Term 2 week 1

Question 1

What assumptions must be satisfied for a consumer to have rational preferences?

Answer 1

Preferences must be:
complete
Transitive

Question 2

What are complete preferences?

Answer 2

agents must be able to compare bundles:

they must prefer a to b or be indifferent or prefer b to a

Question 3

What is important notationally when doing preference

Answer 3

IT IS NOT INEQUALITY IT IS CURVED!

Question 4

What are transitive preferences?

Answer 4

You are able to rank bundles:

If you prefer a to b and you prefer c to b you prefer c to a

Question 5

What are the other axioms of consumer preferences?

Answer 5

Monotonicity - more is better
Convexity - averages are better than extremes
Continuity - utility does not change dramatically if the amount of a good changes slightly

Question 6

What is the difference between cardinal and ordinal?

Answer 6

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

Question 7

What is the outcome notation for an action A?

What is the set up for it under uncertainty?

Answer 7

A = {a , b , c)

a can happen with sigma
b can happen with row
c can happen with 1 - sigma - row

Question 8

What is the difference between capital and lowercase u

Answer 8

Capital U is expected utility
lowercase u is exact utiility

Question 9

How do you know when lottery A is preferred to lottery B?

Answer 9

A > curved B if U(A) > U(B)

Question 10

How can you present the utility of taking action A

what is important to remember?

Answer 10

U(a,b,c) = pu(a) + sigmau(b) + 1-p-sigmau(c)

use small u when computing.

Question 11

What does it mean if there is a Von-Nuemann utility function

Answer 11

It means it is an expected utility function

Question 12

What happens if a expected utility function goes under a transformation?

Answer 12

it can be subjected to monotonic trandormation and still have the expected utility property
Ordering is preserved
Cardinality may change (exact values)

Question 13

What is an example of an affine transofmration

Answer 13

Ax + B

Question 14

How do you formally present lotteries with notation

Answer 14

L = {x1,x2…xs ; p,sigma, theta}

The different states , then semi colon associated probabilities with those states.

Question 15

What is a compound lottery?

Answer 15

One where you can play the lottery more than once

Question 16

What are the axioms of preferences for lotteries?

Answer 16

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

Question 17

Why is independence useful for lotteries?

Answer 17

It allows compound lotteries to be simplfiied into simple lotteries

Question 18

How do you show a lottery graphically?

Answer 18

Branches with p on the line and outcome on the end

Question 19

How do you show graphically a risk function

Answer 19

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

Question 20

What type of functions show the different risk types?

Answer 20

Concave - risk averse
Neutral - risk neutral
Convex - risk loving

Question 21

What is the certainty equivalent?

How do you find it?

Answer 21

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.

Question 22

What is risk premium?

What is the formula?

Answer 22

Difference between certainty equivalent and expected wealth of the lottery

RP = E(L) - C

Question 23

What does certainty equivalent show about nature of risk preferences

Answer 23

A C closer to origin is more risk averse.

Question 24

What is a second way of measuring risk aversion

Answer 24

The level of concavity

Question 25

What is absolute risk aversion?

WHAT IS IMPORTANT

What is it also known as?

Answer 25

-Also known as Arrow-Pratt measure of risk aversion // Rate of decay of MU

MUST AVE NEGATIVE SIGN

-Ra(W)
-u(W)’’ / u’(w)

Question 26

What is a disadvantage of absolute risk aversion?

What is the alternative to this?

Answer 26

It depends on the units!

Relative risk aversion

Rr = - u’‘(w)w/u’(w)