Question

Consider the following Harrod-Domar growth equation: \[ \frac{s}{\theta} = g + \delta \] where \( s \) is the saving rate, \( \theta \) is the capital-output ratio, \( g \) is the overall growth rate, and \( \delta \) is the capital depreciation rate. If \( \delta = 0 \) and \( s = 20% \), then to achieve \( g = 10% \), the capital-output ratio will be ________ (in integer).

Hint:

In the Harrod-Domar growth equation, the capital-output ratio is a crucial factor for determining the growth rate. It helps to understand how efficiently capital is used to produce output.

Answer 1

Step 1: Rearrange the equation to solve for \( \theta \). From the given equation: \[ \frac{s}{\theta} = g + \delta \] Substitute \( \delta = 0 \) and \( g = 10% = 0.10 \), and \( s = 20% = 0.20 \), into the equation: \[ \frac{0.20}{\theta} = 0.10 \] Step 2: Solve for \( \theta \). Rearranging the equation: \[ \theta = \frac{0.20}{0.10} = 2 \] So, the capital-output ratio \( \theta \) is \( 2 \).