Behavioral eco-lect 4: Choice under risk and uncertainty part 2 (Expected…
Behavioral eco-lect 4: Choice under risk and uncertainty part 2
Solution to st-petersburg paradox (Bernouilli, 1738): people maximize expected
, not expected
EU(L) = p1 u(C1) + … + pn u(Cn) = ∑
Question: How much is an EU-maximizer with u(x) = ln(x) willing to pay to play the game?
Suppose u(x) = ln(x), then
EU = ½
ln(2) + ¼
ln(4) + … = 2ln(2) = ln(4) ≈ 1.39
Your certainty equivalent CE of a lottery L is the amount for sure that you find as good as the lottery L:
Every lottery has its own certainty equivalent, which depends on the preferences of the decision maker
consider lottery L=(p:A, 1-p:B)
certainty equivalent to elicit utility
Required assumption: expected utility holds.
N.B. If a person does not satisfy expected utility, the method used to measure utility in tutorial B is not accurate.
Certainty equivalents can be used to measure utility functions
Risk attitudes in general
(100% : EV(L)) ≻ L <=> riskaverse
(100% : EV(L)) ~ L <=> risk neutral
(100% : EV(L)) ≺ L <=> risk seeking (= risk prone)
Risk attitudes in general cont.
The definitions of risk attitudes have the following implications for the certainty equivalents of lotteries:
CE(L) = EV(L) <=> risk neutral
CE(L) > EV(L) <=> risk seeking (=risk prone)
CE(L) < EV(L) <=> risk averse
Risk attitudes under expected utility
Under expected utility we have:
Linear utility <=> risk neutral
Convex utility <=> risk seeking (=risk prone)
Concave utility <=> risk averse
Expected utility and rationality
Standard economics uses expected utility.
NB: utility u in expected utility is cardinal.
Expected utility is considered rational (=normative) by many people.