Al, a Risk- Averse Expected- Utility Maximizer with Utility Over

question 80

Essay

Al, a risk- averse expected- utility maximizer with utility over wealth given by U(W), has W₀ dollars that he can save or invest in a risky asset. With probability p the rate of return on the asset is r_g>0, and with probability 1 - p the rate of return on the asset is r_b <0 . (Note that if you invest x dollars in an asset with rate or return r, you end up with (1 + r)x dollars.)
i)What is Al's expected utility he invests x in the risky asset?
ii)Now suppose that Al's utility for wealth takes the form U(W)=- e^{- aW}. Show that the optimal choice of x does not depend on W_0.

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Definitions:

Persuasive

Having the ability to convince others to change their beliefs, attitudes, or actions through argument or appeal.

Experts

Individuals who possess specialized knowledge, skills, or expertise in a specific field or subject area, typically acquired through extensive study or experience.

Trustworthy

Deserving of trust or confidence, reliable and dependable in truthfulness or accuracy.

Source Likeability

The extent to which an audience perceives a communicator or message source as pleasant, friendly, and charming, which can influence the effectiveness of the communication.