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9. In the Solow growth model, output Y is produced using capital K and labour L. Assume the production function is Y = x/PT'JE, which has total factor productivity constant over time. The change over time in the capital stock is AK = icSK, where i is investment and 6 is the depreciation rate. The population and labour force L are constant over time. Investment i is equal to saving S, which is a fraction 5 of income. Let k = K fl. and y = Y/i. denote capital per worker and output per worker. (a) [5 marks] Show that y = W? and Ak = S\\/l'( 6k, and solve forthe steady-state values of k and y where Ak = 0. (b) [2 marks] Using a diagram, explain intuitively why there is a steady state where growth of output per worker is zero, and why the economy converges to this steady state in the long run. Suppose that around the world, some countries choose to save a higher fraction 3 of income. In all other respects, assume countries are identical. (c) [3 marks] Explain what is meant by the terms absolute convergence and con ditional convergence. Explain which one is predicted by the Solow model. (d) [1 mark] Comparing two countries where one has double the saving rate of the other, what is the Solow model's prediction for their relative levels of in- come per worker in the long run