Question

The equation below describes an economy's macroeconomic structure measured in millions
C =0.5(1 - t)Y
t =0.20
I =800 - 30i
G =700
L=0.3Y - 60i
M/P =600
a) for this economy, use the relevant set of equations to derive and graph the IS-LM relations

Answer 1

$$Solution$$

IS CURVE

$Y=C+I+G\\ Y=0.5(1-t)Y+800-30i+700\\ Y=(0.5-0.5t)Y+1500-30i\\ Y=(0.5-0.1)Y+1500-30i\\ Y=0.4Y+1500-30i\\ Y-0.4Y=1500-30i\\ 0.6Y=1500-30i\\ Y=2500-50i$

LM CURVE

$Md=Ms\\ 600=0.3Y-60i\\ 0.3Y-60i=600\\ 0.3Y=600+60i\\ Y=2000+200i$

$r*=2$ and $Y=2400$

IS=LM

$2500-50i=2000+200i\\ 2500-2000=200+50i\\ 250i=500\\ i=2\%$

EQ

$Y=2000+200i\\ Y=2000+(200\times2)\\ Y=2400$