Desired consumption is Cd $=100+0\mathrm{.}8$Y $-500$r $-0\mathrm{.}5$G$,$ and desired investment is Id $=100-500$r$.$ Real money

demand is Md$/$P $=$ Y $-2000$i$.$ Other variables are e $=0\mathrm{.}05,$ G $=200,=1000,$ and M $=2100.$

$($a$)$ Derive the IS and LM curve.

$($b$)$ Find the equilibrium values of the real interest rate, consumption, investment, and the price level.

$($c$)$ Suppose the money supply increases to $2800.$ Find the equilibrium values of the real interest rate,

consumption, investment, and the price level. $($Assume that the expected inflation rate is unchanged.$)$