b) Consider the case in which rt = r = q/s for all t (the economy starts out with the long run ratio of

human 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?

(c) Using the result from part b, re-derive the Solow-Swan equation. That is, find the expressions

that gives you kt+1 as a function of kt and the parameters.

Set up: The production function is given by: Y = AKg (Nht)1-a where N is a constant population level and he is the per-capita level of human capital. 1 Y = Ct + St Law of motion for per capita physical capital is given by: kt+1 = (18)kt + syt Law of motion for per capita human capital is given by: ht+1 = (1 8)ht + QYt Tt ht is the ratio of human to physical capital at time t kt Set up: The production function is given by: Y = AKg (Nht)1-a where N is a constant population level and he is the per-capita level of human capital. 1 Y = Ct + St Law of motion for per capita physical capital is given by: kt+1 = (18)kt + syt Law of motion for per capita human capital is given by: ht+1 = (1 8)ht + QYt Tt ht is the ratio of human to physical capital at time t kt