Question

Algebra of the income-expenditure model Consider a small economy that is closed to trade, so that its net exports are zero. Suppose that the economy has the following consumption function, where C is consumption, Y is income (real GDP), IP is planned investment, G is government purchases, and T is taxes:________. C = $20 billion+0.75×(Y – T) Suppose G=$35 billion, IP=$60 billion, and T=$20 billion. Given the consumption function and the fact that, in a closed economy, planned expenditure can be calculated as Y=C+IP+G, the equilibrium income level is ______ billion. Suppose that government purchases are increased by $100 billion. The new equilibrium level of income will be equal to ______ billion. Based on the effect of the change in government purchases on equilibrium income, you can tell that this economy's multiplier is equal to _______.

Answer 1

Answer:

a. The equilibrium income level is $100 billion.

b. The new equilibrium level of income will be equal to $500 billion.

c. This economy's multiplier is equal to 4.

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 $100 billion.

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 $500 billion.

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 4.