Reference no: EM131436926
This is a version of the Solow growth model. Country A is a closed economy with no government expenditure. At time t country A has an aggregate capital stock Kt-1 and a total population Nt. Country A's population grows at a constant rate n and its production function is Yt = K1- α1-tNαt. Denote by d the depreciation rate of capital and s the savings rate. Assume that 0 < s <1 and 0 < d < 1. There is no technological progress in this economy.
1. Let define yt = Yt/Nt and Kt-1 ≡ Kt-1/Nt, in which y stands for output per capita and k denotes capital per capita. Derive the formula of output per capita.
2. Assume the law of motion for the stock of capital is Kt = (1-d)Kt-1 + It, where It denotes aggregate investment at time t. Rewrite this equation in terms of the per capita capital stock.
3. Determine the steady state value of the per capita capital, k*, as a function of α, d, n and s.
4. Determine the golden rule quantity of capital per capita in country A, kg, as a function of α, d, n and s.
5. Assume that country A experiences no population growth and that 5 percent of capital depreciates each year. Assume that country A saves 10 percent of output each year. Determine numerically the steady state level of k*, y* and the golden rule quantity of kgr, ygr, and cgr, if labor's share is 0.5.
6. Sketch a diagram to depict your answer from part (e). Make sure that you label everything clearly.
In the following questions, assume that as a result of the war, much of the capital in country A (oil extracting equipment, vehicles, structures etc.) was destroyed. Answer the questions below and use diagrams to support your answer if needed.
7. What will be the effect of this event on per capita capital in country A in the next five years and in the long run?
8. What will be the effect of this event on per capita income in country A in the next five years and in the long run?
9. What will be the effect of this event on the growth rate of per capita income in country A in the next five years and in the long run?
10. Will recovery in country A occur faster if investment by foreigners is permitted?
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Derive the formula of output per capita
: Let define yt = Yt/Nt and Kt-1 ≡ Kt-1/Nt, in which y stands for output per capita and k denotes capital per capita. Derive the formula of output per capita
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Determine the amount of solute
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