Please solve and include steps

$3.$ Consider the following model and again answer related questions.

$1.$ Y $=$ C $+$ I $+$ G $+$ X $-$ M

$2.$ C $=100+0\mathrm{.}50$Y

$3.$ I $=400-1000$r

$4.$ G $=400$

$5.$ X $=300$

$6.$ M $=100+0\mathrm{.}25$Y

a$.$ How much is equilibrium level of income or output if Fed decides to set the rate

of interest at $10$ percent $($r$=0\mathrm{.}10).$

b$.$ In an effort to cool down the economy, the Fed raises the rate of interest to r

$=0\mathrm{.}15.$ By how much will Y change?

c$.$ To coordinate the fiscal and monetary policies, assume government decides to

balance the budget by cutting its spending by $100$ and at the same time Fed

decides to counter the contractionary effect of cutting spending and lowers the

rate of interest to r $=0\mathrm{.}05.$ Can you predict the change in Y$?$