A country's production function is Y=K^1/3L^2/3, where K is capital and L is labor. The saving rate is 20%, and capital depreciates 10% a year. There is no population growth.

1. Derive the production function for output per worker (as a function of capital per worker). Show every step of your derivation.
2. There are two countries, Westoros and Essos, that have the same production function, saving rate and capital depreciation rate as described above. Westoros' capital per worker is 2.7, while Essos' capital worker is 0.8. Which country has a faster economic growth rate? Why? Explain it carefully, with a diagram if necessary.