Question

Aggregate Expenditure

Consider the following AE model:

C=.80Y_d+ 200   Y_d = Y – T    I=125 G=200 T=150 M=100 X=50

1. Find the following:

Y* =	MPC =	MPS =
Budget Deficit =	Trade Surplus =	Autonomous C =
At Y*, C =	At Y*, I =	At Y*, G =
At Y*, T =	At Y*, net exports =	At Y*, Savings =
Leakages =	Injections =

2. Using the ∆RGDP equation, compute the new Y* if autonomous consumption is decreased by 50.

3. Assume that Y_FE = 2000. Compute the ∆G necessary to make Y* = Y_FE.

4. Assume that Y_FE = 2000. Compute the ∆T necessary to make Y* = Y_FE.

Answer 1

1)

C = 0.80Yd + 200

Autonomous C = 200

MPC = 0.80

MPS = 1 - MPC  

MPS = 1 - 0.80 = 0.20

Budget deficit = G -T = 200 - 150 = 50

Trade surplus = X - M = 50 - 100 = - 50

Y = C + I + G + X - M

Y = 200 + 0.80Yd + 125 + 200 + 50 - 100

Y = 475 + 0.80(Y -T)

Y = 475 + 0.80(Y - 150)

Y = 475 + 0.80Y - 120

Y - 0.80Y = 355

0.20Y = 355

Y = 1775

Y* = 1775

C = 200 + 0.80(Y -T)

= 200 + 0.80(1775 - 150)

= 1500

I = 125

G = 200

T = 150

NX = X - M = 50 - 100 = - 50

Savings S = Yd - C

S = Yd - 200 - 0.80Yd

S = - 200 + 0.20Yd

S = - 200 + 0.20(Y -T)

S = - 200 + 0.20(1775 - 150)

S = 125  

Leakages = S + T + M

= 125 + 150 + 100

= 375

Injections = I + G + X

= 125 + 200 + 50

= 375

2)

Now autonomous consumption or expenditure decreases by 50

therefore A = - 50

Y/A = 1/(1- MPC)

Y/A = 1/(1 - 0.80)

Y/A = 1/0.20

Y/A = 5

Y = 5A

Y = 5(- 50)

= - 250

New Y* = Y + 1775

= - 250 + 1775

= 1525

3)

YF = 2000

Y* = 1775

Y = 2000 -1775 = 225

Y/G = 1/(1 - MPC)  

Y/G = 1/(1 - 0.80)

Y/G = 5

Y = 5G  

225 = 5G

G = 225/5

G = 45

Thus G should be increased by 45 to reach at YF = 2000

4)

YF = 2000

Y* = 1775

Y = 2000 -1775 = 225  

Y/T = - MPC/(1 - MPC)

Y/T = - 0.80/(1 - 0.80)

Y/T = - 4

Y = - 4T  

225 = - 4T  

T = - 225/4

= - 56.25

Therefore taxes should be decreased by 56.25 to reach YF = 2000