Question

An economy is described by the following equations:

Y = C + I + G

C = 0.75 Y_D + 20

T = 0.2 Y + 4

G = 20

I = 25

1. Calculate equilibrium output and equilibrium private and public saving.
2. With how much does equilibrium output falls, if government reduces government expenditure with 1 unit?

Explain the event in b) for the multiplier diagram

Answer 1

A.

Y = C + I + G

Y = 20 + .75*YD + I + G

Y = 20 + .75*(Y-T) + 25 + 20

Y = 65 + .75*(Y - .2Y - 4)

Y = 65 + .75*.8Y - 3

Y = 62 + .6Y

Y = 62/(1-.6) = 155

So, equilibrium output is 155.

--------

T = .2*155 + 4 = 35

C = 20 + .75*(Y-T) = 20 + .75*(155 - 35) = 110

Private savings = Y - C - T = 155 - 110 - 35

Private savings = 10

Public savings = T - G = 35 - 20

Public savings = 15

------------------

B.

Multiplier = 1/(1-MPC) = 1/(1-.75)

Multiplier = 4

So, decrease in 1 unit of G, causes 4 unit decrease in equilibrium output.

-----------