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.
ii) Find equilibrium output, and the rate of interest

Answer 1

$$Solution$$

To solve for the equilibrium levels of output (Y) and interest rate (r). We solve the system of two equations with two unknowns (Y and r) from IS and LM relations.

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

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

$200=0.20Y$

$0.20Y=200$

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

$Y= 1,000$

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

Now We have the equilibrium levels of output Y=1,000

We now sub this value for Y into the IS relation to find the corresponding value for r:

$1000=1200−25r\\ 25r=1200-1000 \implies 25r=200 \implies r=8\%$

Interest rate (r)=8%