Suppose that an economy is characterized by the following production function:

\[
Y=3 \sqrt{K} \sqrt{N}
\]

a. Derive the steady-state level of output per worker, and the steady-state level of capital per worker as a function of the savings rate, s, and the depreciation rate, \(\delta\).

b. Derive the equation for the steady-state level of consumption per worker as a function of the savings rate, \(s\), and the depreciation rate, \(\delta\).

c. Suppose that \(\delta=0.02\). Calculate the steady-state level of consumption per worker and output per worker when \(s=0 ; s=0.1 ; s=0.2 ; s=1\). What do you observe?

d. Using spreadsheets, plot your results on a graph showing the relationship between the savings rate (on the \(X\) axis) and consumption per worker (on the \(Y\) axis). Is there a savings rate that maximizes consumption per worker? Explain.