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Consider the following numerical example using the Solow growth model

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Consider the following numerical example using the Solow growth model. Suppose that F(K, N) = K4/13 N9/13, Y = 2F(K.N). Furthermore, assume that the capital depreciation rate is d = 0.04, the savings rate is s = 0.3, the population growth rate is n = 0.035, and the productivity is z = 1.75. Suppose Ko = 200 and No = 100. 1. Compute the values k1, y1, and c1 of the per-worker capital, output and consumption in period one. 2. Find the steady state per-capita capital stock (k*), output per capita (y*), and consumption per capita (c*). 3. Assume the economy is in the steady state of Question 2, compute the percentage change in z that is needed to increase the long run per capita capital by 5%. 4. Assume the economy is in the steady state of Question 2 and suddenly, z decreases by 10%, calculate the percentage change in s that is needed to keep the long run per capita output unchanged. 5. Assume the economy is in the steady state of Question 2 and n goes down by 5% while z increases by 5% and s increases by 5%. Using the Taylor approximation, evaluate the contribution of each variable to the total change in the steady state consumption c