Term 2 week 1 Flashcards
What assumptions must be satisfied for a consumer to have rational preferences?
Preferences must be:
complete
Transitive
What are complete preferences?
agents must be able to compare bundles:
they must prefer a to b or be indifferent or prefer b to a
What is important notationally when doing preference
IT IS NOT INEQUALITY IT IS CURVED!
What are transitive preferences?
You are able to rank bundles:
If you prefer a to b and you prefer c to b you prefer c to a
What are the other axioms of consumer preferences?
Monotonicity - more is better
Convexity - averages are better than extremes
Continuity - utility does not change dramatically if the amount of a good changes slightly
What is the difference between cardinal and ordinal?
ordinal means you can simply rank bundles
cardinal means you can assign a value to it
u(a) > u(b) when a is strictly preffered to b
What is the outcome notation for an action A?
What is the set up for it under uncertainty?
A = {a , b , c)
a can happen with sigma
b can happen with row
c can happen with 1 - sigma - row
What is the difference between capital and lowercase u
Capital U is expected utility
lowercase u is exact utiility
How do you know when lottery A is preferred to lottery B?
A > curved B if U(A) > U(B)
How can you present the utility of taking action A
what is important to remember?
U(a,b,c) = pu(a) + sigmau(b) + 1-p-sigmau(c)
use small u when computing.
What does it mean if there is a Von-Nuemann utility function
It means it is an expected utility function
What happens if a expected utility function goes under a transformation?
it can be subjected to monotonic trandormation and still have the expected utility property
Ordering is preserved
Cardinality may change (exact values)
What is an example of an affine transofmration
Ax + B
How do you formally present lotteries with notation
L = {x1,x2…xs ; p,sigma, theta}
The different states , then semi colon associated probabilities with those states.
What is a compound lottery?
One where you can play the lottery more than once
What are the axioms of preferences for lotteries?
Completeness - you can compare lotteries , you prefer or are indifferent
Transitivity - you can rank different lotteries
Continuity - for any two lotteries changes in probability do not change ordering between lotteries
-Monotonicity - one lottery will be preferred only if it assigns a higher p to getting the better prize
-Independence, if we mix each of two lotteries with a third one the presence of the other impact the lottery does not alter the preference relation
Why is independence useful for lotteries?
It allows compound lotteries to be simplfiied into simple lotteries
How do you show a lottery graphically?
Branches with p on the line and outcome on the end
How do you show graphically a risk function
x axis wealth
y axis utility
How do you see if individual is risk averse or not
you plot the expected value of wealth
you plot expected value of utility
then see which is higher
What type of functions show the different risk types?
Concave - risk averse
Neutral - risk neutral
Convex - risk loving
What is the certainty equivalent?
How do you find it?
Makes you indifferent with that amount for certain and taking the gamble
Go to the expected utility of the lottery and meet the curve and go down.
What is risk premium?
What is the formula?
Difference between certainty equivalent and expected wealth of the lottery
RP = E(L) - C
What does certainty equivalent show about nature of risk preferences
A C closer to origin is more risk averse.
What is a second way of measuring risk aversion
The level of concavity
What is absolute risk aversion?
WHAT IS IMPORTANT
What is it also known as?
-Also known as Arrow-Pratt measure of risk aversion // Rate of decay of MU
MUST AVE NEGATIVE SIGN
-Ra(W)
-u(W)’’ / u’(w)
What is a disadvantage of absolute risk aversion?
What is the alternative to this?
It depends on the units!
Relative risk aversion
Rr = - u’‘(w)w/u’(w)
