a) Assume that Lleuwen has zero initial wealth, prefers more money to less and her preferences satisfy the axioms of Expected Utilty Theory (EUT). She is given a lottery ticket which pays out 1,000 with a probability of 30%, and pays nothing otherwise. Her certainty equivalent to this lottery ticket is 250.

i. Graph her full set of indifference curves in a Machina triangle with 0, 250 and 1,000 as the pure outcomes. Account for the shape of her indifference curves.

[20%]

[5%]

Which of the following two lotteries would Lleuwen prefer?

L1= [$0 pr=0.2, $250 pr=0.3, $1000 pr=0.5]

L2=[$0 pr=0.3, $250 pr=0.1, $1000 pr=0.6]

We are now told that Lleuwen is also indifferent between the certainty of 750 and a lottery ticket which gives an 80% chance of winning 1,000.

iii, Derive and graph Lleuwen's normalised von-Neumann Morgenstern utility function for values between 0 and 1,000.

IV. Describe Lleuwen's attitude to risk.