Uncertainty and Consumer Behavior

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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>

Preferences toward Risk(Risk Aversion)

Preferences toward Risk(Risk Loving)

Risk Aversion and Indifference Curves

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I

U0

U1

U2

U0

U1

U2

Measures for Risk Attitudes

Absolute Risk Aversion

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Measures for Risk Attitudes

Relative Risk Aversion

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Risk Coping Strategies

Diversification Don’t put all your eggs in one basket

Insurance Information