a.
The expected income will be,
"Expected income = (60\\%\u00d710,000) + (40\\%\u00d715,000) \\\\=6,000 + 6,000\\\\= 12,000"
The expected utility will be,
"Expected utility (E(u)) =(60\\%\u00d710) + (40\\%\u00d712)\\\\= 6 + 4.8 \\\\=10.8"
Therefore, expected income will be $12,000 and expected utility 10.8.
b.
The utility from risk free alternative that give the same income as risky alternative is 11 utils. This means,
"E(u) <\u2009U(E(u)) \\\\10.8<11"
This shows that the consumer receives more utility with the same income given to him but with a certainty and risk free alternative, than with the same income but with risky alternative. This shows that the individual is risk averse in nature who wants to avoid risk.
A concave shape utility curve shows a risk-averse individual case.
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