An economy has a per-capita production function y = Akahl-a, where A and a are fixed parameters, y is per-worker output, k is the capital-labour ratio, and h is human capital per worker, a measure of the skills and training of the average worker. The production function implies that for a given capital-labour ratio, increases in average human capital raise output per worker.
The economy's saving rate is s, and all saving is used to create physical capital, which depreciates at rate d. Workers acquire skills on the job by working with capital; the more capital with which they have to work, the more skills they acquire. We capture this idea by assuming that human capital per worker is always proportional to the amount of capital per worker, or h = Bk, where B is a fixed parameter.
Find the long-run growth rates of physical capital, human capital, and output in this economy.