Let p denote a lottery over a finite set of possible prizes denoted by the vector Y; andlet 8x denote another lottery that gives prize X for certain.(i)Using the utility function u(x) = 1 – e-ax, show that for CARA utilityfunctions, adding a constant amount to each lottery prize does not changerisk attitudes i.e. if 8x 2 p, then ôx+z > p' where p' denotes the lottery whichsimply adds an amount Z to each prize in p.х1-р —1(ii)Using the utility function u(x),p 2 0, p + 1, show that CRRA1-рutility functions have the property that proportional changes in prizes do notaffect risk attitudes i.e. if 8x 2 p, then dax z p' where p' denotes the lotterywhich multiplies each prize in p by a > 0.

P is the given lottery considered for a finite set that includes possible prices is the lottery that…

Let p denote a lottery over a finite set of possible prizes denoted by the vector Y; and let 8x denote another lottery that gives prize X for certain. (i) (ii) Using the utility function u(x) = 1- e-ax, show that for CARA utility functions, adding a constant amount to each lottery prize does not change risk attitudes i.e. if xp, then 8x+zp' where p' denotes the lottery which simply adds an amount Z to each prize in p. x¹-P-1 1-p Using the utility function u(x) ,p≥ 0, p = 1, show that CRRA utility functions have the property that proportional changes in prizes do not affect risk attitudes i.e. if &x ≥ p, then Sax p' where p' denotes the lottery which multiplies each prize in p by a > 0. =

Let p denote a lottery over a finite set of possible prizes denoted by the vector Y; and let 8x denote another lottery that gives prize X for certain. (i) (ii) Using the utility function u(x) = 1- e-ax, show that for CARA utility functions, adding a constant amount to each lottery prize does not change risk attitudes i.e. if xp, then 8x+zp' where p' denotes the lottery which simply adds an amount Z to each prize in p. x¹-P-1 1-p Using the utility function u(x) ,p≥ 0, p = 1, show that CRRA utility functions have the property that proportional changes in prizes do not affect risk attitudes i.e. if &x ≥ p, then Sax p' where p' denotes the lottery which multiplies each prize in p by a > 0. =

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter2: Mathematics For Microeconomics

Section: Chapter Questions

Problem 2.7P

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