Danielle is a farmer, with a utility function of U=I0.5, where U is Danielle’s u

Question

Danielle is a farmer, with a utility function of U=I0.5, where U is Danielle’s utility and I is her income. If the weather is good, she will earn $100,000. If there is a hailstorm, she will earn only $50,000. The probability of a hailstorm in any given year is 0.3. Danielle has the option of buying insurance for $16,000 per year that will pay her $34,000 if there is a hailstorm. Buying the insurance results in a __________ change in her expected income and a _________ change in her expected utility.

Explanation / Answer

SOLUTION: Buying the insurance results in a $1000 change in her expected income and a 1.39 change in her expected utility.

WORKING:

Without insurance:

Danielle expected income: 0.70 * $100,000 + 0.30 * $50,000 = $85,000

As $100,000 brings Danielle (100,000)^0.5 = 316.22 units of utility, and $50,000 brings Danielle (50,000)^0.5 = 223.60 units of utility. Danielle’s expected utility is

E(U) = 0.7 * U (100,000) + 0.3 * U (50,000)

= 0.7 * 316.22 + 0.3 * 223.60

= 288.43

With insurance

Danielle expected income: 0.70 * ($100,000 – $16,000) + 0.30 * ($50,000 + $34,000) = $84,000

E(U) = 0.7 * U (84,000) + 0.3 * U (84,000) = U (84,000) = 289.82

Difference:

Danielle expected income: $85,000 - $84000 = $1000

E(U) = 288.43 - 289.82 = 1.39

Related Questions

Navigate

• Browse (All)
• Browse D
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.