Question

In: Economics

Consider two individuals with the same income and probability of experiencing an accident that would cost...

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?

Solutions

Expert Solution

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.


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