Eksamenssett.no
Ressurser
Skolenytt
Hoderegning
ECON1410
Formelark
Mikroøkonomi I
eksamenssett.no
Konsumentteori
•
M
R
S
=
M
U
1
M
U
2
=
p
1
p
2
\displaystyle MRS = \frac{MU_1}{MU_2} = \frac{p_1}{p_2}
MRS
=
M
U
2
M
U
1
=
p
2
p
1
•
V
(
p
,
m
)
=
U
(
x
∗
(
p
,
m
)
)
V(p,m) = U(x^*(p,m))
V
(
p
,
m
)
=
U
(
x
∗
(
p
,
m
))
— indirekte nyttefunksjon
•
e
(
p
,
u
ˉ
)
=
p
⋅
h
(
p
,
u
ˉ
)
e(p,\bar{u}) = p \cdot h(p,\bar{u})
e
(
p
,
u
ˉ
)
=
p
⋅
h
(
p
,
u
ˉ
)
— utgiftsfunksjon
•
Roys identitet:
x
i
∗
=
−
∂
V
/
∂
p
i
∂
V
/
∂
m
\displaystyle x_i^* = -\frac{\partial V/\partial p_i}{\partial V/\partial m}
x
i
∗
=
−
∂
V
/
∂
m
∂
V
/
∂
p
i
•
Shepards lemma:
h
i
=
∂
e
∂
p
i
\displaystyle h_i = \frac{\partial e}{\partial p_i}
h
i
=
∂
p
i
∂
e
•
Slutsky:
∂
x
i
∂
p
j
=
∂
h
i
∂
p
j
−
x
j
∂
x
i
∂
m
\displaystyle \frac{\partial x_i}{\partial p_j} = \frac{\partial h_i}{\partial p_j} - x_j \frac{\partial x_i}{\partial m}
∂
p
j
∂
x
i
=
∂
p
j
∂
h
i
−
x
j
∂
m
∂
x
i
Produsentteori
•
M
R
T
S
=
M
P
L
M
P
K
=
w
r
\displaystyle MRTS = \frac{MP_L}{MP_K} = \frac{w}{r}
MRTS
=
M
P
K
M
P
L
=
r
w
•
M
C
(
y
)
=
C
′
(
y
)
MC(y) = C'(y)
MC
(
y
)
=
C
′
(
y
)
,
A
C
(
y
)
=
C
(
y
)
/
y
AC(y) = C(y)/y
A
C
(
y
)
=
C
(
y
)
/
y
•
Profittmaksimering:
p
=
M
C
p = MC
p
=
MC
(FK),
M
R
=
M
C
MR = MC
MR
=
MC
(monopol)
•
Tilbud kort sikt:
M
C
MC
MC
over
A
V
C
AVC
A
V
C
•
Shepards lemma:
L
∗
=
∂
C
∂
w
\displaystyle L^* = \frac{\partial C}{\partial w}
L
∗
=
∂
w
∂
C
,
K
∗
=
∂
C
∂
r
\displaystyle K^* = \frac{\partial C}{\partial r}
K
∗
=
∂
r
∂
C
Markedsformer
•
Lerner-indeks:
L
=
p
−
M
C
p
=
1
∣
ε
D
∣
\displaystyle L = \frac{p-MC}{p} = \frac{1}{|\varepsilon_D|}
L
=
p
p
−
MC
=
∣
ε
D
∣
1
•
M
R
=
p
(
1
−
1
/
∣
ε
D
∣
)
MR = p(1 - 1/|\varepsilon_D|)
MR
=
p
(
1
−
1/∣
ε
D
∣
)
•
Cournot (
n
n
n
like):
q
i
=
a
−
c
(
n
+
1
)
b
\displaystyle q_i = \frac{a-c}{(n+1)b}
q
i
=
(
n
+
1
)
b
a
−
c
,
p
=
a
+
n
c
n
+
1
\displaystyle p = \frac{a+nc}{n+1}
p
=
n
+
1
a
+
n
c
•
Bertrand (homogene):
p
=
M
C
p = MC
p
=
MC
•
Stackelberg leder:
q
L
=
a
−
c
2
b
\displaystyle q_L = \frac{a-c}{2b}
q
L
=
2
b
a
−
c
•
Todelt tariff:
T
(
Q
)
=
A
+
p
Q
T(Q) = A + pQ
T
(
Q
)
=
A
+
pQ
,
A
=
C
S
A = CS
A
=
CS
ved
p
p
p
Velferd og likevekt
•
C
S
=
∫
0
Q
∗
[
D
(
Q
)
−
p
∗
]
d
Q
\displaystyle CS = \int_0^{Q^*}[D(Q)-p^*]dQ
CS
=
∫
0
Q
∗
[
D
(
Q
)
−
p
∗
]
d
Q
•
D
W
L
=
1
2
t
Δ
Q
\displaystyle DWL = \frac{1}{2} t \Delta Q
D
W
L
=
2
1
t
Δ
Q
(skattetrekant)
•
M
R
S
A
=
M
R
S
B
=
p
1
/
p
2
MRS_A = MRS_B = p_1/p_2
MR
S
A
=
MR
S
B
=
p
1
/
p
2
(Walras-likevekt)
•
Walras lov:
∑
p
j
z
j
=
0
\displaystyle \sum p_j z_j = 0
∑
p
j
z
j
=
0
•
1. VT: Walras → PE | 2. VT: PE → Walras (med omfordeling)
Markedssvikt
•
Pigou:
t
∗
=
M
E
C
(
Q
∗
)
t^* = MEC(Q^*)
t
∗
=
MEC
(
Q
∗
)
•
Samuelson:
∑
M
R
S
i
=
M
R
T
\displaystyle \sum MRS_i = MRT
∑
MR
S
i
=
MRT
•
Signalisering:
c
L
⋅
e
∗
≥
Δ
w
≥
c
H
⋅
e
∗
c_L \cdot e^* \geq \Delta w \geq c_H \cdot e^*
c
L
⋅
e
∗
≥
Δ
w
≥
c
H
⋅
e
∗
•
Informasjonsrente =
U
second-best
−
U
ˉ
U_{\text{second-best}} - \bar{U}
U
second-best
−
U
ˉ
•
Arrow-Pratt:
r
A
=
−
u
′
′
/
u
′
r_A = -u''/u'
r
A
=
−
u
′′
/
u
′
, risikopremie
≈
1
2
r
A
Var
\displaystyle \approx \frac{1}{2}r_A \text{Var}
≈
2
1
r
A
Var
Spillteori
•
Nash:
s
i
∗
∈
B
R
i
(
s
−
i
∗
)
s_i^* \in BR_i(s_{-i}^*)
s
i
∗
∈
B
R
i
(
s
−
i
∗
)
for alle
i
i
i
•
Samarbeid:
δ
≥
π
a
v
v
i
k
−
π
s
a
m
π
a
v
v
i
k
−
π
s
t
r
a
f
f
\displaystyle \delta \geq \frac{\pi_{avvik} - \pi_{sam}}{\pi_{avvik} - \pi_{straff}}
δ
≥
π
a
vv
ik
−
π
s
t
r
a
ff
π
a
vv
ik
−
π
s
am