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Example of 4 sector model

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Example of 4 sector model Let s say we start with a linear model with a consumption function (or schedule ): C = 100 + 0.75(Y T) Let s use a 4 sector ... – PowerPoint PPT presentation

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Title: 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.
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