week 4 uncertainty and risk, behavioral econ

Question 1

To make things easier, in economics we call the list of outcomes and
probabilities a?

Answer 1

Lottery

Question 2

Expected utility
U(L) = π1u(c1) + π2u(c2) + … + πnu(cn)

Answer 2

where u(c) represents how much the consumer enjoys outcome c, and πi is the probability of state i.

Question 3

is expected utility ordinal or cardinal? and what transformations can be made?

Answer 3

cardinal, as a monotonic transformation will not necessarily represent the same prefernces. So only positive affine transformations can be made.

Question 4

Independence Assumption

Answer 4

states that, if two lotteries provide the same utility in one state of nature, consumer’s choice is independent of that state.

Question 5

expected value

Answer 5

probability of an event occuring.

= π1c1 + π2c2 + … + πncn

Question 6

risk averse vs risk lover vs risk neutral

Answer 6

1- risk averse is against taking risks and has a concave curve. prefer to get a smaller amount for sure than risk a larger amount.

2- has a convex curve, happy to risk being paid very little if this comes wih a possibiblity of coming with alot.

3- you are indifferent, given they have the same expected value.

Question 7

The consumer is risk averse if being paid for sure the average outcome of the lottery is better than playing the lottery. what shows this.

Answer 7

u(π1c1 + π2c2) (expected value) > π1u(c1) + π2u(c2) (expected utility)

Question 8

The consumer is risk lover if playing the lottery is better than being paid for sure
its average outcome. what shows this?

Answer 8

u(π1c1 + π2c2) (expected value) < π1u(c1) + π2u(c2) (expected utility)

Question 9

certainty equivalent

Answer 9

is the amount of “sure” cash that makes an individual indifferent between the CE amount and the Lottery.
CE → U(CE) = E[U(L)]

Question 10

Risk Premium (RP)

Answer 10

is the amount that the individual is willing to give up in order to avoid the gamble

RP = Expected Value − CE

Question 11

allais paradox

Answer 11

Notice if p1 ≻ p2 then:
u(1000000) > .01u(0) + .89u(1000000) + .1u(3000000)
which implies:
.11u(1000000) − .01u(0) > .1u(3000000)
add .9u(0) to both sides gives:
.11u(1000000) + .89u(0) > .1u(3000000) + .9u(0)
which implies
p4 ≻ p3
Why is this an issue?
This violates the independence axiom!