ECN 101 Lecture Notes - Lecture 13: Autarky, Factors Of Production, Capital Accumulation

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21 Dec 2020

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Given diminishing marginal product of capital, the less developed economies are likely to experience significant increases in output from capital accumulation because of their current low capital endowment. Y = output per head, a = total factor productivity, k = quantity of capital per worker (capital-labour ratio) Replacement investment (ri) investment expenditure necessary to make good or replace the buildings or equipment worn out during the process of production investment needed to equip the growing labour force. Expenditure in excess of ri that increases the capital labour ratio. Total investment (i) = ri + ni. Change in capital-labour ratio ( k) = ni. We assume capital stock depreciates at a constant rate through time (d) and labour force increases at a constant rate over time (n) In closed economy, i = y = ri + ni. Assume national saving is y, where is saving rate.

Related Questions

Consider an economy with the following production function:

Y = AK.5L.5
The labor force is constant. The rate of depreciation is Î´ = .1, the savings rate is s = .3.

a. Has this production function constant returns to scale? Why?

b. Write the production function in per worker variables.

c. Does the per worker production function have diminishing marginal returns to capital? Why?

d. Write the fundamental Solow equation in per worker variables.

e. Depict the steady state of this economy.

f. What are the growth rates of per worker output and capital in steady state?

g. Calculate the steady state level of capital, output, consumption and savings.

h. Redraw the initial equilibrium and show what happens when the savings rate increases. Do the growth

rates change?

i. Redraw the initial equilibrium and show what happens when there is a one time increase in population.

. Do the growth rates change?

j. Redraw the initial equilibrium and show what happens when there is a one time innovation that increases

productivity. Do the growth rates change?

k. Redraw the initial equilibrium and show what happens when there is constant productivity growth. Do

the growth rates change?

Consider an economy with the following production function:

Y = AK^0.5 L^0.5

The labor force is constant. The rate of depreciation is Î´=0.1, the savings rate is s=0.3

a) Has this production function constant returns to scale? Why?

b) Write the production function in per worker variables.

c) Does the per worker production function have diminishing marginal returns to capital? Why?

d)Write the fundamental Solow equation in per worker variables.

e) Depict the steady state of this economy.

f) What are the growth rates of per worker output and capital in steady state?

g) Calculate the steady state level of capital, output, consumption, and savings.

h) Redraw the initial equilibrium and show what happens when the savings rate increases. Do the growth rates change?

i) Redraw the initial equilibrium and show what happens when there is a one time increase in populatikon. Do the growth rates change?

j) Redraw the initial equilibrium and show what happens when there is a one time innovation that increases productivity. Do the growth rates change?

k) Redraw the initial equilibrium and show what happens when there is constant productivity growth. Do the growth rates change?

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...

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ECN 101 Lecture Notes - Lecture 13: Autarky, Factors Of Production, Capital Accumulation

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