Paula (P) has the following utility function of wealth: uP(y) = y^(4/3). Paula i

Question

Paula (P) has the following utility function of wealth: uP(y) = y^(4/3). Paula is a potential international immigrant to the United States. She works out that she faces the following lottery if she tries to travel to the US to work or to become a student. She starts with wealth of $20 000. She is told that if she goes to the US, she could end up gaining additional wealth of $100 000 with probability (p) and that she could lose all of her $20 000 with probability (1-p). Paula believes that she will be successful with a probability of 10%. True or False & Explain: As a member of the government of the country from which Paula originates, you evaluate Paula’s case and work out that Paula is risk-loving and you would need to compensate Paula the equivalent of approximately $1340 for her to remain in your country

Explanation / Answer

Paula's wealth utility function is uP(y) = y^(4/3)

She starts with a wealth of 20000 and so utility comes out to be = 20000^(4/3)

= 542883.52.

Now it is given that if she goes to US she could end up gaining 100000

So if we calculate probability for that = (100000 / 542883.52) = 0.1842 = 18.42%

So probability of gaining is more than 10%.      

So the statement is false.

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