Q4. Two countries, Richland and Poorland, are described by the Solow growth model. They have the same production function F(K,N) = KaN1-a. Richland saves 32% of its income, Poorland saves 10%. Richland has a population growth rate of 1% per year, Poorland a population growth rate of 3% per year. Both countries have a depreciation rate of 5% per year.
(2) (a) Find the per-worker production function for these two countries. Except where asked to do so, do not assign a numerical value to the parameter a.
For this and all parts of this question, do not forget to show your work.
(3) (b) Find the ratio of Richland's steady state income per worker to Poorland's.
(3) (c) If we set the parameter a = 1/3 as we often do, what numerical value would we obtain for the ratio in part (b)? Carry your answer to two decimal places.
(4) (d) In many cases, the data suggest that the actual ratio in part (b) would be 8 (or more, but stick with 8). Does this match the ratio obtained in part (c) with a = 1/3? If not, what numerical value for a would be required to obtain the ratio of 8? Carry your answer to two decimal places. (Hint: make use of logarithms here. If you do not remember logarithms, then as indicated earlier in the course, review your algebra. If you use a program on some device (calculator, etc.), you must still show explicitly every step needed to obtain the solution.)
(2) (e) The value you obtain in part (d) may be considerably different than 1/3. How might you interpret the input variable K so as to justify the value for a obtained in part (d)? (It may make sense to discuss the interpretation of N simultaneously. You are not required to do this, but if you do, integrate your discussion with that of K.)