IS/LM equation help! 30pts!!!?

Question

I need to find the IS (investment savings) equation and the LM (liquidity/money supply) equation.

C=100+0.6Y

I= 500-40R

G = 200

(I think Y = C + I + G.... so income = consumption + investment + govt spending) ??

L=200-50R+0.4Y

Ms = 600

I need to find the equation using a matrix... so for the aggregate demand equations, i tried putting all the variables on one side and the constants on the other. However, i seem to have too many variables, and not enough equations. The LM curve, i have no idea how to start!

If you know another way to find the IS/LM equation, please let me kno!!

please please please help me!! Really stuck !!

This is the third time i've posted the question, if u can help me...post in all 3, and i will give u 30pts!!

http://au.answers.yahoo.com/question/index;_ylt=AhmuYR0JMwGIO3WgeyXy8.zg5gt.;_ylv=3?qid=20080613054334AAfIPws

http://au.answers.yahoo.com/question/index;_ylt=AqsPGFhKGqtB0.Fd8zewn_rg5gt.;_ylv=3?qid=20080613080031AAx9OPI

Thanks

Answer 1

IS Curve is gven by Investment- Saving equlibrium.

We have Investment = I= 500-40R

Saving is given bu Income minus Consumption or,

S= Y-C= Y- C= Y-(100+0.6Y) = 0.4Y -100

Now with I+S equlibrium , yu get the IS curve as

500-4R= I=S= 0.4Y-100'

or, 0.4Y +4R = 600/

To get the LM curve, we need money market equlibrium.

Demand for Money is given by L=200-50R+0.4Y.

Supply of Money is given by, Ms = 600

So, LM curve is given by

200-50R+0.4Y = L = Ms = 600, or ,

0.4Y-50R = 800

The Variable for Price is nor separately included assuming that Income is expressed at current prices.

Answer 2

Y=C+I+G

Y=100+0.6Y+500-40R+200

0.4Y=800-40R

Y=2000-100R

Rearrange: to

100R=2000-Y

R=2000/100-Y/100

R=20-0.01Y

♦ Here is your IS curve: R=20-0.01Y

Next is LM curve

L=200-50R+0.4Y

But L(r;Y)=M/P and we dont know P I will cheat here and will consider (assume) that Ms=600 in your case means that M/P=600 so L=600 and consequently:

L=200-50R+0.4Y

600=200-50R+0.4Y

400+50R=0.4Y

Y=1000+125R

rearrange to:

125R=Y-1000

R=Y/125 - 1000/125

R=0.008Y-8

♦ Here is your LM curve: R=0.008Y-8

Equilibrium: IS=LM

20-0.01Y=0.008Y-8

28=0.018Y

Y=28/0.018 =28*1000/18 = 14000/9

Y=1555.5(5)≈1556

R=4.4(4)≈4.4%

♦ Answer: IS curve:R=20-0.01*Y and LM curve:R=0.008*Y-8. Current equilibrium R=4.4% Y=1556

Additional info:

C=Ac+MPC*Yd

MPC=0.6

Ac=100

Yd=Y-T

T=0

Yd=Y

R - interest rate

I - Investment

G - gov spending

Y - GDP

C - consumption

Ac - autonomous consumption

(MPC*Yd) - induced consumption

MPC - marginal propensity to consume

Yd - disposable income

T - taxes

M - money supply (=monetary base/(reserve requirement+*currency drains)

P - Price level