An economy has the per-worker production function

y=k^1/3

whereyis output per worker andkis capital per worker.

Capital accumulation follows:

k=sy(n+)k

The saving ratesis 0.2, the depreciation rateis 0.04, and the population growth ratenis 0.01.

a.What are the steady state values of capital per worker, output per worker, and consumption per worker?

b.Repeat Part(a)for a saving rate of 0.4 instead of 0.2.

c.Repeat Part(a)for a population growth rate of 0.02 (with a saving rate of 0.2).d.Repeat Part(a)for a production function of

y= 2k1/3

e.Suppose the economy is not in the steady state. Derive the growth rate of capital per

worker (k) along the transition path as a function ofk,s,nand. Under what conditionk

iskpositive? What is the relationship betweenkandk?kk