We are faced with selecting among three alternatives which a

We are faced with selecting among three alternatives which are:

Offer a new flu clinic

Offer a new healthy eating clinic

Do nothing

There is a 40% chance that there will be a flu epidemic. If the flu epidemic occurs our new flu clinic will make $100, if there is no epidemic we will lose $10.

If we offer the healthy eating clinic we will make $50 but if there is flu we will lose $5.

If we do nothing we, of course, spend and get nothing. All amounts in $10,000 net and we must choose one but only one.

Questions:

1)With an expected value approach, what is the best choice?

2)With a maximin approach, what is the best choice?    

3)If the probability of a flu epidemic changes to 20% will the EV decision change? How?

Solution

a- Offer a new flu clinic

b - Offer a new healthy eating clinic

c - Do nothing

1) Offer a new flu clinic

E(X) = 0.4*100+0.6*(-10)=34

Offer a new healthy eating clinic

= 0.4*50+0.6*(-5) = 17

c) 0

so best choice is \"offer a flu clinic\"

2) maximin approach

We take the smallest payoff under each action (smallest number in each column). You then take the best (largest of these).

so a)-10

b)-5

c) 0

hence we do nothing.

3) if the probability of a flu epidemic changes to 20%

Offer a new flu clinic

E(X) = 0.2*100+0.8*(-10)=12

Offer a new healthy eating clinic

= 0.2*50+0.8*(-5) = 6

c) 0

so best choice is \"offer a flu clinic\"