Question: The equation describing the evolution of capital stock per worker in an economy is the following:
Kt+1/N-Kt/N = sYt/N-dKt/N; where K is capital stock, N labor, Y output, s the saving rate and d the depreciation rate.
The production function expressed in per-worker terms is Yt/N = (Kt/N)1/3.
(a) If s=0.1 and d=0.1, calculate the steady state levels of K/N and Y/N. Show your calculations. Provide a graphical illustration of your answer.
(b) If the saving rate (s) increased from 0.1 to 0.2, (other parameters remaining unchanged) what would be the new steady state levels of K/N and Y/N?
(C) Can an increase in the saving rate make the economy grow permanently at a higher rate? Explain your answer verbally and using a graphical illustration.