! 1. George's utility function over wealth is U(W) = W1/2 and his current wealth is W = 10,000.George is considering investing his entire wealth in the stock of a pharmaceutical company (orcompanies) trying to develop a Covid-19 vaccine. (If he does not invest, he simply retains hiswealth of $10,000.)Exactly 10 companies are trying to develop a vaccine. Each company has a 0.1 probability ofsuccess and a 0.9 probability of failure. If a company succeeds in developing a vaccine, each $1invested in the company turns into $12.10. If a company fails to develop a successful vaccine,each $1 invested in the company turns into $0. It is certain that exactly one (and only one)company will succeed in developing a vaccine but it is unknown which company that will be.SunneCeorso conciders investing all $10 000 in asingle company.i. What is George'scEENndkuAa.i. What is George SeXpected------ UINThe answer is not a roundotecnuH. 150Corge wifling to inve000 m a sīgie company?b. Now suppose that George instead considers investing $1,000 apiece in each of the 10different companies.i. What is George's expected wealth in this case?ii. What is George's expected utility in this case?iii. Is George willing to invest $1,000 apiece in each of the 10 companies?

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utility function

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

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Concept explainers

Form Utility

The term utility in general refers to the satisfaction earned from usage of a particular product or service. Utility always plays an important role because it influences various important elements like demand & thereby the price of the good or service as well. Though utility is not easy to measure, various types of economic models can be used indirectly. There can be various types of utilities like economic utility, marginal utility, cardinal utility, form utility.

Question

1. George's utility function over wealth is U(W) = W1/2 and his current wealth is W = 10,000.
George is considering investing his entire wealth in the stock of a pharmaceutical company (or
companies) trying to develop a Covid-19 vaccine. (If he does not invest, he simply retains his
wealth of $10,000.)
Exactly 10 companies are trying to develop a vaccine. Each company has a 0.1 probability of
success and a 0.9 probability of failure. If a company succeeds in developing a vaccine, each $1
invested in the company turns into $12.10. If a company fails to develop a successful vaccine,
each $1 invested in the company turns into $0. It is certain that exactly one (and only one)
company will succeed in developing a vaccine but it is unknown which company that will be.
Sunne
Ceorso conciders investing all $10 000 in asingle company.
i. What is George'scEENndkuAa.
i. What is George SeXpected------ UIN
The answer is not a round
otec
nu
H. 150Corge wifling to inve
000 m a sīgie company?
b. Now suppose that George instead considers investing $1,000 apiece in each of the 10
different companies.
i. What is George's expected wealth in this case?
ii. What is George's expected utility in this case?
iii. Is George willing to invest $1,000 apiece in each of the 10 companies?

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