1. A standard model of choice under risk is Expected Utility Theory (EUT) in which preferences over lotteries that pay monetary prizes (x₁, x2, ..., xs) with probabilities (P1, P2, ..., Ps) with Eps = 1 are represented by the function L S (a) What does it mean to say that a function represents the consumer's prefer- ences? Σpsu(xs) Choice 1 8=1 (b) State and briefly comment on the axioms required for the EUT representation. (c) Consider the following experiment of decision making under risk in which sub- jects are asked which lottery they prefer in each of the following two choices: Lottery B 0 with prob. 0.01 10 with prob. 0.89 50 with prob. 0.10 Lottery D Choice 2 Lottery A 0 with prob. 0 10 with prob. 1 50 with prob. 0 Lottery C 0 with prob. 0.90 10 with prob. 0 50 with prob. 0.10 Suppose that the modal responses are Lottery A in Choice 1 and Lottery D in Choice 2. Assume that utility of zero is equal to zero and illustrate why it is not possible to reconcile these experimental findings with a EUT formulation. [" 0 with prob. 0.89 10 with prob. 0.11 50 with prob. 0 versus (d) Suppose a decision maker chooses according to prospect theory with value function v(x) = { and probability weighting function π(p) = versus √x -3√-x if x ≥ 0 if x < 0 VP (√P+√1-p) 2 Show that the decision maker's preferences can explain the pattern of choice over lotteries as described in (c).
1. A standard model of choice under risk is Expected Utility Theory (EUT) in which preferences over lotteries that pay monetary prizes (x₁, x2, ..., xs) with probabilities (P1, P2, ..., Ps) with Eps = 1 are represented by the function L S (a) What does it mean to say that a function represents the consumer's prefer- ences? Σpsu(xs) Choice 1 8=1 (b) State and briefly comment on the axioms required for the EUT representation. (c) Consider the following experiment of decision making under risk in which sub- jects are asked which lottery they prefer in each of the following two choices: Lottery B 0 with prob. 0.01 10 with prob. 0.89 50 with prob. 0.10 Lottery D Choice 2 Lottery A 0 with prob. 0 10 with prob. 1 50 with prob. 0 Lottery C 0 with prob. 0.90 10 with prob. 0 50 with prob. 0.10 Suppose that the modal responses are Lottery A in Choice 1 and Lottery D in Choice 2. Assume that utility of zero is equal to zero and illustrate why it is not possible to reconcile these experimental findings with a EUT formulation. [" 0 with prob. 0.89 10 with prob. 0.11 50 with prob. 0 versus (d) Suppose a decision maker chooses according to prospect theory with value function v(x) = { and probability weighting function π(p) = versus √x -3√-x if x ≥ 0 if x < 0 VP (√P+√1-p) 2 Show that the decision maker's preferences can explain the pattern of choice over lotteries as described in (c).
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
Related questions
Question
Transcribed Image Text:1. A standard model of choice under risk is Expected Utility Theory (EUT) in which
preferences over lotteries that pay monetary prizes (x₁, x2, ..., xs) with probabilities
(P1, P2, ..., Ps) with Eps = 1 are represented by the function
L
S
(a) What does it mean to say that a function represents the consumer's prefer-
ences?
Σpsu(xs)
Choice 1
8=1
(b) State and briefly comment on the axioms required for the EUT representation.
(c) Consider the following experiment of decision making under risk in which sub-
jects are asked which lottery they prefer in each of the following two choices:
Lottery B
0 with prob. 0.01
10 with prob. 0.89
50 with prob. 0.10
Lottery D
Choice 2
Lottery A
0 with prob. 0
10 with prob. 1
50 with prob. 0
Lottery C
0 with prob. 0.90
10 with prob. 0
50 with prob. 0.10
Suppose that the modal responses are Lottery A in Choice 1 and Lottery D in
Choice 2. Assume that utility of zero is equal to zero and illustrate why it is
not possible to reconcile these experimental findings with a EUT formulation.
["
0 with prob. 0.89
10 with prob. 0.11
50 with prob. 0
versus
(d) Suppose a decision maker chooses according to prospect theory with value
function
v(x) = {
and probability weighting function
π(p)
=
versus
√x
-3√-x
if x ≥ 0
if x < 0
VP
(√P+√1-p)
2
Show that the decision maker's preferences can explain the pattern of choice
over lotteries as described in (c).
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