B3 (20%). Consider the following version of the Solow growth model. Suppose the relationship between output per worker, y, and capital per worker, k, at any point in time is represented by y=A@, where the function f () exhibits diminishing returns. Suppose also that there is no technological change, population growth is n, the savings rate is s and the rate of depreciation of capital is 6. (a) Suppose there are two such economies (X and Y). The two economies have identical values of n and 6 and face the same production relationship, A f () However, country X has a higher savings rate than B: 8X > 8y. Explain using a diagram what this implies for the relative steadyi state levels of capital and output per worker in each country. (b) Suppose that, in addition to having a higher savings rate, economy X starts out with a higher capital stock per worker than country Y. Which economy grows fastest ? Explain with the aid of a diagram. (0) Suppose that, in addition to having a higher savings rate, economy X also has a higher population growth rate than economy Y: nX > ny. Is it possible that both economies have the same steadyi state output per worker? Explain. (d) If A = 1, 6 = 0.1, 3); = 0.3, 3y 2 0.2, nX = 0.05 and ny = 0.02, which economy has the highest steadyistate output per worker? Explain using a diagram of the production function