Question

Suppose the demand for money is L=0.20Y, the money supply is 200, consumption:
C=90+0.80YD, taxes T=50, Investment: I=140-5r, and government purchases: G=50.
i) Derive the IS and LM equations

Answer 1

Solution:

IS equation is derived from :

$Y=C+I+G$

$Y=90+0.80YD+140-5r+50$

$Y=90+0.80(Y-T)+140-5r+50$

$Y=90+0.80Y-0.80(50)+140-5r+50$

$Y=90+0.80Y-40+140-5r+50$

$Y=0.80Y+240-5r$

$Y-0.80Y=240-5r$

$0.02Y=240-5r$

$Y=1200-25r$

$IS \; equation: Y=1200-25r$

LM equation:

equate Money supply with Money demand

$(M/P)^{s} = (M/P)^{d}$

$200=0.20Y$

$0.20Y=200$

$Y=\frac{200}{0.20}$

$Y= 1,000$

$LM \;equation: Y=1,000$