Suppose a person's utility of wealth is given by $U ( W ) = \sqrt { W }$ and his or her initial wealth is 10,000.What is the maximum amount he or she would pay for insurance against a 50 percent chance of losing 3,600?
A)1,800.
B)1,900.
C)2,000.
D)2,100.

Question

Quizplus · Accepted Answer

The expected utility without insurance is 0.5 * sqrt(10,000) + 0.5 * sqrt(6,400) = 0.5 * 100 + 0.5 * 80 = 90. The utility with insurance is sqrt(10,000 - P), where P is the premium. Setting this equal to 90 gives sqrt(10,000 - P) = 90, so 10,000 - P = 8,100, thus P = 1,900.

Suppose a Person's Utility of Wealth Is Given By U(W)=WU ( W ) = \sqrt { W }U(W)=W​

Suppose a Person's Utility of Wealth Is Given By $U ( W ) = \sqrt { W }$