Exam 17 January 2012 - question 2
EU N I =
1√
3√
1 9
11
9−5+
9= + =
4
4
2 4
4
p
1p
3p
9−p+
9−p= 9−p
4
4
11
EU N I = EU (W + L) =
4
the maximum premium the agent is willing to pay is p such that
EU I =
EU I = EU N I
that is
p=
23
16
The expected cost for the insurance rm is 54 (cost 5 multiplied by the probability
of the event). Since p = 54 the insurance contract is fair and a risk averse agent
is willing to buy full insurance.
U (W ) =
√
9=3
Text 1 2012/2013 - question 2
a.
Assume I invest all my income in the safe asset. tomorrow I will get my
income for sure, therefore my utility is
EU (x) =
1
1
ln (10 − x + 3x) + ln (10 − x)
2
2
EU (0) = ln 10 = 2.3026
EU (1) = 2.3411
b.
maxEU (x) =
x
1
1
ln (10 − x + 3x) + ln (10 − x)
2
2
1
1
∂EU
=
−
=0
∂x
10 + 2x 20 − 2x
10 + 2x = 20 − 2x ⇒ x =
5
2
The individual actually borrows at the risk free interest rate in order to purchase
an amount of risky assets greater than his wealth.
1
Problem set 3B
a.
The carries of utility (the domain of our utility function) are departures of
consumption with respect to a reference point r.
b.
I need to impose x < λx, which implies λ > 1. Loss Aversion: attitudes
towards gains and losses are dierent because people hate losing more
than they like winning.
c.
Diminishing Sensitivity: the further you are from the reference point the less
intense the experience of departing from the reference point is
d.
U 1, −pB |0, 0 = υ (4) + υ −pB = 4 − 2p, U (0, 0|0, 0) = υ (0) + υ (0) = 0.
e.
I need to impose
4 − 2pB = 0 ⇒ pB = 2
U (0, ps |1, 0) = υ (0 − 4) + υ (ps ) = −8 + ps , U (1, 0|1, 0) = υ (0) + υ (0) = 0
−8 + p = 0 ⇒ ps = 8
f.
pS > pB because of loss aversion: I suer from selling the mug...
g.
From point d
From point e
4 − pB = 0 ⇒ pB = 4
−4 + pS = 0 ⇒ pS = 4
2