Uncertainty and Consumer Behavior …Riiiisk….. Uncertainty and Risk Risk is associated to...
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Transcript of Uncertainty and Consumer Behavior …Riiiisk….. Uncertainty and Risk Risk is associated to...
Uncertainty and Risk
Risk is associated to uncertain events. Uncertainty refers to unknown outcomes of stochastic
variables i.e. dices’ throw. Two cases:
Dices: known distribution Unknown distributions: … what the future brings?
A Game
1, 2, 3, 4 s (shine) 5, 6 r (rain) Three dices three days Options
sss ssr srr rrr Probabilities
P(s) = 2/3 P(r) = 1/3
A Game You are given 10 units of money You have to gamble 2 units each time (5 times) Your betting options:
If the outcome doesn’t fit with your bet, you give back the money
At least 1s At least 2s At least 2r 3r
-75% -50% -25% -0%
Distribution Probability
At least 1s: P(3s) + P(2s) + P(1s)
At least 2s: P(3s) + P(2s)
At least 2r: P(2r) + P(3r)
0,296
0,444
0,222
0,037
0
0,25
0,5
3s 2s-r s-2r 3r
3r: P(3r)
Example
Your choice
At least 1s
At least 2s
At least 2r
3r Actual Outcome
First Round
Second Round
Third Round
Fourth Round
Fifth Round
PayoffFinal Payoff
3,50
-2
-0,25
-0,25
-2
-2
-6,50
Theory of Probability P(3s) =?
P(s) = 2/3 P(3s) = P(s) P(s) P(s)
P(2s and r)=? P(s) = 2/3 P(r) = 1/3 ssr srs rss P(2s and r) = 3P(s)P(s)P(r)
P(s and 2r)=? P(s and 2r) = 3P(s)P(r)P(r)
P(3r) =? P(3r) = P(r)P(r)P(r)
P(3s) =2/3*2/3*2/3 = 8/27 P(3s) = 8/27= 0,296
P(2s and r)= 3*2/3*2/3*1/3 = 12/27 P(2s and r) = 12/27 = 0,444
P(s and 2r)= 3*2/3*1/3*1/3 = 6/27 P(s and 2r) = 6/27 = 0,222
P(3r) = 1/3*1/3*1/3 = 1/27 P(3r) = 1/27 = 0,037
The Expected Value of the Distribution
0,296
0,444
0,222
0,037
0
0,25
0,5
0 1 2 3
<x> = 0*p(3s) + 1*p(2s and r) + 2*p(s and 2r) + 3*p(3r)
<x> = 0*0,296 + 1*0,444 + 2*0,222 + 3*0,037 = 1,00
<x> = n*p(r) = 3*1/3
<x>
The Variance of the Distribution
2<x> = (0 -1)2 P(3s)+ (1-1)2 P(2s and r)+ (2 -1)2 P(s and 2r) + (3 -1)2 P(3r)
2<x> = 1*0,29 + 0*0,44 + 1*0,22 + 22*0,037
2<x> = 0,29 + 0,22 + 4*0,037
2<x> = 0,658
2<x> = nP(s)P(r)
2<x> = 3*2/3*1/3
0,296
0,444
0,222
0,037
0
0,25
0,5
0 1 2 3
<x>
22<x><x>