Consider a numerical example using the Solow growth model. Suppose that F(K, N) = K^ 0.5N^ 0.5, with d = 0.1, s = 0.2, n = 0.01, and z = 1, and take a period to be a year.
(a) Determine capital per worker, income per capita, and consumption per capita in the steady state.
(b) Now, suppose that the economy is initially in the steady state that you calculated in part (a). Then, s increases to 0.4.
i. Determine capital per worker, income per capita, and consumption per capita in each of the 10 years following the increase in the savings rate.
ii. Determine capital per worker, income per capita, and consumption per capita in the new steady state.
iii. Discuss your results; in particular comment on the speed of adjustment to the new steady state after the change in the savings rate, and the paths followed by capital per worker, income per capita, and consumption per capita.