Supposeyt=6kt0.5 (the per worker production function), d=0.1, n=0.02, and the aggregate savings function is given bySt=0.3Y (the savings rate is 0.3).

1) Solve for the steady state level of capital per worker (k), the steady state level of output per worker (y), the steady state level of consumption per worker (c), the steady state level of investment per worker, and the steady state level of savings per worker.

2) Suppose that the savings rate falls. What will be the impact on the steady state values of k, y, and c? Use a diagram to illustrate the fall in the savings rate and then state the impact on k, y, and c. (Label everything: including all axes and all curves)

3) Continue with question 2. Provide an discussion of the impact of the FALL in savings rate on the economy; elaborate on what is the economic reasoning for the changes, especially changes in k, y, and c.

4) Use the information above to calculate the maximum consumption per worker possible at steady state and the capital-per-worker that yields this maximum steady state consumption (c_max).