. The production function is given by: 1 - AAT (Nb, )" where NV is a constant population level and he is the por-capita level of human capital. . Y=0+5 . Low of motion for per capita physical capital is given by: & +1 = (1 - 6)k, + sur . Law of motion for per capita Inman capital is given boys been = (1 - $)k, + on . my - to the ratio of human to physical capital at time f Questions (al Divide the laws of motion for per capita physical capital and per capita human capital by by and h, mapactively. Express the growth rate of per mpita physical capital (g) and the growth rate of per capita human capital (ox ) solely as a function of parameters 4, 6, a.9. 9 and r. (b) Consider the case in which my= r = ] for all t (the economy starts out with the long run ratio of luann to physical capital). Rewrite the per capita production function just in terms of per capita capital. Does the production function exhibit diminishing returns in capital anymore? (el Using the result from part b, re-derive the Solow-Swan equation, That is, find the expressions that gives you bet as a function of &, and the parameters. (d) What is different about this version of the Solow-Swan equation? Is your law of motion for per capita capital still concave or be it linear? What does this imply for the evolution of per-capita ranitalt