Question

Suppose there has been an outbreak of virus X. As head of the CDC, you have three options. (1) Administer only medicine M1 to the population, (2) Administer only medicine M2 to the population or (3) do nothing.(M1 and M2 are produced from a rare mineral so you can only manufacture either M1 or M2 but not both). Unfortunately, there are two strands of virus X, X1 and X2 only one of which is spread in the population. You don't know which strand is spread. What you do know is that there is a 20% chance that it is X1 and it is an 80% chance that it is X2. Here's the other relevant info. --If X1 is the strand and you administer M1, then 100 people will die --If X1 is the strand and you administer M2, then 25 people will die --If X1 is the strand and you do nothing, 1000 people will die --If X2 is the strand and you administer M1, then 20 people will die --If X2 is the strand and you administer M2, then 110 people will die --If X2 is the strand and you do nothing, no one dies. Calculate the expected utility of administering M1 (assume that 1 death has a -1 utility)

Answer 1

Solution

‘If X1 is the strand and you administer M1, then 100 people will die’, ‘assume that 1 death has

a -1 utility’ and ‘there is a 20% chance that it is X1’

=> utility of administering M1 = - 100 with probability 0.2 ………………………………........…….. (1)

Similarly,

‘If X2 is the strand and you administer M1, then 20 people will die’, ‘assume that 1 death has

a -1 utility’ and ‘there is a 80% chance that it is X2’

=> utility of administering M1 = - 20 with probability 0.8 …………………………….........……….. (2)

(1) and (2) =>

Expected utility of administering M1 = (- 100 x 0.2) + (- 20 x 0.8)

= - 36 Answer

DONE