Answer:
a) Jane's utility function is \( U = x^{1/2} \). To draw this utility function, plot points on a graph where the x-axis represents Jane's wealth (house value) and the y-axis represents her utility. The curve will be concave upward.
b) Jane is risk-averse. Risk aversion is indicated by a concave utility function, where the marginal utility of wealth decreases as wealth increases. In this case, as the house value increases, the increase in utility becomes smaller.
c) The expected monetary value (EMV) is calculated by multiplying each possible outcome by its probability and summing them. In this case:
\[ (0.8 \times \$100,000) + (0.2 \times \$30,000) \]
d) To fully insure her house, Jane would be willing to pay an amount equal to the expected loss. Therefore, she would be willing to pay \(0.2 \times (\$100,000 - \$30,000)\).
e) For a risk-neutral person like Homer, a beneficial insurance contract occurs when the expected utility without insurance is equal to the expected utility with insurance. The insurance premium Jane is willing to pay is the difference in expected wealth. Therefore, the prices for a beneficial insurance contract would be between \( \$30,000 \) and \( \$100,000 \) (the house value without insurance).