1. Behavioral Finance
Economics 437

2. Imagine that one in every thousand athletes use steroids
Imagine that one in every thousand athletes use steroids. Imagine also that the test for steroids has a 5 % false positive rate. If a particular athlete tested positive for steroids what is the probability that that athlete was a steroid user
[0.001]
[0.020]
[0.65]
[0.95]

3. A Few More Thoughts on Expected Utility

4. Expected Utility Theory
Begin with a utility function defined only for certain dollar amounts:
Increasing in wealth (positive marginal utility)
Risk averse (diminishing marginal utility)
Then, using U(W), define expected utility as:
U(lottery) = p1 U(X1) + p2 U(X2)
Expected Utility is the “expected value of utility gained from different outcomes (X’s)”
If U(W) = W, then expected utility equals expected value

5. Risk Aversion
U(Y)
Utility
αU(X) + (1 – α)U(Y)
U(X)
Wealth X Y

6. Risk Preference
U(Y)
Utility
αU(X) + (1 – α)U(Y)
U(X)
Wealth X Y

7. A Dilemna
US is preparing for the outbreak of an unusual foreign disease which is expected to kill 600 people
Program A: 200 people will be saved
Program B: 1/3 probability that 600 will be saved; 2/3 probability that no one will be saved

8. Another Dilemna Program C: If adopted 400 people will die
Program D: 1/3 probability that no one will die and 2/3 probability that 600 people will die

9. Concurrent Decisions:
Choose Between:
A: A sure gain of $ 240
B: 25 % gain of $ 1,000 and 75 % chance to gain nothing
C: A sure loss of $ 750
D: 75 % chance to lose $ 1,000 and 25 % chance to lose nothing

10. Oops If you chose A & D: {B & C} dominates {A & D} Choose Between:
A: A sure gain of $ 240
B: 25 % gain of $ 1,000 and 75 % chance to gain nothing
C: A sure loss of $ 750
D: 75 % chance to lose $ 1,000 and 25 % chance to lose nothing
If you chose A & D:
25 % gain of $ 240 and 75 % chance to lose $ 760
{B & C} dominates {A & D}
25 % gain of $ 250 and 75 % chance to lose $ 750

11. Make a choice You have been given $ 2,000
Choose between A and B
A: 50 % chance of losing $ 1,000 or receiving nothing
B: A sure loss of $ 500

12. Make a choice You have been given $ 1,000
Choose between C and D
C: 50 % chance of winning $ 1,000 or receiving nothing
D: A sure $ 500

13. Make a choice
Choose between A and B (assuming you have been given $ 1,000)
A: 50 % chance of winning $ 1,000
B: A sure gain of $ 500
Choose between C and D (assuming you have been given $ 2,000)
C: 50 % chance of losing $ 1,000 or receiving nothing
D: A sure loss of $ 500
A and C are identical
B and D are identical

14. Another Choice Which would you prefer? A: Certain gain of $ 30
B: 80% chance to win $ 45 and 20% chance to win $ 0

15. Another C: 25 % chance to win $ 30 and 75 % chance to win nothing, or
D: 20 % chance to win $ 45 and 80 % chance to win nothing

16. And again A Two Stage Game
75 % chance of ending the game winning nothing and 25 % chance of going to second stage of the game
At second stage
R:Certain win of $ 30, or
S:80% chance to win $ 45 and 20% chance to win nothing

17. Two kinds of schools School A has 65 % boys; 35 % girls
School B has 45 % boys; 55 % girls
A class has 55 % boys: Which school is it most likely to be taken from?

18. The End