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In 2000, the country of Cobra Island has an initial level of capital set at 10 units. The population of Cobra Island is unknown, but we do know that it grows each year at some constant rate. The level of total income is 500 cobra dollars. Finally, the total production function of Cobra Island can be described as Y=10*L1/2k1/2

  1. What is the initial population of Cobra Island?

 

2. Let the wage of labor is 0.4, and the rental rate of capital is 0.6. The capital to labor ratio after two years (in 2002) is 50 while the amount of workers is 1000. The growth rate of capital is 6,970%. The growth rate of labor is 100%.  Find the GDP of Cobra Island.

 

3. How much labor is there in Cobra Island one year after the initial year (or in 2001)?

 

4. The growth rate of income is 1,089%. Find the Solow Residual. Do not give the answer as a percentage.

 

(You don't need to answer questions 1 & 2) Please help homework is due at 11 pm today. 

 

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Lincoln Chr.
Lincoln Chr.Lv7
6 Mar 2021

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Related questions

Let the wage of labor is 0.4, and the rental rate of capital is 0.6. The capital to labor ratio after two years (in 2002) is 50 while the amount of workers is 1000. The growth rate of capital is 6,970%. The growth rate of labor is 100%. 

 

  1. How much labor is there in Cobra Island one year after the initial year (or in 2001)?

 

    2. The growth rate of income is 1,089%. Find the Solow Residual. Do not give the answer as a percentage.

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)

Suppose the output per effective worker is production function is y=10k1/2, where k equals the amount of capital per effective worker and the capital lasts an average of 10 years. Assume that the saving rate is 32 percent, the rate of growth of population is 4 percent and the rate of technological growth is 2 percent.

a) Solve for the steady state levels of capital per effective worker, output per effective worker, investment per effective worker and consumption per effective worker.

b) Calculate the growth rate of total capital income and the growth rate of total labor income at the steady state.(Hint: Capital and labor each earn a constant share of the economy's income ).

c) Prove, at the steady state, (i) the capital-output ratio is constant;(ii) the real wage grows at the rate of 2 percent.

d) Calculate all of the following at their Golden Rule levels: Capital per effective worker, output per effective worker, saving and investment per effective worker, and the consumption per effective worker.

e) Whether the saving rate is too high or too low?

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