Use the production function in equation (5.6 in your book) which is Y= ÃK^1/3 \overline{L}^2/3 and the rules for computing growth rates to write the growth rate of per capita GDP as a function of the growth rate of the capital stock. (Hint: Because the labor force is constant, the growth rates of GDP and per capita GDP are the same.)

(b) Combine this result with the last equation in footnote 7 (Section 5.9) which is AKt+1/Kt= \overline{s} x ((K^2/3/Kt^2/3)-1) to get a solution for the growth rate of per capita GDP as a function of the current level of capital Kt. Be sure to write your answer in terms of Kt and parameters of the model only. For example, use the fact that Sy*/ K*= \overline{d}

2) Suppose an economy begins in steady state and is characterized by the following parameter values: S=0.2 \overline{d}=0.1 A=1 L=100 n=0 Apply your answer to part (b) to calculate the growth of per capita GDP in the period immediately after each of the changes listed below. (Hint: Since the economy begins in steady state, its growth rate is initially zero and (Kt=K*.)

(a) The investment rate doubles.

(b) The productivity level rises by 10%.

(c) An earthquake destroys 75% of the capital stock.

(d) A more generous immigration policy leads the population to double.

PLEASE USE THE BOOK MACROECONOMICS THIRD EDITION BY CHARLES I. JONES IF YOU DO NOT UNDERSTAND SOMETHING, EXERCISES 8 AND 9 OF THE END OF THE CHAPTER.