Question

6. The income-expenditure model Consider a small economy that is closed to trade, so its net exports are equal to zero. Suppose that the economy has the following consumption function, where C is consumption, Y is real GDP, I is investment, G is government purchases, and T stands for net taxes: C = 45+0.75×(Y – T) Suppose G = $60 billion, I = $60 billion, and T = $20 billion. Given the consumption function and the fact that for a closed economy total expenditure can be calculated as Y=C+I+G , the equilibrium output level is equal to $ billion. Suppose the government purchases are reduced by $50 billion. The new equilibrium level of output will be equal to . Based on the effect of the change in government purchases on equilibrium output, you can tell that this economy's spending multiplier is equal to .

Answer 1

C = 45 + 0.75(Y - T)

G = 60

I = 60  

T = 20

In equilibrium Y = C + I + G

Y = 45 + 0.75(Y -T) + 60 + 60

= 165 + 0.75(Y - 20)

= 165 + 0.75Y - 15

Y - 0.75Y = 150

0.25Y = 150

Y/4 = 150  

Y = 600

Now G reduced by 50 therefore new G = 60 - 50 = 10

Y = C + I + G

= 45 + 0.75(Y - T) + 10 + 60

= 45 + 0.75(Y - 20) + 70

= 115 + 0.75Y - 15

Y - 0.75Y = 100

0.25Y = 100

Y/4 = 100

Y = 400

So new equilibrium output level is 400

c) govt. spending multiplier = Y/G   

Y = 200

G = 50

govt. spending multiplier = Y/G  

= 200/50

= 4

We can find govt. spending multiplier by this formula as well

govt. spending multiplier = Y/G = 1/(1 - MPC)  

MPC = 0.75

  Y/G = 1/(1 - 0.75)

= 1/0.25

= 4