Question

Suppose that the country of Xanadu saves 20% of its income and has a capital-output ratio of 4 . Assume capital does not depreciate. a. Using the Harrod- Domar model, calculate the rate of growth of total GNP in Xanadu. b. If population growth were 3% per year and Xanadu wanted to achieve a growth rate per capita of 4% per year, what would its savings rate have to be to get to this growth rate?

Answer 1

Using the Harrod-Domar model, the rate of growth of total GNP in Xanadu is 5%. To achieve a per capita growth rate of 4% with a population growth of 3%, Xanadu would need to increase its savings rate to 28%.

Step-by-step explanation:

The student's question involves the Harrod-Domar growth model to calculate the growth rate of a country's Gross National Product (GNP). To calculate the growth rate using the Harrod-Domar model, we use the formula: growth rate = (Savings Rate) / (Capital-Output Ratio). In this case, the savings rate is 20% or 0.2, and the capital-output ratio is 4. Plugging these numbers into the formula, we get a growth rate of 0.2 / 4 = 0.05, or 5% for total GNP growth in Xanadu.

To calculate the required savings rate for Xanadu to achieve a growth rate per capita of 4% per year with a population growth of 3% per year, we rearrange the Harrod-Domar growth formula to solve for the savings rate. The formula becomes savings rate = (growth rate of GDP per capita + population growth rate) x (capital-output ratio). Plugging in the desired growth rate of 4% plus the 3% population growth (totaling 7%) and the capital-output ratio of 4, we calculate the necessary savings rate: savings rate = (0.07) x 4 = 0.28 or 28%.