Question

Suppose that everyone has the same utility function and an annual income of $50000 but people face different risks to health. Person A has a 0.20 chance of experiencing a health shock that requires $400 in expenses while Person B has a 0.002 percent chance of experiencing a health shock that requires $40,000. Graphically illustrate that Person B would be willing to pay a greater risk premium for insurance that Person A although the expected loss is the same for both types of people. Explain your answer.

Answer 1

Expected loss for Person A = 0.20 * $ 400

= $ 80

Expected loss for Person B = 0.002 * $ 40,000

= $ 80

Here expected loss is same for both persons.

For person A :

Expected Utility = P Ln ( Y - L) + (1-P) Ln Y

= 0.20 * ln ( $ 50000 - $ 400) + ( 1 - 0.20) ln $ 50000

= 2.162 + 8.648

= 10.81

Premium = $ 50000 - exp(10.8)= $ 979.

For person B :

Expected Utility = P Ln ( Y - L) + (1-P) Ln Y

= 0.002 * ln ( $ 50000 - $ 40000) + ( 1 - 0.002) ln $ 50000

= 0.002* 9.21 + 0.998* 10.81

= 0.01842 + 10.78

= 10.79

Premium = $ 50000 - exp(10.7)= $ 1467

Person B willing to pay mre premium than person A but expected loss is same.