ECO 438/3140 Winter 2021: Assignment 1 (due 1/27 @
23:59)
For this assignment use the material in the lecture, in Kahneman and Tversky
1979 and Machina’s JEP 1987 survey.
1. (2 points) Consider the Marschak-Machina triangle of preferences over
lotteries with 3 outcomes x1 < x2 < x3
(a) Show that the indierence curves of a decision maker (DM) who
satises the Independence Axiom will be parallel straight lines.
(b) Show (graphically) how risk aversion of a decision maker who satises
expected utility is captured in the M-M triangle.
2. (2 points) Consider the Allais Paradox in which a DM exhibits the following preferences p
1=(1000000, 1) (5000000, .1; 10000000, .89; 0, .01) = p
2
and q
1 = (1000000, .11; 0, .89) ≺ (5000000, .1; 0, .9) = q
2
(a) Show that you cannot nd a vNM utility function u (·) that will
rationalize the above preferences.
(b) Show in a M-M triangle that the above preferences are inconsistent
with the DM having indierence curves that are parallel straight
lines.
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