IS LM curves?

Question

C=100+0.6Y

I= 500-40R

G = 200

L=200-50R+0.4Y

Ms = 600

Write the equations for the IS and LM curves.

Answer 1

Closed economy (NX=0)

Y=C+I+G

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

0.4Y=800-40R

Y=2000-100R

IS curve: Y=2000-100R or R=20-0.01Y

Initial price level=1

200-50R+0.4Y=600

400+50R=0.4Y

Y=1000+125R

LM curve: Y=1000+125R or R=0.008Y-8

Equilibrium:

Y=1000+125R

Y=2000-100R

1000+125R=2000-100R

1000=225R

R=4.44%

Y=1'556

Equilibrium: R=4.44%, Y=1'556

Aggregate demand:

200-50R+0.4Y=600/P

Y=2000-100R

100R=Y-2000

50R=0.5Y-1000

200-(0.5Y-1000)+0.4Y=600/P

200-0.5Y+0.4Y+1000=600/P

1200-600/P=0.1Y

Y=12'000-6'000/P

Aggregate demand: Y=12'000-6'000/P or P=6'000/(12'000-Y)

{P≥0.5; Y<12'000; R≥0}

Answer 2

Why similar questions are being asked again. Thie answer is so simple. The IS curve / function gives the alternative combinations of Interest Rate (R) and National Income(Y) which ensures Saving - Investment market equilibrium in the sense that Saving = Investment. In this case Saving= Y-C= Y-(100+0.6Y)= 0.4Y-100.

So, equlibrium demands that 0.4Y-100= S= I= 500-40R

or, 0.4Y +40R -600=) is the IS function representing the Saving-Investment marklet equilibrium. Here we treat G=0

The existence of G=200 creates a confusion. G should be partly Investment Expenditure or partly Consumption Expenditure or all Investment or all Consumption. Since nothing is mentioned, we will assume that it is all investment expenditure. If this is so, the saving-Investment market equilibrium will be given by 0.4Y-100= S= I+G = 500-40R+200, or, 0.4Y +40R -800= 0 will be the IS Curve defining the saving-Investment market equilibrium.

For the money market equilibrium, we need

600 = Money supply = Ms = Demand for money (liquidity) = L=200-50R+0.4Y, or, 0.4Y-50R+800= 0. This is the LM function.

If you want both the markets to be in equlibrium, solve for R and Y satisfying the IS and the LM functions simultaneously.