Continuing with the logic from Problem 7, suppose that the economy's production function is given by \(Y=K^{1 / 3} N^{2 / 3}\) and that both the saving rate, \(s\), and the depreciation rate, \(\delta\) are equal to 0. 10 .

a. What is the steady-state level of capital per worker?

b. What is the steady-state level of output per worker?

Suppose that the economy is in steady state and that, in period \(t\), the depreciation rate increases permanently from 0. 10 to 0. 20 .

c. What will be the new steady-state levels of capital per worker and output per worker?

d. Compute the path of capital per worker and output per worker over the first three periods after the change in the depreciation rate.

Data from problem 7

The Cobb-Douglas production function and the steady state This problem is based on the material in the chapter appendix. Suppose that the economy's production function is given by

\[
Y=K^{\alpha} N^{1-\alpha}
\]

and assume that \(\alpha=1 / 3\).