Question

the following information about an economy is givicen: C=100+0.7YD, I=80-150i, G=60, T=40, Md=Y-3000i and Ms=1000. a. Derive the IS curve b. Derive the LM curve c. find the equilibruim value of Y and i

Answer 1

a

$\text{Y=C+I+G}\\ \text{Y=100+0.7YD+80-150i+60}\\ \text{Y-0.7YD=240-150i}\\ Y=\frac{240-150i}{1-0.7D}\\$

b

$Y-3000i=1000\\ Y=1000+3000i\\$

c

$10000+250i=4250-125i$

$\text{i}=\dfrac{5750}{375}=15.33\%$

$\text{Y}=0.8(1-0.25)Y+900-50i+1000$

$\text{Y}=0.6Y+1900-50i$

$Y=4750-125i$

Equilibrium interest rate is:

$4750-125i=250i+10000$

$i=\dfrac{5250}{375}=14\%$

Equilibrium national income will, therefore, be:

$Y=4750-125\times 0.14=4732.5$