Question

3. Keiko has $100, but there is a 50% chance she will lose all her money in the stock market. Ndola offers
to fully insure Keiko’s loss for a premium of $36. If Keiko’s utility over wealth is given by u(w) =√w, which of the following is true?
I. Keiko should accept Ndola’s offer
II. Ndola will have positive expected profit if Keiko accepts
(a) Both
(b) Just I
(c) Just II
(d) Neither

Answer 1

option b)

Now actuarially fair insurance premium = loss* probability of loss

= 100*.5

= 50

Thus since offer is only at 36, so keiko will accept the offer

Also without insurance,

EU = .5*√100 +. 5*0

= 5

With insurance, income in both states = 100-36 = 64

Then EU = √64

= 8

So as EU rise, with insurance , so accept the offer.

(I) is right

now at actuarially fair insurance premium, insurance firm earns zero profit, & if premium is less than actuarially fair insurance premium level, then firm earns Negative profit

(II) is false