Penny is an expected utility maximiser with utility function u(x)=ln(x) and wealth of $300 . Paddy makes decisions in accordance with prospect theory, has wealth $300 and value function: v(x)={ x 2 1 −2(−x) 2 1 where where x≥0 x<0 Penny and Paddy are offered the following bet A: - a 60% probability to win $150 - a 40% probability to lose $100 . a) Does Penny or Paddy accept bet A? [3 marks] b) Following some bad economic news, each of Penny and Paddy's wealth declines to $150 . Paddy cannot get over the loss, so his reference point remains his former wealth of $300 . Penny and Paddy are offered bet A again. Does Penny or Paddy accept the bet? [ 3 marks] c) For the bets in parts a) and b), draw a diagram (or two diagrams) showing Paddy's value function, the bets and the value of the bets. Explain how the diagram(s) show whether Paddy accepts or rejects the bet.
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Penny is an expected utility maximiser with utility function
u(x)=ln(x)
and wealth of
$300
. Paddy makes decisions in accordance with prospect theory, has wealth
$300
and value function:
v(x)={
x
2
1
−2(−x)
2
1
where
where
x≥0
x<0
Penny and Paddy are offered the following bet A: - a
60%
probability to win
$150
- a
40%
probability to lose
$100
. a) Does Penny or Paddy accept bet A? [3 marks] b) Following some bad economic news, each of Penny and Paddy's wealth declines to
$150
. Paddy cannot get over the loss, so his reference point remains his former wealth of
$300
. Penny and Paddy are offered bet A again. Does Penny or Paddy accept the bet? [ 3 marks] c) For the bets in parts a) and b), draw a diagram (or two diagrams) showing Paddy's value function, the bets and the value of the bets. Explain how the diagram(s) show whether Paddy accepts or rejects the bet.
