Answer:
a. The equilibrium income level is <u>$100 billion.</u>
b. The new equilibrium level of income will be equal to <u>$500 billion</u>.
c. This economy's multiplier is equal to<u> 4</u>.
Explanation:
a. Calculation of the equilibrium income level
Since;
Y= C + IP + G ........................... (1)
Where;
C = $20 billion + 0.75 × (Y – T)
G = $35 billion
IP=$60 billion
T = $20 billion.
Remove the billion now for simplicity purpose to include later, substitute the values into equation (1) and solve for Y, we have:
Y = $20 + 0.75 * (Y – $120) + $60 + $35
Y = $20 + 0.75Y - (0.75 * $120) + $95
Y - 0.75Y = $20 + $95 - $90
0.25Y = $25
Y = $25 / 0.25
Y = $100
Therefore, the equilibrium income level is <u>$100 billion.</u>
b. Suppose that government purchases are increased by $100 billion. The new equilibrium level of income will be equal to ______ billion.
With this, we now have:
G = $35 billion + $100 billion = $135 billion
Replace this with G in part a and substitute other values as already given in part a into equation (1) and solve for Y, we have:
Y = $20 + 0.75 * (Y – $120) + $60 + $135
Y = $20 + 0.75Y - (0.75 * $120) + $195
Y - 0.75Y = $20 + $195 - $90
0.25Y = $125
Y = $125 / 0.25
Y = $500
Therefore, the new equilibrium level of income will be equal to <u>$500 billion</u>.
c. Based on the effect of the change in government purchases on equilibrium income, you can tell that this economy's multiplier is equal to _______.
Since the change in government purchases makes equilibrium income level to increase from $100 billion to $500 billion, we can calculate the rate of change in the equilibrium income level as follows:
Rate of change in equilibrium income = (New income – Previous income) / Previous income = ($500 - $100) / $100 = 4
With the rate of change of 4, we can tell that this economy's multiplier is equal to 4.
This can be confirmed using the multiplier formula as follows:
Multiplier = 1 / (1 – MPC) ……………………….. (2)
Where;
MPC = 0.75 from the consumption equation given C = $20 billion + 0.75 × (Y – T).
Substitute for MPC in equation (2), we have:
Multiplier = 1 / (1 – 0.75)
Multiplier = 1 / 0.25
Multiplier = 4
Which is the same as already obtained above.
Therefore, this economy's multiplier is equal to<u> 4</u>.
