Economía Internacional - Ejercicios
Short Description
Descripción: Ejercicios resueltos de los modelos de comercio internacional de Ricardo y Heckscher-Ohlin...
Description
C
V
C 1 2
U = C V
V
1 2
( LL )o ∗
o
¯ L 30 1 = ¯ = = 60 2 L
L L
∗
w w
i
∗
≤
∗
∗
ai ai
i ( LL )d ∗
d
L
=
L
∗
δ 1 1 − δ w/w
∗
δ ac =3 ac 3 av = av 2 ∗
∗
w w
∗
> 3 w w
∗
>
∗
ac ac
>
∗
av av
δ = = 0 d
L L
∗
w w
∗
=3
=0
C w w
V
∗
=
0 ≤ δ ≤ ≤ d
L L
∗
3 >
w w
∗
>
δ = =
d
L L
∗
P M C
∗
av av
∗
ac ac
V
1 2
>
δ 1 1 = ∈ 0, 1 − δ 3 3
3 2
C
1 2
∗
ac ac
1 1 2 = , ∈ w/w 3 3 ∗
>
w w
∗
>
∗
av av
C
w w
∗
=
3 2
C ∗
ac ac
V 1 2
≤ δ ≤ 1 d
L L
∗
δ 2 1 = ,∞ ∈ 1 − δ 3 3
o
d
L L =
L
∗
L
1 1 = 2 w/w
∗
∗
w =2 w ∗
w = p i /ai C
V w pc /ac = w pv /av ∗
∗
pc w ac 3 = =2 =2 pv w av 3 ∗
w w
∗
OR
∗
3 2
DR
3 2
1 1 2 3 2 3
d
L L
∗
=
1 2
L L
∗
>
w w
∗
=
∗
av av
C d V
tL = 450
tE = 600
pi pj
i pi pj
j
=
1 ( pc /pv )
=
pi pj
ai aj
> ai aj
<
ai aj )
ac =3 av ac =5 av ∗
∗
C o V
pc pv
∗
C +C V +V
=
1 X
w w
L L
≤ δ ≤ 1 d
L L
∗
δ 1 ∈ = ,∞ 1 − δ 2
2/9 w/w = 2 ∗
X
X AUT
w
CCIO
=
px
AUT
w
=
px
CCIO
=
py
w
w py
1 1 = ax 2 E
w px = px py
Y
∗
∗
E
w px /ax px = =⇒ w py /ay py
=
w ax 2 4 =2 = w ay 3 3 ∗
∗
>
w w
∗
=
∗
ay ay
CCIO
w
=
py
14 2 = 23 3
Y Y
c/v = 1/( pc /pv )
L
p 3 = p p 2 c
v
E
c
=3
pv
tL = 30
pc pv
3 2
<
tE = 30
pc pv
C C = C = 0 V = ∗
tL av
= 15
V = ∗
tE av
<
ac av
<
ac av
∗ ∗
= 10
∗
o
C
=0
V
pc pv
=
3 2
C pc pv
V
=
V
ac av
<
ac av
∗ ∗
V C = C = 0 ∗
V = V
tL av
tE av
= 15 V = = 10 tL C C = ac = 10 C = 0 V = 0 ∗
∗
V =
∗
∗
tE av
∗
= 10
o
C
∈ [0, 1]
V
3 2
< ppvc 45
U = QV S 2 D
L = 1200 D
w /w
E
L = 6000 pQ /pV D pD S /pS
E
U mgi − λpi = 0 ∀i ∈ {Q , V , S}
max [U (x)] s.a. px < wL
U mgV pV QS 2 pV = =⇒ = =⇒ U mgQ pQ V S 2 pQ
d
Q V
=
1 pQ /pV
Q Q/V D E E aD Q /aV < aQ /aV
0, Q 0, , = , < V , ∞ , o
2 5 2 2 5 3 2 5
pQ pV pQ pV pQ pV pQ pV
< =
2 3 2 3
∗
aA aA
>
∗
aB aB
>
∗
aC aC
δ = 0 d
L L
∗
w w
=4
∗
∗
aB aB
>
A ∗
aC aC
B A
w w
C
∗
d
L L
∗
4 >
w w
∗
aC aC
B δ =
δ 1 1 = ∈ 0, 1 − δ 4 8
∗
aA aA
C
1 3 d
L L
∗
P M C
∗
= aaAA > 0 ≤ δ ≤ 31
> 2 A
∗
=0
1 1 1 1 ∈ = , 2 w/w 8 4 ∗
>
w w
∗
>
∗
aB aB
>
w w
= 2
∗
A
B ∗
aA aA d
L ∗
>
3 4
A δ =
B
L
∗
∗
= C 2 3
3 4
A
>
C
∗
aC aC
∗
2 3 d
∗
aB aB
aA aA
C
L w w
∗
=
1 3
≤ δ ≤
2 3
∗
w w
w w
δ 1 1 = ,1 ∈ 1 − δ 2 4
L
2 >
>
∗
>
aB aB
>
aB aB
∗
>
w w
>
aC aC
>
w w
=
aC aC
∗
1 8 =2 ∈ 1, w/w 3 ∗
B ∗
aA aA
≤ δ ≤ 1 d
L L
∗
δ 4 8 ∈ = ,∞ 1 − δ 3 3
0, , L [1/8, 1/4][0, 1/8] , 4 > = [1/4, 1] , L [1, 8/3] , 2 > [8/3, ∞] , d
∗
o
d
L L L
∗
=
L
1 1 1 = 6 2 w/w w =3 w ∗
d
L L
∗
=
1 6
∗
∗
w w w w w w w w w w w w
∗
> 4
∗
=4
∗
> 2
∗
=2
∗
>
∗
=
3 4 3 4
∗
∗
∗
w w
∗
4 3 2 3 4
1
11 1 86 4
8 3
L L
∗
U (x, y) = xy max [U (x, y) = xy] s.a. px x + py y ≤ w ¯l + r t¯
w¯l + rt¯ 2 px ¯ wl + rt¯ y = 2 py
x =
x py = y px 1 4
x
3 4
y t
l
1 4
g(ly , ty ) = l y ty
x maxΠx = p x x − wlx − rtx
1 4
3 4
maxΠx = p x lx tx − wlx − rtx
∂ Πx ∂l x ∂ Πx ∂t x
3 4
1 4
3 4
1 4
=
1 1 tx lx 1 px x 1x w px lx tx − w = px = − w = − w = 0 =⇒ 4 4 l l 4 lx 4 lx px x x
=
3 px lx tx 4
−
1 4
3 4
−
3 4
1 4
3 4
f (lx , tx ) = lx tx
1 4
3 4
1 4
3 4
3 lx tx 3 px x 3x r = − r = px − r = − r = 0 =⇒ 4 tx tx 4 tx 4 tx px
w r
Y Y
XX
T L
1 tx w = 3 lx r y maxΠy = py y − wly − rty
3 4
1 4
maxΠy = py ly ty − wly − rty
∂ Πy ∂l y ∂ Πy ∂t y
1 4
3 4
1 4
3 4
=
3 3 ty ly 3 py y 3y w − w = − w = 0 =⇒ py ly ty − w = py = 4 4 ly ly 4 ly 4 ly py
=
1 py ly ty 4
−
3 4
1 4
−
1 4
3 4
3 4
1 4
3 4
1 4
1 ly ty 1 py y 1y r − r = py − r = − r = 0 =⇒ = 4 tx ty 4 ty 4 ty py
3
ty w = ly r x
t
lx + ly = ¯l tx + ty = ¯t
1 x ly py = 3 y lx px
1 ly =1 3 lx
y
l
ly = 3lx
lx + ly = ¯l =⇒ l x + 3lx = ¯l
1¯ l 4 3 ly = ¯l 4
lx =
3
x ty py = y tx px
3
ty =1 tx
3ty = t x
tx + ty = ¯t =⇒ 3ty + ty = ¯t
3¯ t 4 1 ty = t¯ 4
tx =
px py
w r
1 4
3 4
3 4
1 4
lx tx
=
ly ty
1 4
¯l t¯ ¯l t¯ 1 4 3 4
3 4
3 4 1 4
py = px
py px
3 4
1 4
=
t¯ ¯l
1 2
py px
w r
Y Y
XX
py px
T L
1 34 t¯ w = 3 14 ¯l r w t¯ = ¯ r l 2
w py = r px w/r
py/px
ty/ly
x py/px
w/r
x tx /lx x w/px
y ty /ly y w/py
1 px x 4 w 3 px x tx = 4 r 3 py y ly = 4 w 1 py y ty = 4 r lx =
tx/lx y
lx + ly = ¯l =⇒
1 px x 3 py y ¯ + = l =⇒ p x x + 3 py y = 4w¯l 4 w 4 w
tx + ty = ¯t =⇒
3 px x 1 py y ¯ + = t =⇒ 3 px x + py y = 4rt¯ 4 r 4 r
3 ¯ 1 ¯ r t − wl 2 2 3 ¯ 1 py y = wl − rt¯ 2 2
px x =
px
t¯
py
x
y
¯l
px x = py y
3 ¯ 1 ¯ 2 r t − 2 wl 3 ¯ 1 ¯ 2 wl − 2 rt
=⇒
x py 3t¯ − wr ¯l = y px 3 wr ¯l − t¯
2
¯l ¯l − t¯
¯ x py 3t − = y px p 3 pxy
py px 2
X
Y
¯ L y ¯ L x
y
x x y
u(x1 , x2 ) = x 1 x2
x
0 lY
Y Y
¯ K
1 lY
¯ K
Y Y
1 kY 0 kY
1 kX 0 kX
XX
¯ L
0 lX
XX
1 lX
Y
Y 1 Y
0
px py
px py
X X 0 X 1
¯ L
l1
l2
k1
k2
x1
x2
x1 = f (k1 , l1 ) = min k1 , l2 ¯ 16 ¯l = 14 k =
k2 2
x = f (k , l ) = min , l 1
2
2
2
2
max [U (x1 , x2 ) = x 1 x2 ] s.a. p1 x1 + p2 x2 ≤ w ¯l + rk¯
x1 = x2 =
w¯l + rk¯ 2 p1 w¯l + rk¯ 2 p2 x1 p2 = x2 p1
k1 = l 1 /2
k2 /2 = l2 k1 1 = l1 2 k2 =2 l2 x1
x1
x2
x2
x2
8 6
4
x1
7
l1 + l2 = 14 k1 + k2 = 16 k1 = l 1 /2 l1 + l2 = 14 l1 + 2l2 = 16 2
l1 k1 l2 k2
= = = =
8 4 6 12
8 x = f (4, 8) = min 4, = 4 12 2 1
x2 = f (12, 6) = min
2
, 6 = 6
p2 4 2 = = p1 6 3
Π1 = p 1 x1 − wl1 − rk 1 Π2 = p 2 x2 − wl2 − rk 2
=⇒ Π1 = 4 p1 − 8w − 4r =⇒ Π2 = 6 p2 − 6w − 12r
k2 /2 = l 2
Πi = 0 ∀i ∈ {1, 2} 0 = p1 x1 − wl1 − rk1 =⇒ p1 = 2w + r 0 = p2 x2 − wl2 − rk2 =⇒ p2 = w + 2r w
r p1 w p2 w p1 r p2 r
r w r = 1+2 w w = 2 +1 r w = +2 r = 2+
2 + wr p1 = p2 1 + 2 rw p1 /p2 = 3/2 2 + wr 3 r r r 1 = =⇒ = r =⇒ 3 + 6 = 4 + 2 2 1+2w w w w 4
p1 1 =2 + w 4 p2 1 = 1 +2 w 4 p1 = 2(4) + 1 r p2 = (4) + 2 r
w p1 w =⇒ p2 r =⇒ p1 r =⇒ p2 =⇒
4 9 2 = 3 1 = 9 1 = 6 =
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