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Attitude toward risk. Problem : Costello likes to ride his bike to school. If it is raining when he gets up, he can take the bus. If it isn’t, he can ride, but runs the risk of it raining on the way home. Value of riding bike = $2, value of taking bus = -$1.

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Attitude toward risk
Attitude toward risk

  • Problem: Costello likes to ride his bike to school. If it is raining when he gets up, he can take the bus. If it isn’t, he can ride, but runs the risk of it raining on the way home.

  • Value of riding bike = $2, value of taking bus = -$1.

  • Value of riding in rain = -$6.


Costello s options the states of nature
Costello’s options & the “states of nature”

  • Costello can either ride his bike or take the bus.

  • Bus: He loses $1 each way: -$2

  • Bike: Depends on the “state of nature”

    • Rain: $2 - $6 = -$4.

    • No rain: $2 + $2 = $4.


Which does he prefer
Which does he prefer?

  • If Costello takes the bus, he knows he’ll lose $2.

  • If Costello rides his bike:

    • If it rains, he loses $4.

    • If it doesn’t rain, he gains $4.

  • Whether he is better taking the bike or bus depends on 2 things:

    • The probability of rain

    • His attitude toward risk


The probability of rain
The probability of rain

  • Suppose Pr(rain) = .5……Pr(no rain) = .5

    • Bus: -$2

    • Bike: .5(4) - .5(-4) = $0

    • If he is risk neutral, he takes his bike ($0 > $-2)

  • Suppose Pr(rain) = .8….Pr(no rain) = .2

    • Bus: -$2

    • Bike: .2(4) + .8(-4) = -$2.40

    • If he is risk neutral, he rides the bus (-2 > -2.40)


Risk more generally
Risk more generally

Q: Would this person rather

get 15 for sure or 10 w.p.

0.5, and 20 w.p. 0.5?

Utility

U(15)

This person is

RISK AVERSE

.5*U(10)

+ .5*U(20)

15

10

20

Some good (or $)


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