5: Choice under Uncertainty Flashcards
goal
model of the choice of an individual faced with actions whose consequences are uncertain
degree of risk aversion
how curved the function is
- the more curved, the willingness to pay to avoid risk increases
- straight linear line means the individual is risk-neutral and indifferent between risk of getting 0 or a lot, and getting the average for certain
absolute risk aversion
measures of curvature for the Bernoulli curve
rate of change of the tangent line over the tangent line
- negative because bigger numbers mean you’re more risk averse
relative risk aversion
unit measure of risk aversion normalising for your amount of wealth
- add an x in front
absolute vs. relative risk aversion
use absolute when thinking about gambles for a particular dollar amount
use relative when thinking about gambles of a particular proportionate amount
absolute risk aversion interpretation
negative means you’re a risk-lover
what does it mean to be risk averse?
prefer some amount for sure over a gamble whose expected value is that amount
consequentialism assumption and EUT
EUT maximiser cares about the final probability distribution over final consequences
independence axiom
if you mix in the same probability of a third lottery to construct other choices, the independence axiom says that an EUT maximiser’s preference can’t flip
allais paradox
inability to model Bernoulli and EUT
statements together are mathematically impossible and cannot simultaneously be true under the model
pushes us to consider how DM values objects
ellsberg paradox
people sometimes pick options even when facing ambiguity
- presented with two similar options (urn with 300 balls - 100 red/ 200 blue or green ball)
- doesn’t make sense to pick red because you face ambiguity
pushes us to consider how DM perceives probabilities
machina paradox
pushes us to consider our own feelings (disappointment, etc.)
disappointment/regret theory
framing effects
can have identical options in every respect apart from the language used to describe the choice
mindset where you’re thinking about losses/gains can change decisions
Bernoulli function and diminishing marginal utility of money
rate at which utility increases as wealth increases is smaller when wealth is higher
each subsequent dollar of wealth increases utility by less than the previous dollar
slope of the Bernoulli function gets flatter
- second derivative is negative
what does an increasing ARA mean?
more risk-averse as wealth increases
