Download Comparative Static Analysis of the Keynesian Model

Comparative Static Analysis
of the Keynesian Model
Macroeconomics I
ECON 309 -- Cunningham
Simple IS-LM Analysis
S(Y )  I (r )  G  0
M
L(Y , r )   0
P
Two equations, two endogenous variables (Y and r), and one
exogenous variable G. Real money supply (M/ P) is taken as
constant since nominal money (M) and (P) are exogenous as well.
Take total differentials:
SY dY  I r dr  dG
LY dY  Lr dr  0
Write in matrix form:
SY
L
 Y
 I r  dY  dG 
 



Lr   dr   0 
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Simple IS-LM, Continued
Applying Cramer’s rule for solution:
1
0
dY

SY
dG
LY
SY
L
dr
 Y
dG SY
LY
 Ir
Lr
Lr

0
 I r SY Lr  I r LY
Lr
1
0
 LY

0
 I r SY Lr  I r LY
Lr
So, in a Keynesian economy,
under the conditions given,
cet. par. (i.e., prices), an
increase in government
spending increases GDP and
interest rates.
Because, by assumption, the following hold:
Lr  0, LY  0
SY  0, I r  0
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Extension
What if prices are flexible? To examine this, we must include the
labor market and real wage computation.
w 
Nd    N  0
P 
Y  F (N )  0
S (Y )  I (r )  G  0
M
L(Y , r )   0
P
Define the following variable as a convenience:
N d  w 
X 

0
 w P   P 2 
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Extension (Continued)
0 1
0  FN
0
0
1
0
 Ir
0
dY

0
dG
1
0
Lr
1
0
 FN
0
SY
0
 Ir
LY
0
Lr
X
0
0
M
P 2   Lr FN X  0
X
Jac
0
0
M
P2
Similarly:
dN
LX
 r 0
dG
Jac
dr
0
dG
dP
0
dG
w 
d 
P  0
dG
(Note that the denominator turns out to be positive.)
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