Deficits and the capital stock For the production function, \(Y=\sqrt{K} \sqrt{N}\) equation (11.9) gives the solution for the steady-state capital stock per worker.

a. Retrace the steps in the text that derive equation (11.9).

b. Suppose that the saving rate, \(s\), is initially \(15 \%\) per year, and the depreciation rate, \(\delta\), is \(7.5 \%\). What is the steadystate capital stock per worker? What is steady-state output per worker?

c. Suppose that there is a government deficit of \(5 \%\) of GDP and that the government eliminates this deficit. Assume that private saving is unchanged so that total saving increases to \(20 \%\). What is the new steady-state capital stock per worker? What is the new steady-state output per worker? How does this compare to your answer to part b?