(5) (Again, a possible exam question, this time on the Solow model.) A country has a production function which depends on capital and labor, and it is given by Y = 100K1/3L2/3. (a) Find a formula for per-capita production :9 as a function of the per-capita capital stock k. (b) Assume that capital does not depreciate at all, and that there is no technical progress. Let the savings rate be given by s and the rate of growth of population (=labor) be given by n. Show that steady state output per-capita is given by (1) y* = wows, describing precisely all the steps that lead to this conclusion. (0) Provide intuitive economic reasoning to explain why equal percentage increases in savings rates and population growth rates appear to nullify each other in equation (1), in the sense of leaving per-capita income unchanged