Unformatted text preview: ), so C falls by MPC ∗ (500)
Y = C + I + G + NX , so Y falls by MPC ∗ (500)
C = C + MPC (Y − T ), so C falls by MPC ∗ MPC ∗ (500)
Y = C + I + G + NX , so Y falls by MPC ∗ MPC ∗ (500)
This process keeps repeating. Ryan W. Herzog (GU) Aggregate Expenditures February 25, 2014 32 / 43 ShortRun Equilibrium Mathematical Solution Solving for Equilibrium Mathematically
It might help to solve the model in a more general format.
We are going to start with planned aggregate expenditure:
PAE = C + I p + G + NX (11) Recall the consumption function:
C = C + MPC (Y − T )
Assuming I, T, G, and NX are autonomous. The PAE line becomes:
PAE = [C + MPC (Y − T )] + I + G + NX
or
PAE = [C − (MPC )T + I + G + NX ] +(MPC )Y (12) Intercept
Ryan W. Herzog (GU) Aggregate Expenditures February 25, 2014 33 / 43 ShortRun Equilibrium Mathematical Solution Solving for Equilibrium
To ﬁnd shortrun equilibrium output we set Y = PAE
Y = PAE (13) Substituting for PAE:
Y = [C − (MPC )T + I + G + NX ] + (MPC )Y
Solving for Y:
Y − (MPC )Y = [C − (MPC )T + I + G + NX ]
or
Y (1 − MPC ) = [C − (MPC )T + I + G + NX ] Ryan W. Herzog (GU) Aggregate Expenditures February 25, 2014 34 / 43 ShortRun Equilibrium Mathematical Solution Example
Dividing both sides by (1 − MPC ):
Y= 1
[C − (MPC )T + I + G + NX ]
1 − MPC (14) Assuming C = 800, T = 100, NX = 180, G = 1000, I p = 300, and
MPC = 0.8.
Y= 1
[800 − (0.8)100 + 300 + 1000 + 180],
1 − 0.8
Multiplier or
Y = (5)(2200) = 11, 000 Ryan W. Herzog (GU) Aggregate Expenditures February 25, 2014 35 / 43 ShortRun Equilibrium Mathematical Solution Example Notice that whenever the numbers change in the brackets, output will
change by a multiple of 5. Suppose investment declines by $500.
Y = (5)(1700) = 8, 500
Notice that the $500 decrease in investment lowered the autonomous
component by 500, which was then multiplied by 5 to ﬁnd the new
shortrun level of output....
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 Spring '09
 LYONS
 Macroeconomics, Ryan W. Herzog

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