question 4

4. Total claims for a health plan have a Pareto distribution with a: = 2 and 9 = 500. The health plan implements an incentive to physicians that will pay a bonus of 50% of the amount by which total claims are less than 500; otherwise no bonus is paid. It is anticipated that with the incentive plan, the claim distribution will change to become Pareto with a = 2 and 9 = K. With the new distribution, it turns out that expected claims plus the expected 1 bonus is equal to expected claims prior to the bonus system. Determine the value of K