Help with keynesian economics question?

Question

In the simple Keynesian model that does not have any government or foreign sectors, let's say that the economy is in equilibrium at an output of $2 billion with an MPC of 0.9. If investment spending decreases by $.05 billion, what is the new equilibrium output level?

a) $2.50 billion

b) $1.90 billion

c) $1.95 billion

d) $1.50 billion

Answer 1

d) $1.50 billion

ΔY/ΔI=1/(1-MPC)

ΔY=ΔI/(1-MPC)

MPC=0.9

ΔI= -0.05

ΔY= -0.05/(1-0.9) = -0.05/0.1= -0.5

2.0-0.5=1.5

Answer 2

according to the concept of mutiplier i.e. dY/dI = 1/1-MPC we get the value of multiplier "10".  Now it is very simple:

dY/dI = 10

dy = 10*dI

dY = 10*-.05

dy = -0.5

New equlibrium = Y + dY

                            = 2 - 0.5

New equlibrium = $1.50 billion

I hope it will work