Help with IS-LM model-Economics?

Question

could someone please help me with the is-lm model equation below, i have attempted it several times however i am not having any luck if you could please help me by determining and laying out the is-lm equilibrium with the following equations:

C(Y-T)=40+0.6(Y-T)

I(Y,i)= Y/1000i

Md(Y,i)= PY/i where P=2

G=50

T=100

M=300000

Your help would be very much appreciated

Answer 1

(closed economy?)

Y=C+I+G

C=40+0.6(Y-100) = 0.6Y+40-60 = 0.6Y-20

I=Y/1000i

G=50

Y=0.6Y-20+ Y/1000i +50 = Y(0.6+1/1000i) + 30

Y - Y(0.6+1/1000i) = 30

Y(1-0.6 - 1/1000i) = 30

Y(0.4 - 1/1000i) = 30

Y= 30/ (0.4 - 1/1000i)

Multiply denominator and divident by 1000i

30 / (0.4 - 1/1000i)

30*1000i=30000i

(0.4 - 1/1000i)*1000i = 400i - 1

Y=30000i / (400i-1)

♦ IS equation: Y=30000i / (400i-1)

Md=M

300000 = 2Y/i

♦ LM equation: Y=150000i

i=Y/150000

Now substitute i by LM equation in IS equation to find equilibrium:

Y=30000i / (400i-1)

i=Y/150000

Y=30000(Y/150000) / (400(Y/150000)-1)

And solve to find equilibrium Y:

30000(Y/150000) = 3Y/15 = Y/5

400(Y/150000) = 4Y/1500 = Y/375

Y = (Y/5) / (Y/375 - 1)

(Y/375 - 1) Y = Y/5 [Ignore possible outcome of Y=0 value because of economics specifics - it's not math priority in this case]

Y/375 - 1 = 1/5

Y/375 = 6/5

Y= 375 * 6 / 5 = 75*6 = 450

Y=450

i=0.003

P.S. Aggregate demand for this model will be:

Y=(750/P)+75