prof. Teresa Kamińska
Microeconomics
DEALING WITH UNCERTAINTY (RISK THEORY)
Attitudes to risk
Risk aversion: risk-averse people prefer a sure thing to a gamble with the same
expected value
Risk neutrality: risk-neutral people are indifferent between a sure thing and a gamble
with the same expected value.
Risk love: risk lovers prefer a gamble to a sure thing with the same expected value.
If two gambles have the same expected value but one is riskier than the other because
there is a higher probability of winning the lowest valued prize but also a lower probability of
winning the highest valued prize:
 Risk lovers prefer the riskier gamble
 Risk-averse people prefer the safer gamble
 Risk-neutral people are indifferent between the two gambles.
If one gamble has a higher expected value than another then:
 Risk lovers and risk-neutral people will always choose the gamble with the
higher expected value
 Some risk-averse people may choose the gamble with the lower expected value
if it appears less risky.
The usefulness of achieving benefits (The von Neumann- Morgenstern model) by:
 Risk-neutral person takes the formula of utility function U(w) = aw
 Risk-averse person U ( w)  a w
 Risk lover U(w) = aw2.
(a)
concave
(b)
convex
U(w)
U(w)=aw1/2
U(w2)
U(EV)
EU
U(w) = aw2
B
p1
M
E
p2
U(w2)
B
U(w1)
p1
A
EU
U(EV)
U(w1)
0
w1
CE EV
w2
E
p2
A
income 0
Expected utility EU = p1 U(w1) + p2 U(w2)
Expected value EV= p1w1 +p2w2
w1 EV CE
p1 = EB
w2
p2 = EA
w1 EV p 2

EVw2
p1
Certainty equivalent CE (0CE)
Graphically, expected value (EV) there, where
Risk premium = CE EV (segment)
Risk cost = EV CE (segment)
M
prof. Teresa Kamińska
Microeconomics
Risk-averse vs. risk lover’s utility functions
U (I)
UR
UA
UEVA
EU
UEVR
0
EV
income
If the expected utility of the game was the same for the risk-averse person and the risk lover
(involved in the same game and with the assumptions in both cases, the utility of having
identical expected value is the same), it would be the same as the expected value of the game.
These people are different and the utility of having the amount corresponding to the expected
value of the game is higher for the risk –averse individual than for the risk lover:
UA (EV)> UR (EV).
The risk-averse person will certainly have an amount corresponding to the expected value of
the game than actually playing, so in his case U(EV)A>EU.
The risk lover would rather play than take an offered amount equal to expected value of the
game, so in this case expected utility from the gamble exceeds the utility of expected value:
UEVR<EU.
prof. Teresa Kamińska
Microeconomics
Task
Emily is the owner of the deposit and the car. The probability of loss due to theft of the
car is estimated 0.2. Emily’s situation is shown in the chart below. Calculate how
much Emily is willing to pay for the entire car insurance. Complete the chart with
appropriate values and symbols.
U(w)
40
……..
U= 4 w
12
0
9
100
w