Problem $1$: Deriving the Aggregate Demand Function $[14$ Points$]$

Suppose that we are considering the AEF, which is made up of desired C$,$ G$,$ I, and NX$.$ As in

lecture, we will assume that both C and NX respond to prices $($p$)$ in the economy. I and G do

not. All four are given by the following functions for a price level of p $=50$:

$=400+0\mathrm{.}85$

$=200$

$=300$

$=2000\mathrm{.}1$