Derivation of the IS-LM equation and finding out the equilibrium values of all the variables like C, I, G, S, etc..

Assume the following model of the economy, with the price level fixed at 1.0:

C = 0.8(Y - T),
T = 1,000,
I = 800 - 20r,
G = 1,000,
Y = C + I + G Ms/P = Md/P = 0.4Y - 40r
Ms = 1,200

a. prepare a numerical formula for the IS curve, showing Y as a function of r alone. (Hint: Substitute out C, I, G, and T.)

b. prepare a numerical formula for the LM curve, showing Y as a function of r alone. (Hint: Substitute out M/P.)

c. What are the short-run equilibrium values of Y, r, Y - T, C, I, private saving, public saving, and national saving? Check by ensuring that C + I + G = Y and national saving equals I.

d. Assume that G increases by 200. By how much will Y increase in short-run equilibrium? What is the government-purchases multiplier (the change in Y divided by the change in G)?

e. Suppose that G is back at its original level of 1,000, but Ms (the money supply) increases by 200. describe by how much will Y increase in short-run equilibrium? What is the multiplier for money supply (the change in Y divided by the change in Ms)?