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. George considers investing all $10,000 in a single company. i. What is George's nected week! . What is George's expected makey in u number Case (Hint: The answer is not a round Is George willing to invest $10,000 m a sinīgic 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?
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. George considers investing all $10,000 in a single company. i. What is George's nected week! . What is George's expected makey in u number Case (Hint: The answer is not a round Is George willing to invest $10,000 m a sinīgic 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?
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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Transcribed Image Text: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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