Example of 4 sector model

1
Example of 4 sector model

• Lets say we start with a linear model with a
  consumption function (or schedule)
• C 100 0.75(Y T)
• Lets use a 4 sector model of AE with
• I 80
• G 60
• T 40
• NX 30

2
Example of 4 sector model

• Firstly graph the consumption function.
• If we plug in 40 for T, we get (0.7540 30)
• C 100 0.75Y 30
• C 70 0.75Y
• We know the vertical intercept (Y0)
• C 70 0.75 (0) 70

C
C70 0.75Y
70
Slope is 0.75
0
Y
3
Example of a 4 sector model

• From the C function, we know our MPC is 0.75- a
  fact we will use later.
• Now we need to derive our AE curve. We use the 4
  sector AE equation
• AE C I G NX
• Plugging in the facts above, we get
• AE 70 0.75Y 80 60 30

I
G
NX
C
4
Example of a 4 sector model

• Adding all those together, we get
• AE 240 0.75 Y
• Just like we did with the C function, we can
  graph this AE function

C, AE
AE240 0.75Y
240
C70 0.75Y
70
0
Y
5
Example of a 4 sector model

• Now we need to find the equilibrium of this
  model. This occurs where goods demand, AE, is
  equal to goods supply, Y.
• Note that AE is a function of income, Y, and we
  are also requiring that in equilibrium goods
  supply, Y, is equal to AE. We are using Y in two
  different senses, as income and as output. But
  remember from the first lecture, we can calculate
  GDP either from income or from production and get
  the same value.
• We are looking for an income level, Y, that
  produces an AE level equal to Y.

6
Example of a 4 sector model

• Using our equation for AE, we get
• AE 240 0.75Y
• Y AE 240 0.75Y
• 0.25Y 240
• Y 960

AE
45 deg line
AE 240 0.75Y
960
240
0
Y
960
7
Example of a 4 sector model

• Since our MPC 0.75, we know that the multiplier
  for autonomous expenditure is
• Multiplier 1/(1-MPC) 1/(1-0.75) 4
• So a 1 change in I or G or NX would lead to a 4
  change in equilibrium GDP, Y.