Answer to Question #286695 in Macroeconomics for Msb

Question

In the Keynesian cross model, assume that the consumption function is given by 

C = 120+ 0.8 (Y - T). Planned investment is 200, government purchases and taxes are both 400. 

a) What is the equilibrium level of income?

b) If government purchases increase to 420, what is the new equilibrium income? What is the 

multiplier for government purchases?

c) What level of government purchases is needed to achieve an income of 2,400? (Taxes remain 

at 400.)

d) What level of taxes is needed to achieve an income of 2,400? (Government purchases remain 

at 400.)

Answer 1

Solution:

a.). At equilibrium: AS = AD

Y = C + I + G

C = 120 + 0.8 (Y – 400) = 120 + 0.8Y – 320

Y = 120 + 0.8Y – 320 + 200 + 400

Y – 0.8Y = 120 + 200 + 400 – 320

0.2Y = 400

Y = 2000

The equilibrium level of income = 2,000

 

b.). Y = C + I + G

C = 120 + 0.8 (Y – 400) = 120 + 0.8Y – 320

Y = 120 + 0.8Y – 320 + 200 + 420

Y – 0.8Y = 120 + 200 + 420 – 320

0.2Y = 420

Y = 2100

New equilibrium level of income = 2,100

 

Multiplier = $\frac{1}{(1 - MPC)} = \frac{1}{(1 - 0.8)} = \frac{1}{0.2} = 5$

The multiplier for government purchases = 5

 

c.). Y = C + I + G

C = 120 + 0.8 (Y – 400) = 120 + 0.8Y – 320

2,400 = 120 + 0.8(2,400) – 320 + 200 + G

2,400 = 120 + 1,920 – 320 + 200 + G

2,400 = 1,920 + G

G = 480

Government purchases needed to achieve an equilibrium level of income of 2,400 = 480

 

d.). Y = C + I + G

C = 120 + 0.8 (Y – T) = 120 + 0.8Y – 0.8T

2,400 = 120 + 0.8(2,400) – 0.8T + 200 + 400

2,400 = 120 + 1,920 – 0.8T + 200 + 400

2,400 = 2,640 – 0.8T

0.8T = 2,640 – 2,400

0.8T = 240

T = 300

The level of taxes needed to achieve an equilibrium level of income of 2,400 = 300