Choice under uncertainty Flashcards
How are risky choices presented?
List all possible outcomes and assign to them their probabilities
What does economic jargon call outcomes and risky choices?
Prizes and lotteries
Whats a fair gamble and give an example?
If the expected value is equal to 0 or the cost of participating in the game (entry fee).
E.g 2 players flip a coin, if its head 1 pays 2 £1, if tails 2 pays 1 £1.
EV for player 1 = (0.5 x 1) + (0.5x-1) = 0 (same for player 2.)
What is the St Petersburg Paradox?
determines the value that someone would be willing to pay in order to play a lottery game such as follows;
a coin is flipped until a head appears, if it appears on the nth the player pays £2 to the power of n.
What is a favourable game?
Where the expected value isnt equal to 0 or what the player started with.
Give an example of a favourable game?
If heads player 1 gives player 2 £1. If tails player 2 gives player 1 £2.
EV for player 1 - (0.5 x -1) + (0.5 x -2) = 0.5 so not favourable
EV for player 2 - (0.5 x 1) + (0.5 x 2) = -0.5 so not favourable
What are three types of economic agents :
- risk averse agent (avoids taking risk)
- risk loving agent (willing to spend money on the gamble
- risk neutral (indifferent to taking the gamble)
What are the followings type of MU of wealth:
- risk averse
-risk loving
- risk neutral
- positive but diminishing (their MU falls as they get wealthier)
- positive and increasing (their MU increases as they get wealthier)
- positive and constant (their MU stays the same as they get wealthier.)
What is Bernoullis solution to the St Petersbrug Paradox?
People maximise expected utility not expected value. They dont make decisions on how to maximise expected value as they dont like risk.
Utility function in terms of wealth is derived from this U(w) - utility of wealth function
Why do risk averse agents not take risks?
Because their utility of expected wealth is greater than their expected utility of wealth. They prefer to have the expected value of wealth rather than gamble.
Why do risk loving agents takes gambles?
Their expected utility of wealth is greater than their utility of expected value of wealth.
What does the shape of a utility wealth function tell us?
The more concave it is the more risk averse they are
the more convex it is the more risk loving they are
if linear then they are indifferent to risk.
Why are risk neutral agents indifferent to gambles?
utility of expected value of wealth = expected utility of wealth
