Suppose Economy A’s aggregate production function has the following Cobb- Douglas form: Y = AK^1/3 L^2/3 Where output (Y

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Suppose Economy A’s aggregate production function has the
following Cobb- Douglas form:
Y = AK^1/3 L^2/3
Where output (Y) is produced using capital (K) and labour (L),
and A is total factor productivity. The rate of population growth
(n) is 2% per year (0.02). The rate of depreciation of capital is
10% per year (0.10). Total factor productivity equals 100 (A=100)
and we assume the growth rate of A is zero.
a) If the country’s savings rate (s) is 10% (0.10), find
its steady state capital stock per capita, income per capita,
consumption per capita and investment per capita. (50%)
b) Now assume that another economy (Economy B) has the
same production function, depreciation rate, population growth, and
total factor productivity but it saves 40% of its income. Find the
same values as in question a) for this case. Will there be absolute
convergence between countries A and B? (20%)
c) What is the optimal (Golden Rule) level of capital per
worker in steady state for Economies A and B? Which of these
economies is dynamically efficient? Explain why. (30%)