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? c. Now go back to the case where the savings rate is 20% and the capital-output ratio is 4. Imagine, now, that the economy of Xanadu suffers from labor strikes every year, so that whatever the capital stock is in any given year, a quarter of it goes unused because of these labor disputes. If population growth is 2% per year, calculate the rate of per capita income growth in Xanadu under this new scenario.

Answer 1

Using the Harrod-Domar growth model, the estimated GNP growth rate in Xanadu is 5%. To reach a 4% per capita growth with a 3% population growth, Xanadu needs a 28% savings rate. With a quarter of capital unused due to strikes and a 2% population growth, the per capita growth rate reduces to 1.75%.

Step-by-step explanation:

To answer the student's questions based on the Harrod-Domar model:

1. For part a, if Xanadu saves 20% of its income and has a capital-output ratio of 4, the rate of growth of total GNP can be calculated using the formula growth rate = savings rate / capital-output ratio. Plugging in the numbers, we get growth rate = 0.20 / 4 = 0.05, or 5%.

2. For part b, to achieve a per capita growth rate of 4%, with a population growth of 3% per year, the total growth rate needed is 7% (since per capita growth is total growth minus population growth). Using the same formula, savings rate = growth rate * capital-output ratio, the required savings rate is 0.07 * 4 = 0.28, or 28%.

3. For part c, with labor strikes, 1/4 of the capital is unused. Thus, the effective capital-output ratio becomes 4 / (3/4), which is 5.33. The growth rate, therefore, based on the savings rate of 0.20 would now be 0.20 / 5.33 = 0.0375, or 3.75%. After accounting for a 2% population growth, the growth rate per capita would be 1.75%.