Refer to the data provided in Table 17.4 below to answer the following question(s). The table shows the relationship between income and utility for Celeste.
Table 17.4
$$\begin{array} { | c | c | }
\hline { \text { Income } } & \text { Total Utility } \
\hline \$ 0 & 0 \
\hline \$ 40,000 & 50 \
\hline \$ 80,000 & 90 \
\hline \$ 120,000 & 120 \
\hline \$ 160,000 & 140 \
\hline
\end{array}$$
-Refer to Table 17.4. Suppose Celeste has a 1/3 chance of becoming disabled in any given year. If she does become disabled, she will earn $0. If Celeste does not become disabled, she will earn her usual salary of $120,000. Celeste has the opportunity to purchase disability insurance which will pay her her full salary in the event she becomes disabled. Such an insurance policy would be worth ________ to Celeste.
A) $0
B) $40,000 or less
C) more than $40,000 but less than $80,000
D) $80,000 or more

Question

Refer to the data provided in Table 17.4 below to answer the following question(s). The table shows the relationship between income and utility for Celeste.
Table 17.4
 $$\begin{array} { | c | c | } 
\hline  { \text { Income } } & \text { Total Utility } \
\hline \$ 0 & 0 \
\hline \$ 40,000 & 50 \
\hline \$ 80,000 & 90 \
\hline \$ 120,000 & 120 \
\hline \$ 160,000 & 140 \
\hline
\end{array}$$
-Refer to Table 17.4. Suppose Celeste has a 1/3 chance of becoming disabled in any given year. If she does become disabled, she will earn $0. If Celeste does not become disabled, she will earn her usual salary of $120,000. Celeste has the opportunity to purchase disability insurance which will pay her her full salary in the event she becomes disabled. Such an insurance policy would be worth ________ to Celeste.
A) $0
B) $40,000 or less
C) more than $40,000 but less than $80,000
D) $80,000 or more

Quizplus · Accepted Answer

To determine the value of the disability insurance to Celeste, we need to calculate the expected utility without and with insurance. Without insurance, her expected utility is a weighted average of the utility of earning $0 (with a probability of 1/3) and the utility of earning $120,000 (with a probability of 2/3). From the table, the utility of earning $0 is 0, and the utility of earning $120,000 is 120. Thus, her expected utility without insurance is $(1/3)*0 + (2/3)*120 = 80$.With insurance, she is guaranteed to earn $120,000 regardless of disability, giving her a utility of 120. To find the value of the insurance, we look for the income level that corresponds to a utility of 80 (her expected utility without insurance). From the table, an income of $80,000 gives a utility of 90, and an income of $40,000 gives a utility of 50. Therefore, the utility of 80 would fall between these two income levels, indicating that the insurance would be worth more than $40,000 but less than $80,000 to Celeste, as it ensures her utility is maintained at the level of earning $120,000 (120 utility) versus the expected utility without insurance (80).

Refer to the Data Provided in Table 17 -Refer to Table 17