Question 4
Consider an economy described by the production function: $Y=F(K,L)=K^{1/3}L^{2/3}$
(a) Is this production function characterized by constant returns to scale? Explain
(b) What is the per-worker production function?
(c) Assuming no population growth or technical progress find the steady-state capital stock per worker ($k^*$), output per worker ($y^*$), and consumption per worker ($c^*$) as a function of the savings rate (s) and depreciation rate ($\delta$).
(d) Solve for the steady state level of capital per worker and output per worker when $\delta=0.08$ and s=0.32.
(e) Suppose that the depreciation rate remains constant at $\delta=0.08$, whereas savings rate is reduced by half to s=0.16. What happens to the steady state level of capital per worker and output per worker?
