Question

Consider a scenario where an individual faces a choice between a “good” life choice and an “ungood” life choice. Both option result in a risky health situation, although the risk is conditional on the choice made. There is also a guaranteed positive benefit ($U) from making the ungood life choice. The tables below depict odds and costs associated with each choice:

Good:

	Probability	Cost
Healthy	0.99	0
Sick	0.01	-1000

Ungood:

	Probability	Cost
Healthy	0.8	0
Sick	0.2	-1000

Given these situations, how much must you value the guaranteed positive benefit ($U) to rationally choose the Ungood choice?

Answer 1

In case of good life

Probability of not being sick=p=0.99

Probability of being sick=1-p=1-0.99=0.01

Cost in case of not being sick=X=0

Cost in case of being sick=Y=-1000

Expected cost in case of good life=E(G)=p*X+(1-p)*Y=0.99*0+0.01*(-1000)=-$10

In case of Ungood life

Probability of not being sick=p=0.80

Probability of being sick=1-p=1-0.80=0.20

Cost in case of not being sick=X=0

Cost in case of being sick=Y=-1000

Expected cost in case of ungood life=E(UG)=p*X+(1-p)*Y=0.80*0+0.2*(-1000)=-$200

Minimum guaranteed benefit=E(G)-E(UG)=-10-(-200)=$190