(i) For a given constant a > 0, let an investor's preference be represented by the Gaussian utility function U(w)=1-e-aw² For what range of wealth level w will the investor be non-satiated and risk-averse? Explain your answer. (ii) Give an example of a utility function that exhibits DARA and verify it. (iii) Determine the class of utility functions with relative risk aversion coefficient R(w)= w², w> 0.

Big Ideas Math A Bridge To Success Algebra 1: Student Edition 2015
1st Edition
ISBN:9781680331141
Author:HOUGHTON MIFFLIN HARCOURT
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Chapter11: Data Analysis And Displays
Section11.4: Two-ways Tables
Problem 12E
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(i) For a given constant a > 0, let an investor's preference be represented by the
Gaussian utility function
U(w)=1-e-aw²
For what range of wealth level w will the investor be non-satiated and risk-averse?
Explain your answer.
(ii) Give an example of a utility function that exhibits DARA and verify it.
(iii) Determine the class of utility functions with relative risk aversion coefficient
R(w)= w², w> 0.
Transcribed Image Text:(i) For a given constant a > 0, let an investor's preference be represented by the Gaussian utility function U(w)=1-e-aw² For what range of wealth level w will the investor be non-satiated and risk-averse? Explain your answer. (ii) Give an example of a utility function that exhibits DARA and verify it. (iii) Determine the class of utility functions with relative risk aversion coefficient R(w)= w², w> 0.
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