Analyse économique : Macroéconomie Séance d`exercices 1 : DA

G=T+M
P+D P
G T M
P
D
P
G−T=M
P+D P
dG −dT =dM
P+dDette P
dG =dM
P
dT =dDette = 0
dY
dG |dG=dM/P
dY =C0(Y−T)(dY −dT
|{z}
=0
) + I0(r)dr +dG
dM
P
|{z}
=dG
=L0
Y(Y, r)dY +L0 r(Y, r)dr
dr =dG −L0
Y(Y, r)dY
L0
r(Y, r)

dY =C0(Y−T)dY +I0(r)dG −L0
Y(Y, r)dY
L0
r(Y, r)+dG
=C0(Y−T)dY +I0(r)
L0
r(Y, r)dG −I0(r)L0
Y(Y, r)
L0
r(Y, r)dY +dG
=⇒1−C0(Y−T) + I0(r)L0
Y(Y, r)
L0
r(Y, r)dY =1 + I0(r)
L0
r(Y, r)dG
dY
dG |dG=dM/P =1 + I0(r)
L0
r(Y,r)
1−C0(Y−T) + I0(r)L0
Y(Y,r)
L0
r(Y,r)
>0
r
Y
LM
IS
LM’
IS’
(1)
(2)
r0
Y0Y0+ΔY
r0+Δr
(3)
dG =dM
P

dr = 0
dY =1
1−C0(Y−T)dG > dG 0< C0(Y−
T)<1
dY =C0(Y−T)(dY −dT
|{z}
=0
) + I0(r)dr
|{z}
=0
+dG
⇒dY =dG
|{z}
(1a)
+C0(Y−T)dY
| {z }
(1b)
dY =1
1−C0(Y−T)dG
1
1−C0(Y−T)
dr > 0
I0(r)<0
G↑−→IS(1) Y↑−→LM (2) r↑−→IS Y↓
M↑−→ M
P↑−→LM(3) r↓−→IS Y↑
dY =dG +C0dG + (C0)2dG + (C0)3dG +.. + (C0)∞dG =1
1−C0dG
0< C0=C0(Y−T)<1

dG =dT
dM
P=dDette = 0
dY =C0(Y−T)(dY −dT
|{z}
=dG
) + I0(r)dr +dG
dM
P
|{z}
=0
=L0
Y(Y, r)dY +L0 r(Y, r)dr
dr =−L0
Y(Y, r)dY
L0
r(Y, r)
dY =C0(Y−T)(dY −dG) + I0(r)−L0
Y(Y, r)dY
L0
r(Y, r)+dG
=C0(Y−T)dY −C0(Y−T)dG −I0(r)L0
Y(Y, r)
L0
r(Y, r)dY +dG
=⇒1−C0(Y−T) + I0(r)L0
Y(Y, r)
L0
r(Y, r)dY =1−C0(Y−T)dG
dY
dG |dG=dT =1−C0(Y−T)
1−C0(Y−T) + I0(r)L0
Y(Y,r)
L0
r(Y,r)
>0