Calculate the steady state levels of k-n and y-n

Question

Problem

The equation describing the evolution of capital stock per worker in an economy is the following:

K_t+1/N-K_t/N = sY_t/N-dK_t/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 = (K_t/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.

The response should include a reference list. Double-space, using Times New Roman 12 pnt font, one-inch margins, and APA style of writing and citations.