Question

1.     Drive the AD (Aggregate Demand) curve using the following: IS curve is given as Y = 20XX-100i, LM₁ is Y= 1000+25i (when P = 1) and LM₂ is Y = 500+25i (when P =2), where XX is the last two digits of your student ID number. Show the derivation in (interest rate-income) and (price level-income) spaces. (You may insert a snapshot of the graphs if drawn manually).

Answer 1

The student ID number being S1117895. Therefore the last two digits are 95.

Given IS CURVE is :

$Y=20XX-100i\\ substitute\ for \ XX \ above:\\ therefore\ the \ IS \ curve \ is \ :\\ Y=2095-100i$

Given :$LM_1 \ is \ Y=1000+25i\ (P=1)\\$

and $LM_2 \ is \ Y=500+25i\ (P=2)$

$IS : Y=2095-100i\\ LM_1:Y=1000+25i\\ IS=LM\\ 2095-100i=100+25i\\ 2095-1000=25i+100i\\ 1095=125i\\ i=\frac{219}{125}=8.76\\ i=8.76$

$IS:Y=2095-100i\\ LM_2:Y=500+25i\\ IS=LM\\ 2095-100i=500+25i\\ 2095-500=25i+100i\\ 1595=125i\\ i=\frac{319}{25}=12.76\\ i=12.76$

$Y^*_1=2095-(100\times 8.76)=1219\\ Y^*_2=2095-(100\times12.76)=819$

Derivation =$1219-819=\$400$

price level income :$Y_1=1000+(25\times1)=1025\\$

$Y_2=500+(25\times2)=550$

Derivation=$1025-550=\$475$