20 Danielle is a farmer with a utility function of U I 05 where U is Danielles

# 20 danielle is a farmer with a utility function of u

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20. Danielle is a farmer, with a utility function of U= I0.5,where Uis Danielle’s utility and Iis her income. If the weather is good, she will earn \$100,000. If there is a hailstorm, she will earn only \$50,000. The prob-ability of a hailstorm in any given year is 30%.a. What is Danielle’s expected income if she is uninsured? Her expected utility?b. Suppose a crop insurer makes the following offer to Danielle: In years when there is no hailstorm, Danielle pays the insurer \$16,000. In years when there is a hailstorm, the insurer pays Danielle \$34,000. What is Danielle’s expected income? Her expected utility?c. Comment on the following statement referring to your answers to parts (a) and (b): “The insurance agreement in (b) reduces Danielle’s expected income. Therefore, it must make her worse off.”d. Suppose instead the insurer offers Danielle the following: In years when there is no hailstorm, Danielle pays the insurer \$10,000; in years when there is a hailstorm, the insurer pays Danielle \$20,000. How does Danielle’s expected income and expected utility compare to the uninsured outcome in (a) and the insured outcome in (b)? Goolsbee1e_Solutions_Manual_Ch13.indd 194 Goolsbee1e_Solutions_Manual_Ch13.indd 194 11/15/12 3:10 PM 11/15/12 3:10 PM