In: Economics
Consider two individuals with the same income and probability of experiencing an accident that would cost them $15,000 in medical expenses. The first individual has the utility function U=ln(Y) and the second has the utility function U=ln(Y)+10. How would their willingness to pay for an insurance policy to cover all of their medical expenses differ between the two individuals?
Lets us do a comparative analysis of their respective utility functions :
First Individual :U = ln(Y)
Cost = $ 15,000
Let us consider an insurance policy which costs X
Hence U = ln (X) of the money X right now
and U = ln(15000) = 9.615 of the money after insurance
if ln(x) < ln(15000)
ln(x) < 9.615
=> x<14987.922 $
=> if more utility is derived from ln(15000) than ln(x) then the individual will invest in the insurance policy
i.e if the value of insurance is less than 14987.22 $ then the individual will invest money in the insurance policy..
Second Individual :U = ln(Y)+10
Cost = $ 15,000
Let us consider an insurance policy which costs X
Hence U = ln (X) +10 of the money X right now
and U = ln(15000) + 10 of the money after insurance
U = 9.615+10 = 19.615
i.e if ln(X)+10 < ln(15000)+10 then the second individual will invest money in the insurance policy
ln(X) +10 < 19.615
i.e X < 14987.922 $ , hence the individual will invest in the insurance policy if the policy costs less than 14987.922 $
i.e both the individuals will have the same preferences over the investment in insurance policy.