/Y). In this model, the capital-output ratio is determined by the saving rate (s), the rate of population growth (n), the rate of technological progress (g), and the rate of depreciation (δ).

To calculate the steady-state capital-output ratio, we need to calculate the values of investment (I) and capital (K) in the steady state. In the Solow model, investment is equal to the saving rate multiplied by output (I = sY), and capital is equal to the investment rate divided by the depreciation rate (K = I/δ).

Using the given values, we can calculate the steady-state capital-output ratio as follows:

1. Calculate investment: I = sY = 0.3Y
2. Calculate capital: K = I/δ = 0.3Y/0.05 = 6Y
3. Calculate the capital-output ratio: K/Y = (6Y)/Y = 6

Answer 2

The steady-state value of the capital-output ratio (K/Y) in the Solow model can be calculated using the formula K/Y = [(s/(n+g+δ))^2]. Plugging in the given values, we find K/Y = 9.52381.

Step-by-step explanation:

The Solow model with population growth and technological progress is used to describe the economy of Solovia. The production function is given by Y = K^(1/2)(EL)^(1/2), where Y is output, K is capital, E is the labor force, and L is labor. The steady-state values of the capital-output ratio (K/Y) can be calculated using the following formula:

K/Y = [(s/(n+g+δ))^2]

where s is the saving rate, n is the population growth rate, g is the technological progress rate, and δ is the depreciation rate.

Plugging in the given values, we have K/Y = [(0.3/(0.03+0.02+0.05))^2] = 9.52381.