Suppose that wealth, w, is a continuous random variable on [0, 1]. Let F and G denote two distribution functions (lotteries) over w€ [0, 1] where F first order stochastically dominates G. Let EF[w] and Ec[w] denote the expected value of the lotteries F and G respectively. (a) Show both mathematically and graphically that Er[w]> EG[w]. (b) Show both mathematically and graphically that the converse is not true, i.e. EF[w]> EG [w] does not imply that F first order stochas- tically dominates G.

Suppose that wealth, w, is a continuous random variable on [0, 1]. Let F and G denote two distribution functions (lotteries) over w€ [0, 1] where F first order stochastically dominates G. Let EF[w] and Ec[w] denote the expected value of the lotteries F and G respectively. (a) Show both mathematically and graphically that Er[w]> EG[w]. (b) Show both mathematically and graphically that the converse is not true, i.e. EF[w]> EG [w] does not imply that F first order stochas- tically dominates G.

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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