risk-averse, non-satiated investor is trying to determine their utility of wealth function, U(w).
They have decided to use the utility function U(w) = w + dw2, where d < 0 is a constant that the
investor has chosen.
2.1 Derive an upper bound in terms of d for the range of values of w over which U(w) can be
used.
2.2 Explain why d < 0 is a necessary condition for U(w) to be a valid utility function.
The investor lives on a tropical island. On this island, root vegetables can be bought once
a week for $10 per box. The investor knows that they will be able to sell any vegetables
they buy for $30, $12, $10 or $0.5 per box with equal probability. All boxes of vegetables
sold at a given time will be sold for the same price.
The investor’s current wealth is $100. If the investor were to buy seven boxes of vegetables,
their expected utility of wealth after selling them would be 50 .
2.3 Calculate the value of d.
2.4 Calculate the expected utility of wealth of the investor, if they do not buy any vegetables.
The investor has decided they want to buy seven boxes of vegetables.
2.5 Discuss whether U(w) is appropriate for the investor.