(Table: The Utility from Income for Alexandra) Use Table: The Utility from Income for Alexandra. Alexandra runs her own business, which generates an annual income of $40,000. Alexandra is considering developing a new product. The probability that the new product will increase Alexandra's income by $30,000 is 0.5, and the probability that it will reduce Alexandra's income by $10,000 is 0.5. Suppose Alexandra can buy a fair insurance policy that will compensate her for any losses. Alexandra's premium will be _____, her guaranteed income will be _____, and her expected utility will be _____ utils. $$\text { Table: The Utility from Income for Alexandra } \
\begin{array} { | l | l | }
\hline \text { Income } & \text { Total Utility } \
\hline \$ 0 & 0 \
\hline 10,000 & 200 \
\hline 20,000 & 360 \
\hline 30,000 & 500 \
\hline 40,000 & 620 \
\hline 50,000 & 720 \
\hline 60,000 & 800 \
\hline 70,000 & 860 \
\hline
\end{array}$$

Question

(Table: The Utility from Income for Alexandra) Use Table: The Utility from Income for Alexandra. Alexandra runs her own business, which generates an annual income of $40,000. Alexandra is considering developing a new product. The probability that the new product will increase Alexandra's income by $30,000 is 0.5, and the probability that it will reduce Alexandra's income by $10,000 is 0.5. Suppose Alexandra can buy a fair insurance policy that will compensate her for any losses. Alexandra's premium will be _____, her guaranteed income will be _____, and her expected utility will be _____ utils. $$\text { Table: The Utility from Income for Alexandra } \
\begin{array} { | l | l | } 
\hline \text { Income } & \text { Total Utility } \
\hline \$ 0 & 0 \
\hline 10,000 & 200 \
\hline 20,000 & 360 \
\hline 30,000 & 500 \
\hline 40,000 & 620 \
\hline 50,000 & 720 \
\hline 60,000 & 800 \
\hline 70,000 & 860 \
\hline
\end{array}$$

Quizplus · Accepted Answer

The fair insurance premium would be calculated based on the expected loss, which is the average of the potential outcomes. With a 0.5 probability of losing $10,000, the expected loss is $5,000. Therefore, to guarantee her current income of $40,000, Alexandra would need to pay a premium of $5,000, not $10,000 as any option suggests directly. However, the correct understanding of the insurance premium in this context is that it ensures her income does not decrease, thus maintaining her utility at 620 utils, which corresponds to her current income without considering the insurance premium directly in the options provided. The misunderstanding in the question's phrasing about the premium's direct impact on guaranteed income and expected utility leads to selecting the option that correctly identifies her utility at her current income level, despite the confusion about the premium's calculation.

(Table: the Utility from Income for Alexandra) Use Table: the Utility