You are given the production function Y = AK1/4H1/4N1/2, where A = 4. The population growth rate n is 0.025, the depreciation rate d is 0.075 (both physical and human capital depreciate at the same rate), and the growth rate of autonomous factors is zero. Investment I is the sum of two components, investment in physical capital IK and investment in human capital IH. The fraction of GDP that goes to physical capital investment is sK = 0.05 and the fraction of GDP that goes to human capital investment is sH = 0.05.
(a) Convert the production function to a function relating Y/N to both K/N and H/N.
(b) Consider two countries that have access to the same technology and have the same quality of labor and capital, as well as the same production function, given above. Suppose that one country has per-person output 10 times as high and a physical capital-labor 100 times as the second country. To what other factor is the difference attributable? Quantify the difference between the countries with respect to that factor.
(c) Find the steady-state physical capital-labor ratio and the steady-state human capital-labor ratio.
(d) Find the steady-state per person output.