An economy has a per-capita production functiony=Ak^ah^1-a, whereAandaare fixed parameters,yis per-worker output,kis the capital-labor ratio, andhis human capital per worker, a measure of the skills and training of the average worker. The production function implies that, for a given capital-labor ratio, increases in average human capital raise output per worker.

The economy's saving rate iss, and all saving is used to create physical capital, which depreciates at rated. 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 physical capital per worker, orh=Bk, whereBis a fixed parameter.

Find the long-run growth rates of physical capital, human capital, and output in this economy.