Problem $2$:

Consider the following numerical example using the Solow growth model.

$F(K,L)=z{K}^{0\mathrm{.}5}{L}^{0\mathrm{.}5}$ and $d=0\mathrm{.}05,s=0\mathrm{.}2,n=$

$0\mathrm{.}025,L_0=100$ and $z=0\mathrm{.}1.$

Suppose $K=400$ in period $0$ and the unit period is one year.

Determine the aggregate quantities $K,C$ and Y of the capital stock, consumption and output for years $1,2$ and $3.$ Summarize your results using a table.

Find the per worker production function.

Find $k$ the steady state per$-$capita capital stock, consumption per capita and output per capita.

Assume the government wants to implement a policy that will increase the long run per capita output by $25\%.$ Determine the change in the savings rate s that will help achieve this goal.

Find the Golden rule level of capital per worker, output per worker, and consumption per worker.