This is an advanced microeconomics question. a) Consider the exponential utility

Question

This is an advanced microeconomics question.

a) Consider the exponential utility function, u = -exp (-pc), where c is consumption. Show that it is increasing (u' < 0) for all c > 0 as long as p > 0. Show that this function has constant relative risk aversion coefficient rR given by p.

b) Consider the poiwer utility function c1-p /(1-p) for p not equals to 1. Show that it is increasing (u' > 0) and concave (u'' < 0) for all c > 0. Show that this function has constant relative risk aversion coefficient rR given p.

c) Consider the log utility function ln (c). Show that it is increasing (u' > 0) and concave (u'' < 0) for all c > 0. Show that this function has constant relative risk aversion coefficient rR equal to 1. (Infact, it is possible to show limp 1 c1-p - 1/ 1-p = ln(c), prove this.

Explanation / Answer

This is an advanced microeconomics question. a) Consider the exponential utility

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