Consider the Solow growth model with a Cobb-Douglas production function with capital share a, a constant savings rate s, a constant depreciation rate 8, and a constant population growth rate n (0 0. 1. Derive the law of motion of capital per capita. 2. Derive the steady state levels of capital and output per capita. 3. Explain intuitively why there is a steady state. Now suppose that productivity increases by 10% to A2. 4. Derive the new steady state levels of capital and output per capita. Compare them to the old ones. 5. In three separate figures, draw the evolution through time of productivity A, capital per capita Kit, and output per capita Yit. Make sure to include several periods of the pre-shock steady state, the time of the shock, the transition to the final steady state, and several periods of the final steady state. Discuss the differences between the two figures. 6. Suppose that the economy has converged to its new steady state. Do a growth accounting exercise on output per capita. How much of the change in output per capita was due to changes in productivity, how much due to changes in capital per capita? 7. Does this result reflect well what actually occurred? 8. In the last decades, East Asian economies have grown strongly. Some studies attribute this mainly to capital accumulation. Discuss. Consider the Solow growth model with a Cobb-Douglas production function with capital share a, a constant savings rate s, a constant depreciation rate 8, and a constant population growth rate n (0 0. 1. Derive the law of motion of capital per capita. 2. Derive the steady state levels of capital and output per capita. 3. Explain intuitively why there is a steady state. Now suppose that productivity increases by 10% to A2. 4. Derive the new steady state levels of capital and output per capita. Compare them to the old ones. 5. In three separate figures, draw the evolution through time of productivity A, capital per capita Kit, and output per capita Yit. Make sure to include several periods of the pre-shock steady state, the time of the shock, the transition to the final steady state, and several periods of the final steady state. Discuss the differences between the two figures. 6. Suppose that the economy has converged to its new steady state. Do a growth accounting exercise on output per capita. How much of the change in output per capita was due to changes in productivity, how much due to changes in capital per capita? 7. Does this result reflect well what actually occurred? 8. In the last decades, East Asian economies have grown strongly. Some studies attribute this mainly to capital accumulation. Discuss