3. Consider an economy described by the following structural equations
\[
\mathrm{Y}=\mathrm{C}+\mathrm{I}+\mathrm{G}, \quad \mathrm{C}=\mathrm{Cg}+\mathrm{c}(\mathrm{Y}-\mathrm{T}), \mathrm{J}=\mathrm{lg}-50 \mathrm{r}
\]
where, \( Y=5000, G=T=1000, G g=250, l u=1000 \) and \( c=0.75 \)
(a) Compute private, public and national savirg
(b) Find the equilibrium interest rate
(c) Now suppose that \( G \) increases to 1250 . Compute private savings, public savings and national savings.
(d) If ICOR is 3 , what wou^d be the growth rate? Using rule of 70 , estimate the time double the national income.