Suppose that the country of Xanadu saves 20% of its income and has a capital-out

Question

Suppose that the country of Xanadu saves 20% of its income and has a capital-output ratio of 4.

a) Using the Harrod-Domar model,calculate the rate of total GDP in Xanadu.

b) If population growth were 3% per year and Xanadu wanted to achieve a growth rate of per capita GDP of 4% per year, what would its savings rate have to be to get to this growth rate?

c) Now return to the case where the savings rate is 20% and the capital-output ratio is 4. Imagine ,now, that the economy of Xanadu suffers violent labour strikes every year , a quarter of it goes unused because of these labour disputes. if population growth is 2% per year, calculate the rate of per capita income growth in Xanadu under the new scenario?

Explanation / Answer

a) If the savings rateof XANADU is 20% and the capital output ratio is 4, then country of XANADU would grow at 5% per year.
As: Rate of growth of GDP = Savings ratio / capital output ratio .

b)  We know that the per-capita growth rate is the aggregate growth rate minus the population growth rate. Therefore, if the required per-capita growth rate is 4% and the population growth rate is 3%, the required aggregate growth rate is 7% per year, or 7/100. Using the Harrod-Domar equation, we see, therefore, that the required rate of savings is g × ?, which in this case is (7/100) × 4, or 28% of income.

c) You have to calculate what is the effectivecapital-output ratio in Xanadu because of the labor problems. Basically, if ?is the amount of capital you need to produce a single unit of output, you will now effectively end up using more than that. How much more? Well, it must be ?× (4/3). If you take away a quarter of this, you will get back exactly ?. So the effective capital-output ratio is now 4 × (4/3) = 16/3. Using this in the Harrod-Domar equation with a rate of savings is 1/5, we see that g = 3/80, which is 3.75% per year. Subtract the population growth rate. The answer for per-capita growth is 1.75% per year.

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