Uncertainty and Consumer Behavior

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For the Introductory Course on Economics for the Master on European Studies

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: An Example

10 20 30

p = 0,5 q = 0,5

10

18

14

16

16

Risk Neutrality: An Example

10 20 30

p = 0,5 q = 0,5

6

18

12

16

16

Risk Loving: An Example

10 20 30

p = 0,5 q = 0,5

3

18

10,5

16

16

8

Risk Premium

10 20 30

p = 0,5 q = 0,5

10

18

14

16

16

Risk premium

Risk Aversion and Indifference Curves

I

I

U0

U1

U2

U0

U1

U2

Measures for Risk Attitudes

Absolute Risk Aversion

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urARA u

Measures for Risk Attitudes

Relative Risk Aversion

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wuwrRRA u

Risk Coping Strategies

Diversification Don’t put all your eggs in one basket

Insurance Information