a) Consider a set of monetary outcomes X = {x1,...,Xk} where the outcomes are arrangedin increasing order x, < .. < xK. Let p and q be simple lotteries. We say that lottery pfirst-order stochastically dominates lottery q, if the following holds:KKE P(x,) > E q(x,) for all i = 1, ... K,j=ij=iwith at least one of the inequalities being strict. Explain the intuition of first-order stochas-tic dominance. Show that, for expected utility preferences with vNM utility u that is strictlyincreasing in money, if p first-order stochastically dominates q then p > q.

a) Consider a set of monetary outcomes X = {x,..., xx} where the outcomes are arranged in increasing order x, < … < < xx. Let p and q be simple lotteries. We say that lottery P ... first-order stochastically dominates lottery q, if the following holds: 2 P(x) > q(x)) for all i = 1, ... K, j=i j=i

a) Consider a set of monetary outcomes X = {x,..., xx} where the outcomes are arranged in increasing order x, < … < < xx. Let p and q be simple lotteries. We say that lottery P ... first-order stochastically dominates lottery q, if the following holds: 2 P(x) > q(x)) for all i = 1, ... K, j=i j=i

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Question

a) Consider a set of monetary outcomes X = {x1,...,Xk} where the outcomes are arranged
in increasing order x, < .. < xK. Let p and q be simple lotteries. We say that lottery p
first-order stochastically dominates lottery q, if the following holds:
K
K
E P(x,) > E q(x,) for all i = 1, ... K,
j=i
j=i
with at least one of the inequalities being strict. Explain the intuition of first-order stochas-
tic dominance. Show that, for expected utility preferences with vNM utility u that is strictly
increasing in money, if p first-order stochastically dominates q then p > q.

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