Problem
Three lottery prospects, each with up to three outcomes (x3,x2,x1) = ($1,000, $500, $0) are available.
Suppose that an individual attaches these utility values to each of the lottery outcomes u(x3 )=1, u(x2 )=0.7, and u(x1 )=0.
Prospect A: ($1,000, 0.3, $0, 0.7)
Prospect B: ($1,000, 0.4; $0, 0.6)
Prospect C: ($500, 0.5; $0, 0.5)
I. Draw a probability triangle in (p3, p1) space (the y-axis being the p3, the probability of the best outcome, and the x-axis being p1, the probability of the worst outcome). Plot each of the three prospects (A, B, and C) on the triangle.
II. Calculate the expected utility of the three prospects.
III. What is the equation of the indifference curve passing through lottery A? Represent this on the diagram from part (I) of this question.