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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?

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Related questions

Suppose that Xanadu now has a savings rate of s=S/Y=20% and has a capital output ratio θ= K/Y= 4 and depreciation is equal to zero (δ=0).


1) Using the Harrod-Domer model, calculate the rate of growth of total GNP in Xanadu.

2) What is the rate of population growth that would eliminate all per capita growth?

3) If Xanadu

4. Consider a farmer who can either plant or market/consume his crop. Whatever amount he plants becomes a crop twice the size the following year. For example, if he plants seed from 2 ears of corn, he gets 4 ears of corn at harvest. Assume he starts off with 50 bushels of corn.

a. If he decides every year to market/consume half his crop and plant the rest, what will his harvest be next year? What will his consumption be? How fast will his production and consumption grow over time?

b. If he decides every year to market/consume 2/5 of his crop and plant the rest, what will his harvest be next year? What will his consumption be? How fast will his production and consumption grow over time?

c. Compare the consumption of the farmer in each of the first five years under plans a. and b.

d. Why might the results of plan b. not be realistic?

5. Imagine the following goal of Lenin/Stalin at the beginning of the Soviet regime in Russia: to overtake (i.e. equal) and surpass the world’s industrialized economies in terms of GDP per capita. To achieve this goal, the main instrument of control is the fraction of national production that is devoted to building the nation’s productive capacity: new machines, factories, transportation equipment, and roads. That is, the main instrument to achieve this goal is what fraction of GDP to devote to investment. The rest of national production is used for consumption, i.e. to produce consumer items like clothing and food. The country begins with relatively little capital, being mostly rural and non-industrialized. Assume each of the following:  GDP per capita starts in USSR at $300/year.  The world’s industrialized economies start with GDP per capita of $5000/year.  Population growth rates are 2% everywhere in the world.  All capital depreciates at 8% per year.

a. At what average annual rate will income per capita in the USSR have to grow in order to overtake (i.e. to equal) the industrialized nations’ income per capita in exactly 30 years? Assume the industrialized nations’ income per capita is growing at 2% per year.

b. If the USSR sustains the growth rate of part a., how long after it has overtaken the industrialized nations’ GDP per capita will it take for it to attain double the industrialized nations’ GDP per capita? Again, assume the industrialized nations’ GDP per capita is growing at 2% per year. For parts c.-e., assume the basic growth framework of Harrod-Domar, and that 1 ruble’s worth of capital always produces 0.5 ruble’s worth of output (i.e. A=0.5). Also, assume inputs are used more efficiently in the industrialized countries, so that A=0.6 there.

c. What fraction of national output must the USSR devote to building new capital goods in order to attain the growth rate of part a.? What fraction would be left for consumer items? [Hint: another word for the fraction of output devoted to building new capital goods is the investment rate, i.e. the ratio It/Yt. And, remember that savings equals investment, so the investment rate equals the savings rate.]

d. At what rate are the industrialized countries saving if they are growing at 2% per year? e. What would you calculate the ratio of consumption per capita in the USSR to consumption per capita in the industrialized countries when the USSR overtakes the industrialized countries (i.e. when GDP per capita is equal)? Assume the savings rates of parts c. & d. What would the ratio be when the USSR reaches double the industrialized nations’ GDP per capita?

1. What does the term s*Y represent in the capital-accumulation equation of Solow growth model?

a) The labor-income share of GDP.

b) Net investment.

c) Gross investment.

d) The net change in the capital stock from one year to the other.

2. In the Solow growth model, suppose that the savings rate is 25%, the depreciation rate is 10%, the current capital stock is 10 trillion $ and current output of a country is 4 trillion $. What will the capital stock of this country be in the following period?

a) 10 trillion $.

b) 11 trillion $.

c) We cannot tell since we are not given information about technological progress.

d) We cannot tell since population growth is not known.

3. Consider a country which starts with a capital stock below its steady-state level in the Solow model (without technological change). Why is growth slowing down over time for this country?

a) Population growth is becoming stronger over time since the population is growing, which makes it harder to accumulate high levels of capital per capita.

b) A country cannot maintain the same savings rate forever, so investment must decrease at some point.

c) The more capital there is, the more of it depreciates. As the country becomes richer, it becomes ever harder to replace depreciated capital.

d) There are diminishing returns to the factor capital. Thus investment, capital and GDP per capita grow by ever smaller amounts as the country becomes richer.

4. Suppose Pakistan has a higher savings rate than Iran. Both start out with the same capital per worker. All other parameters are the same for both countries (population growth and depreciation rate). The Solow growth model (without technological change) predicts that...

a)

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