Suppose that the elasticity of output with respect to the capital input, b, equals 0.3.
(a) If the country’s income has been growing at 3.1 percent per year over the past 25 years, while the labor input has been growing at 1.5 percent per year and the capital input has been growing at 2.5 percent per year, what part of the total growth is accounted for by autonomous growth factor?
(b) Suppose that over the next 25 years, the retirement of the baby boomers causes the growth rate of labor to fall to 1.0 percent per year. Given your answer to part a for the autonomous growth factor and given no change in the growth rate of capital, compute the new steady-state growth rate of income. What does this new steady-state growth of income imply concerning the ability of the country to pay the higher medical care costs associated with the retirement of the baby boomers?
c) Suppose that the country wanted to maintain its 3.1 percent per year growth of income, given the retirement of the baby boomers. Given the autonomous growth factor that you computed in part a, compute what the growth rate of capital would have to be in order for the country to achieve that goal. What would have to happen to the savings rate in the country for it to be able to maintain a 3.1 percent per year growth of income?