Title: Microeconomics / Q1 / lecture11

Q: probability premium
A: denoted by π(x, ε, u), is the excess in winning probability over fair (50%) odds that makes the decision maker indifferent between the certain outcome x and a gamble/lottery between the two outcomes x + ε and x – ε. That is:

Q: Absolute Risk Aversion
A: The degree to which an individual is risk-averse, independent of the size of the gamble.
The reasoning behind this definition is fairly intuitive. First, it is very intuitive that a utility function that is linear in x shows no risk aversion, and has u′′(x) = 0. This suggests that a measure of risk aversion should be related to the curvature of u( ), which suggests defining it in terms of u′′( ). Yet using u′′( ) alone is not sufficient because choices under uncertainty are unaffected by linear transformations of u( ). To “control for” linear transformations the easiest thing to do is divide u′ʹ( ) by u′( ), which is what rA(x) does. The last thing to do is to make rA(x) increasing as u′′( ) increases in absolute value, so we put a negative sign in front of u′′(x)/u′(x).

Q: more-risk-averse-than
A: The “more-risk-averse-than” relation between two
Bernoulli utility functions is only a partial ordering.
That is, it is quite possible that one utility function is
“more risk averse” at some levels of wealth while the
other is “more risk averse” at other levels. In this case, it
is not possible, in general, to rank the two utility functions
in terms of their risk aversion.

Q: decreasing absolute risk aversion
A: if rA(x, u) is a decreasing function of x. That is, ∂rA(x, u)/∂x < 0

constant relative risk aversion (CRRA)