Consider the Solow growth model with a Cobb-Douglas production function with capital share, a constant savings rates, a constant depreciation rate, and a constant population growth rate. Suppose equals alpha = 1/3, and TFP initially is A1>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 graphs, 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 new steady state, and several

periods of the new steady state. Discuss the differences between the two graphs.

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?