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 $=50$:

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

$=200$

$=300$

$=2000\mathrm{.}1$

Suppose also that for every $$10$ increase in prices, C decreases by $$10$ and NX decreases by $$10$

as well.

$1.$ What is the expression for the AEF here? Simplify your answer as much as you can.

$[3$ points$]$

$2.$ What is the equilibrium Y if $($i$)$ p $=50,$ and if $($ii$)$ p $=100?[2$ points$]$

$3.$ Use your answer from Q$2$ to derive the Aggregate Demand Curve, with Aggregate

Demand for Y as a function of the price level. $[3$ points$]$

$4.$ What is the Simple Multiplier in this example? $[2$ points$]$

$5.$ Suppose that Investment increased from $$200$ to $$400.$ What would be our new

Aggregate Demand Curve? $[4$ points$]$