1
Von NeumannMorgenstern Utility
±
Special Functional Form of Preferences
U =
Π
1
V(X
1
) +
Π
2
V(X
2
)
±
V(X) is called the “Scaling function.”
±
Π
1
and
Π
2
are
probabilities of
the
states (
Π
1
+
Π
2
= 1)
X
1
X
2
Indifference
Curves
45º
±
MRS =
Π
1
V
′
(X
1
)
/Π
2
V
′
(X
2
)
MRS =
Π
1
2
whenever X
1
= X
2
smaller expected
values
Fair Insurance Premium
±
Definition:
The expected value of a lottery is the
probabilityweighted average of its prizes:
Π
1
X
1
+
Π
2
X
2
X
1
X
2
ω
larger expected values
slope =
isoexpected value locus
through endowment
±
Definition: “Fair” premium permits purchase of
lotteries with the same expected value as endowment
γ
/ (1
γ
) =
Π
1
/
Π
2
Fair Insurance Premium
±
Risk averse
consumer chooses riskless point on
certainty line if premium is fair (
γ
=
Π
1
)
X
1
X
2
ω
γ
/ (1
γ
) =
Π
1
/
Π
2
45º
MRS =
Π
1
/
Π
2
±
Definition:
The expected value of a lottery is the
probabilityweighted average of its prizes:
Π
1
X
1
+
Π
2
X
2
±
Definition: “Fair” premium permits purchase of
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview.
Sign up
to
access the rest of the document.
 Fall '08
 KUHN
 Utility

Click to edit the document details